Angra Mainyu's blog: A Reply To Theistic Arguments from Contingency (v 5.3)

Arguments from contingency use some causal or explanatory principle, in combination with other hypotheses, to derive the existence of a causally effective being that exists necessarily. After reaching that conclusion, theistic arguments give further reasons to support the conclusion that the being in question has some specific essential properties, like agency, great power, moral goodness, moral perfection, etc.

In this essay, I will raise objections to both the first and the second part of the theistic argumentation just outlined, considering both specific theistic arguments from contingency and general principles and/or reasons that might be used in such arguments.

Also, and while this essay is not about the Kalam Cosmological Argument (KCA), I will address also arguments against an infinite past commonly raised in the context of the KCA, since they are relevant also in the context of some arguments from contingency, and in the assessment of some competing hypotheses. In my assessment, the arguments in this essay are sufficient to block the KCA as well.

Unless otherwise specified, I will grant for the sake of the argument that essentialism is true whenever a theistic argument assumes so.

As usual, I do not claim that there is any novelty in the arguments I post. Some of them are already found in a number of other sources, and in some other cases, for all I know someone might have come up with them before I did.

To close this introduction, I would like to thank Joshua Rasmussen for his thoughtful and useful comments, ideas and objections on a number of issues involving contingency arguments. Even though his main conclusions are very different from mine – and on that note, I'm not suggesting that he'd endorse anything in this essay -, I value his insight, and his willingness to share his views with me.

2. Some terminology.

a. I will use the term 'argument' broadly, to talk both about formal arguments (i.e., premises and conclusions), and the reasoning given in support of their premises (i.e., 'arguments' in the sense of 'arguing a case'). I think that these usages are common enough, and context should prevent any ambiguity.

b. I will sometimes use terms like 'universe', 'physical being', 'unembodied', etc., even though they're imprecise, because they are often used in contingency arguments, and I'm considering objections to them. It does not seem to me that terminological imprecision is generally any more of a problem for an objector to contingency arguments than for a defender of them, though the matter may vary depending on the particular case. At any rate, I will add some definitions to make matters somewhat more precise if that appears to be needed.

c. By 'X is fully caused by Y', I mean that Y is a sufficient cause of X; i.e., Y is sufficient to bring about that X obtains or that X will obtain.

d. By 'unicorn' I mean 'a horse-like living organism with a single horn and large wings', and nothing more or less. Unicorns needn't be capable of flight.

e. By a 'moral agent' I mean an agent who has moral properties – like being morally good or morally bad, perhaps to some degree -, and/or some of whose actions have moral properties.

f. I will refer to the parts of this essay as 'sections' and 'sub-sections' only – i.e., no 'sub-sub-sections'.

g. While I don't believe that abstracta are beings, I would use expressions like 'concrete being', to reduce the risk of ambiguity.

h. While usually the discussion is about whether God exists, under any of the common conceptions of the term, I will introduce two definitions for the sake of (slightly) greater clarity. There is no need to include uniqueness conditions or names explicitly in the definitions, so I will simply call them 'a god', 'gods', etc., but the definitions cover usual forms of philosophical theism.

Definitions:

Type 1: An agent E is a god of type 1 if and only if E is essentially omnipotent, omniscient, morally perfect, and is the creator of all other concrete beings if there are any others. I will call such an entity a 1-god.

Type 2: An agent E is a god of type 2 if and only if E essentially has great power, knowledge and moral goodness, and she is the creator of all other concrete beings that coexist with her, if any, and the supreme ruler of her creation.

By 'supreme ruler of her creation' I mean she's always aware of what every one of her creatures is doing, and she has the knowledge, power and opportunity to effortlessly prevent any creature from acting, and/or to annihilate any creature and/or create a different one.

Also, while she has great power, knowledge and moral goodness essentially, there is no stipulation that they can't increase contingently.

I will call such an entity a 2-god.

Type 3: An agent E is a god of type 3 if and only if she is the creator of all other concrete beings that coexist with her, and the supreme ruler of her creation. I will call such an entity a 3-god.

I acknowledge that the definitions given above aren't very precise, either, but they seem to be good enough for the purposes of this essay.

Also, I take no stance here on whether any of the definitions are equivalent.

3. Metaphysical possibility, conceivability, and visualization.

The question of how to use conceivability as a guide to metaphysical possibility is a difficult one, but in my assessment, if conceivability is usable at all, at least the following seems to hold:

Using the conceivability criterion as a guide to metaphysical possibility requires stipulating that a certain scenario obtains, and then trying to find contradictions in it, after taking into account the (epistemic) possibility of fixed referents[1]. If there is no apparent contradiction in the scenario in question, then that seems to provide support for the conclusion that the scenario is metaphysically possible.

In the case of a given scenario, generally speaking, the more we try to find a contradiction without finding it, the more confident in its possibility we're justified to be.

However, a difficulty here is to assess what kind of scenario may properly be used in this context – i.e., what counts as a scenario.

I will not try to give a definition of 'scenario', but I will briefly consider a matter that I think relevant matter, regarding scenarios defined in modal terms.

For instance, we can conceive of unicorns, and it seems to me that if the conceivability criterion works at all, that gives us some reason to believe that unicorns are metaphysically possible. Someone might suggest that we can also conceive that there is a 3-god that exists necessarily and who is necessarily bent on preventing the existence of unicorns, and so allegedly the conceivability criterion would not support the metaphysical possibility of unicorns because the two scenarios would cancel each other out. But it seems intuitively plausible to me that the objection would fail, and further that the conceivability criterion supports the conclusion that no such necessary being exists, precisely because scenarios that contain unicorns are conceivable. [2]

A suggestion to explain that difference and other examples would be as follows:

In order to use the conceivability criterion as a guide to metaphysical possibility, the scenarios we try to conceive of should not be defined in modal terms. That includes the definition of the properties of the entities that exist in the scenarios in question. So, if a hypothesis H includes such modal terms, the conceivability criterion would support its impossibility if we're able to conceive of a scenario S without modal terms in its definition and which contradicts H.

That would appear to explain the unicorns example, in which the conceivability of the scenario stipulating that there are unicorns – which contains no such claims – would provide evidence against the hypothesis that there is a 3-god that exists necessarily and who is necessarily bent on preventing the existence of unicorns.

An alternative suggestion would not exclude scenarios defined in modal terms, but would hold that in case of conflict, a scenario without such terms prevails.

Another alternative suggestion would be that in the case of unicorns, we're able to visualize them, but that's not true of the hypothesis that there is a 3-god that exists necessarily and who is necessarily bent on preventing the existence of unicorns, and that is what makes the difference, rather than whether the scenarios are defined in modal terms.

On that note, and more generally, a contentious point is whether being able to visualize a scenario is required for conceiving of it, in the sense that is relevant here – i.e., as a guide to metaphysical possibility -, or at least provides a stronger criterion than conceivability without visualization.

We're never or almost never able to fully visualize a scenario, so the issue is whether partial visualization is required, and to which degree we need to be able to visualize a scenario in order to use the conceivability criterion.

It's a difficult matter, but personally, I'm rather skeptical of the view that conceivability plus visualization is a better guide to metaphysical possibility than conceivability without visualization – i.e., just stipulating a scenario and finding no contradiction, after taking into account the (epistemic) possibility of fixed referents[1] – for the following reasons:

1. When we visualize a being – or a scenario with one or more beings in it -, what we're doing is forming a mental image of something that represents the being or beings in question. But it's not clear to me why our ability to form a mental image representing a being would be in any way related to whether the being so represented is metaphysically possible. The same goes for scenarios that lack a certain being. In particular:

2. If a scenario is metaphysically possible if it's logically possible after one counts fixed referents[1], but causal properties of actual beings are not relevant to metaphysical possibility, then it seems to me that conceivability without visualization is a good a guide to possibility, and our ability to form a mental image that represents some being or beings would not add anything to it. I will sketch a very partial account of metaphysical possibility – i.e., limited to some scenarios – along those lines later.

3. If metaphysical possibility depends also on the causal properties of actual beings – e.g., if it reduces to causal possibility -, then I see no good reason to think that our ability to visualize something that represents an object, or our ability to conceive of it without visualization, for that matter, is related to the matter of what actual causal properties exist, and so in that case I would be skeptical of the conceivability criterion in general, with or without visualization.

In any case, it's not clear to me why visualization would be an improvement.

4. It's true that without visualization, there might be a hidden contradiction. However, visualization is always partial, so hidden contradictions may exist anyway. Examples of that are contradictory fictional stories involving time travel, in which we can surely visualize part of the stories – they're even sometimes on TV -, but we can still find contradictions between different parts of it. In very complex stories, we might not be able to easily find a contradiction between some of the parts we're unable to visualize, or to visualize together, etc.

5. I recognize that there might be good reasons why conceivability plus visualization may turn out to be a good guide to metaphysical possibility while conceivability without visualization isn't, but I've not been able to find them, with the potential exception of hidden contradictions in case they're significantly more frequent in cases in which there is no visualization at all, but that's not clear to me, either.

So, it seems to me that the previous suggestions based on whether the scenario is defined in modal terms are more adequate to explain our intuitions in the unicorns case, and similar ones, and that visualization is probably not an important factor.

That said, I will not assume that that is the case in this essay, and most of my objections to theistic arguments from contingency will not rely on the previous assessments.

In the next section, I'll introduce a scenario in which at least partial visualization appears to be doable – though I'll consider an objection to that as well -, in order to compare it with theistic alternatives later. I will take a look at conceivability criteria again later, when assessing some evidence.

4. A difficulty for some gods.

Let's consider the following scenario:

There is an intelligent, self-aware being, Malo, who brings some other beings into existence.

Each of those beings (let's call them 'sufridores') has a mind that is similar to the mind of an average two-years old human kid.

In particular, a sufridor has an amount of knowledge and intelligence similar to that of an average two-years-old kid. Further, he can feel pain to an intensity similar to the intensity to which an average two-years old kid can feel pain.

However, a sufridor never grows old, never loses consciousness unless a significant portion of his brain is destroyed, and if his body is damaged – no matter how badly, and including the brain -, instead of dying he regenerates in seconds at most, regaining consciousness if he had lost it.

Malo brings sufridores into existence at a rate of one a year, with the only purpose of torturing them for fun. He always achieves his goals: he tortures them, and enjoys that very much.

The mechanism by which Malo achieves this goal is not important. He might (for instance) make one computer-operated torture chamber with one sufridor in it per year, such that the chamber burns the victim alive from the waist down constantly, or just stimulates the brain directly, causing a similar amount of pain. But whatever the mechanism, the point is that Malo always succeeds.

If there is a possible world W at which Malo tortures sufridores like that, with n sufridores after n years, it seems there is no 1-god at W, because it's clear that such a being would not create Malo, or at the very least would not allow him to torture sufridores like that.

If possible worlds are problematic, we may put it as follows: if a scenario like that is metaphysically possible, then no 1-god is metaphysically necessary, since it's not possible that a 1-god would create such an entity, or at least not possible that she would allow Malo to do as he pleases. Similarly, if Malo is possible, there is no necessary 2-god.

Also, and while I personally doubt it's important, it seems to me that the Malo scenario is partially visualizable; still, a potential objection to even the partial visualization in the case of Malo would be as follows:

We can't actually visualize suffering. The being that appears to suffer may be pretending, or it may be a mindless zombie. So, even partial visualization of the Malo scenario is not possible.

That objection, if correct, would severely restrict the scope of the visualization criterion, since – assuming such criterion is a good guide to metaphysical possibility – it would not allow us to, say, establish that it's possible for a person to fly like Superman, since the flying being we visualize might be a mindless zombie.

In any case, at this point I'm just introducing the Malo scenario for the purposes of comparing it with theistic claims about metaphysical possibility later.

5. Extending causal and explanatory principles. Some general considerations.

A common point of contention in the context of arguments from contingency is whether and/or when to generalize a principle from familiar situations, objects, etc., to other categories of objects we're not so familiar with, or even not familiar at all.

It seems to me that in a number of cases, there are some reasons to be cautious about extensions to arbitrary categories.

For instance, while our intuitions about, say, time, space, and how things move work pretty well in daily life, modern physics has taught us that they do not hold without exception, and there are situations (e.g., objects moving near black holes, events in the subatomic realm) in which they don't seem to work well at all.

Modern science aside, there is perhaps a stronger reason to be cautious when extending principles to arbitrary categories. For instance, in daily life, the states of affairs we see (e.g., a state consisting of a number of people interacting with one another and with the rest of their environment, etc.), have both internal causes – which are causal interactions between different things that constitute that state of affairs – and external causes – which are causes that are not part of, or members of the state in question.

For instance, if we look at a house standing on a hill, there are causes of the state consisting of the house standing on the hill that are external to it – e.g., different stuff in the rest of the Earth – and causes that are internal to it – like interactions between different parts of the house.

However, we should not extend to any arbitrary category of states of affairs a principle stating that every state of affairs has an external cause (allowing states of affairs to be extended arbitrarily in time as well), since the state of affairs consisting in all concrete objects' existing, having relations between them, instantiating properties, etc., only has internal causes. Of course, this is not an actual exception or anomaly in the causal structure of the world, but simply the result of our decision to define a state that contains all of the causes inside it.

In other cases, we may not know whether a certain category contains all concrete objects – for instance.

Given all that, an alternative may be to extend principles that work in familiar environments to principles that state that normally, something obtains in a broader category. Those extensions would put the burden on a skeptic who accepted the principle but believes that some particular case might be abnormal.

That alternative may be an epistemically better approach, but even leaving the issue of the potential vagueness of 'normally' aside, I would say that one should be careful, as there are a number of difficulties, and some of them are relevant in the context of arguments from contingency.

On that note, a difficulty arises when two or more extensions from clear cases we observe or contemplate to arbitrary categories adding the 'normally' condition would lead to what looks like having to pick between two or more abnormalities.

For instance, let's consider the following scenario:

We have the following evidence E₁:

We have observed many objects x that are in category C₁, and are also in category T₁.

For nearly all x that we know are in C₁, we also know that they're in T₁: in all those cases, we have checked that they're in both categories by two reliable methods.

We do not know that any x is in C₁ but not in T₁, though there might be some x such that we know x is in C₁, but we have no method so far to tell whether that particular x is in T₁, other than generalizations from other cases.

Based on evidence E₁[4], we may wish to generalize and assert the following principle:

NP₁: Normally, for all x such that x is in C₁, x is in T₁.

In a similar fashion, and based on evidence E₂, we may wish to generalize as follows:

NP₂: Normally, for all x such that x is in C₂, x is in T₂.

But let us now suppose that we find an x, say x₁, such that x₁ is in C₁, but we have no direct method (i.e., a method other than NP₁) to check whether x₁ is in T₁, and moreover, we can tell that if x₁ is in T₁, then there is some y such that y is in C₂, but y is not in T₂.

What should we do?

The following approach might be suggested:

Since x₁ is in C₁, NP 1 applies unless there is a specific reason to think otherwise, and NP₂ does not provide a specific reason. Hence, and unless such a specific reason is given, we should conclude that x₁ is in T₁ as well, and thus also conclude that there is some y such that y is in C₂, but y is not in T₂.

However, it seems that that would not be a correct approach, because it would amount to ignoring or at least improperly assessing evidence E₂, which is also relevant with regard to whether there are objects that are in C₂ but not in T₂, and which may actually be much stronger than the evidence E₁, or at least strong enough to warrant skepticism on the matter.

In my assessment, a correct way to approach the matter would be to keep in mind that those generalized principles are merely that – i.e., generalizations from some body of evidence based on familiar cases to much larger categories – and then justifiably apply the relevant evidence directly to the case under consideration, instead of trying to apply any generalized rule or principle.

An alternative approach would be to accept that one principle holds normally, but accept also the evidence used in support of other principles as evidence for an abnormality. For instance, in the example above, NP 1 would suggest that x₁ is in T₁, but one would take into consideration that E₂, together with the fact that if x₁ is in T₁, there would be some y such that y is in C₂ but y is not in T₂, provides evidence for the abnormality of the case of x₁, and thus against the application of NP 1. Whether that's enough to warrant skepticism, etc., depends on the strength of the respective pieces of evidence, so in the end one assesses the overall evidence.

In any case, as always, the strength of the evidence ought to be assessed in each particular case – or cases, if we find more than one -, and it may well be a difficult matter. But the important point here is that E₂ is at least some evidence against the conclusion that x₁ is in T₁, and its strength should be assessed when assessing whether x₁ is in T₁.

That aside, and on a different note, some principles that involve generalizations to all possible worlds have another difficulty: at least to some of us, they appear to be highly counterintuitive.

For example, I would be very willing to affirm that at the actual world, normally, every macroscopic object of finite volume has an external cause of its existence. However, I do not see why worlds in which such objects exist without external causes would be impossible, even when it comes to familiar objects, like bricks or cats.

Of course, someone may reject the use of possible worlds as a proper characterization of modality, and/or propose weaker principles, challenge my assessments, etc., so these matters (e.g., whether to extend a principle) usually need to be assessed on a case by case basis.

Leaving that aside as well, another potentially problematic issue is the choice of the categories.

For instance, extending a principle from categories such as 'chairs', 'trees', 'cats', etc., to categories like 'planets', 'galaxies', 'black holes', etc., would be an extension from familiar to less familiar categories, but none of the categories involved contains modality in their definitions.

It's not clear to me that extensions to categories defined in modal terms like 'wholly contingent', or 'contingent' are relevantly similar or equally justified, especially given that contingency is not a property of things. Still, unless otherwise specified, I will not raise this particular issue in the rest of this essay.

6. Infinities, an infinite past, and some related matters.

In this section, I will raise objections to a number of arguments intended to establish that the past is finite and/or that the past cannot be infinite, that time cannot be dense, and/or some other hypotheses.

The reason I address these arguments is that they're relevant in the context of a number of arguments for contingency. For instance, some of those arguments, or similar ones, might be raised against hypothesis 0, or as support for an argument from the instantiation of properties, at least if some of the objections I will raise failed.

I also address these arguments in a reply to the Kalam Cosmological Argument [5], in some cases in greater detail.

Before I go on, I'd like to point out that the hypothesis that time has no beginning seems to be simpler, in terms of uniformity, than the hypothesis that it does. If time has no beginning, for every event – i.e., everything that happens -, there are previous events, and later events, with no special first event.

6.1. Hilbert's Hotel

The first argument I will consider is the 'Hilbert Hotel' argument, intended to show that an actual infinity is metaphysically impossible. Based on that, it's argued that an infinite past is metaphysically impossible.[6] In this section, I will address William Lane Craig and J.P. Sinclair's arguments[7 ], but the same points apply to similar variants of it.

According to the authors, the 'Hilbert Hotel' argument shows that an actual infinity is counterintuitive, and based on that, they claim that an actual infinity is plausibly metaphysically impossible.

The Hilbert Hotel is a hotel with a denumerable number of rooms, [8 ] and the authors suggest that it's the actual application of the concept of infinity to the real world, rather than the consideration of abstract sets, what brings the counterintuitiveness of an infinity to one's attention.

Of course, a hotel like the one they propose is counterintuitive, since (for example) we would never be able to build it, we wouldn't be able to communicate with the rooms in real time as in the proposed scenario, etc. However, all of that particular counterintuitiveness seems to have everything to do with an infinite hotel, and nothing to do with an actual infinity.

On the other hand, the counterintuitiveness claimed by Craig and Sinclair seems to result from a misunderstanding of the meaning of the words, and disappears once the claims are clarified. To see this, let's consider the scenarios they propose as supporting the claim of counterintuitiveness:

First, Craig and Sinclair present a scenario in which all of the rooms are occupied, and a new guest arrives.

According to the authors, somehow that there are no more guests after the arrival is a problem, or counterintuitive. However, that is not the case, once it's clear what one means by 'more guests', for the following reasons:

In the sense of cardinality, there are no more guests after the new guest arrived than there were before. However, that merely means that there is a bijection between the set of guests before the new arrival, and the set of guests after the arrival, which is as clear as the fact that there is a bijection between the set of positive integers and the set of positive integers plus zero.

On the other hand, clearly there is at least one sense in which there are more guests after the new arrival than there were before, namely the sense that all of the previous guests are still there, and there is also a guest who wasn't there before. In terms of sets, the set of guests before the new guest arrives is strictly contained in the set of guests after the new guest arrives. All of this is unproblematic.

Of course, shifting infinitely many guests from one room to the next would not be doable for any human being, alien from another planet, etc., but that's not relevant, since if any of that is a problem also for the metaphysical possibility of that hotel, it's clearly a problem for Craig's hotel, not for actual infinities in general, as is clear from the fact that such problems do not affect – for instance – the hypothesis that there are infinitely many galaxies, which is a live hypothesis in modern science.

In addition to the previous scenario, Craig and Sinclair consider a scenario in which infinitely new guests arrive at the desk, and the proprietor talks to them, etc.

However, it may be that the meaning of the word 'desk' is such that it's not coherent to say that infinitely many show up at the desk. But that scenario in which infinitely many guests arrive is not a condition included in the definition of the Hotel in question, so if it is an incoherent scenario due to the meaning of 'desk', that is not enough to rule out the possibility of the Hotel.

On the other hand, if there is nothing in the meaning of the word 'desk' preventing that infinite arrival, then still things like building such a hotel, or communicating at arbitrarily fast speed with infinitely many people, etc., look counterintuitive.

However, as before, any counterintuitiveness is not a consequence of assuming an actual infinity, but of assuming the infinite hotel that Craig and Sinclair describe. For instance, also as before, there seems to be no similar counterintuitiveness in the hypothesis that, say, there are infinitely many galaxies.

As for the number of guests after denumerably many new ones arrive, it's the same as before the arrival in terms of cardinality, but again that merely means that there is a bijection between the set of guests before the arrival and the set of guests after the arrival, which is as clear as the fact that there is a bijection between the set of positive integers and, say, the set of even positive integers.

On the other hand, there is at least one sense in which there are infinitely more guests after the arrival, namely, that all of the guests who were in the hotel before infinitely new ones arrived remain there, and infinitely many guests who were not in the hotel before the arrival are in the hotel after the arrival.

That is also unproblematic. As long as one keeps in mind what's meant by 'more guests', any counterintuitiveness related to the 'more guests' issue is gone, and any counterintuitiveness left has to do with the specific features of an infinite hotel.

Similarly, if one guest departs, there are as many guests as before in the sense of cardinality, but there is a sense in which there were more guests before the departure, namely that all of the guests that are in the hotel after the departure were in the hotel before the departure, but there was also one guest before the departure that is no longer in the hotel after she departed (obviously). In terms of sets, the set of guests after the departure is strictly contained in the set of guests before the departure. Once again, all of this is unproblematic, and any issues related to the number of guests are not counterintuitive as long as one keeps in mind what one means by 'more guests'.

Now, if denumerably many guests leave, whether there are as many as before in the sense of cardinality depends on which set we remove, just as we can subtract an infinite set A from the set of natural numbers N such that N\A has the same cardinality as N (e.g., A:={x: x is a prime natural number}), or subtract a set B such that N\B is finite (e.g., B:={x: x is a natural number greater than 1}).

As before, there are no problems in terms of how many guests there are, or in terms of subtractions.

Craig raises other scenarios based on Hilbert's Hotel, but they're handled in a similar fashion.

Once it's clear what one means by 'more guests', etc., it should also be clear that any of the issues raised by Craig vanish, and any counterintuitiveness left is not the result of the fact that the scenario involves an actual infinity, but of the fact that it involves an infinite hotel, with certain specific properties, like infinitely people arriving at once, a proprietor communicating with and moving infinitely many guests, etc.

So, in short, the 'Hilbert Hotel' argument is not a good argument against the possibility of actual infinities.

The Hotel itself appears counterintuitive, though it's not clear at all that it's metaphysically impossible. For instance, if the 'co nceivability without visualization ' criterion is a good guide to metaphysical possibility, then it seems the Hilbert Hotel is plausibly metaphysically possible, even if one or more of Craig's scenarios might be impossible, depending on the meaning of some words like 'desk'.

In any event, even if Hilbert's Hotel is impossible because of particular features of the Hotel, that would not give us any good reason to think that all other infinities are impossible, like infinitely many galaxies, or – more relevantly in this context – infinitely many past events, and Hilbert's Hotel provides no good reason to suspect that those scenarios aren't possible.

6.2. Grim reapers.

The 'grim reapers' argument has different forms, and it may be offered in support of the hypothesis that actual infinities are impossible, and/or that infinite temporal regress is impossible, or that time is necessarily discrete, among others.

The conclusion that time is necessarily discrete would not appear to be a problem for hypothesis 0, but the impossibility of infinite temporal regress – and, of course, of any actual infinity – would be so.

In this subsection, I will focus on some of Alexander Pruss' arguments. [9]

Briefly, the scenario is as follows:

Fred is alive at t₀– 11.00 am. in Pruss' scenario -, and then, there is a grim reaper (say, GR_n), set to kill Fred at t_n=(t₀+(1/n) seconds), if Fred is alive. Fred cannot survive a grim reaper attack, and nothing else possibly kills him.

At first glance, there are some difficulties that might affect our intuitions and assessments, such as:

a. Death is a gradual process, and also the words that we use to describe the world around us are imprecise.

b. Modern science still does not have a way of handling arbitrarily short amounts of time, and our regular intuitions about time and space do not seem to work well when certain quantum effects are involved.

But let's say that difficulties of that sort are resolved. Then, there is another potential difficulty:

Pruss' 'grim reapers' scenario is strictly logically impossible, but an infinite regress of events is not.

In other words, assuming a scenario in which there is an infinite regress of events, a contradiction does not follow. Instead, what would be impossible in that scenario, would be Pruss' construction.

I suppose there might be a way around that potential difficulty, by rewording the argument as an argument forcing us to choose between different intuitions, though, so let's leave that aside for now as well.

6.2.1. Discrete time.

Pruss distinguishes between the following two types of discrete time.

1. Time is rigidly discrete if there necessarily is a minimum temporal unit.

2. Time is discrete in an Aristotelian sense if there are in fact finitely many moments of time, but each interval can be subdivided infinitely many times.

In his version of the grim reapers argument, Pruss is assuming that time is not rigidly discrete. He argues against rigid discreteness based on relativity, and on Zeno's Stadium.

I don't find Zeno's Stadium to be a persuasive argument against rigid discreteness, but I won't address the matter here. I will just point out that the Stadium is at least a contentious matter.

As for relativity arguments, they seem to be based on the usual interpretation of time in physics, which holds that time is relative, and is based on empirical evidence. That would not be a problem on its own, in my assessment, since I don't see any good reasons to think that our observations are illusory and metaphysical time is actually absolute.

However, temporal relativity seems to be problematic for theism. Let's consider the following scenario:

There are astronauts on Mars, and one of them prays to the creator, asking her to establish a communication between her (i.e., the astronaut) and her loved ones on Earth, with no more than a, say, five seconds delay (or five minutes, for that matter).

Then, it seems to me that even if there were a creator of the universe and she were listening, she would not have the power to grant the request even if she wanted to, since that would seem to result in paradoxes, resulting from sending information faster than the speed of light.

Granted, someone might suggest that, perhaps, metaphysical time is relative but in a way very different from what modern physics proposes, but if one leaves aside modern physics, it seems one also leaves aside any support for the hypothesis that time is relative.

In particular, without the speed of light limitation, there would be no support for the hypothesis that time is relative, since we would be leaving aside a crucial part of the empirical basis for the hypothesis that time is relative.

Also, someone might suggest that physical time is relative, but not metaphysical time. But what matters in this context is metaphysical time, and as long as it's not relative, it seems relativity provides no evidence against rigidly discrete time.

But potential consequences of accepting relativity for theism aside – which, as a non-theist, I would not find problematic -, let's grant that time is not rigidly discrete for the moment, and let's consider Aristotelian discreteness.

The definition of Aristotelian discreteness given by Pruss might give the impression that it implies immediately that there is no infinite temporal regress of any kind – since it's stipulated that there are only finitely many moments -, but that would not be a proper interpretation of Aristotelian discreteness, which is clear by the fact that he argues then against infinite regress under Aristotelian-discrete time rather than just point out that it's immediately implied by the definition, and even more clearly by his proposed specification of Aristotelian discreteness. [9]

To simplify, we may consider the following alternative definition.

3.Time is discrete in the Aristotelian-2 sense if and only if, necessarily, there are finitely many moments of time between two given ones, but any temporal interval is possibly subdivided in smaller subintervals.

Alternatively, we may consider Pruss' suggestion. [9] I will use the definition above, but the reply I offer works equally under Pruss' suggestion.

So, Aristotelian-2 discreteness is clearly incompatible with an infinite regress of events plus a time at which Fred is alive before that infinite regress.

Thus, if there were an infinite regress of events under Aristotelian-2 discreteness, that would be an infinite sequence of events without any time prior to the whole sequence, and so Pruss' argument from grim reapers would not apply to it, since Fred could not be alive before the sequence.

Hence, Pruss' argument is not applicable if time is discrete in the Aristotelian sense.

On the other hand, Pruss argument is also not applicable if time is rigidly discrete. [9]

So, it seems that if the argument under consideration were successful, it would work as an argument against the hypothesis that time is possibly dense. Different arguments would still be required to rule out an infinite past if time is necessarily not dense. I will consider one argument given by Pruss under Aristotelian-discrete time later.

6.2.2. Grim reapers, infinite regress, and the Hilbert Hotel.

According to Pruss, if an infinite temporal regress were possible, then the Hilbert Hotel would be possible. His argument from infinite temporal regress to the Hilbert Hotel holds that assuming that an infinite series of events going backwards in time is possible, each event could be the creation of one room, and no room gets destroyed.

Also, he argues that if Hilbert's Hotel were possible, it would be possible for there to be one reaper produced in each room, and it would be possible for the Hotel's staff to set the reaper in room #n to kill at t_n.

So, Pruss claims that if the Hilbert Hotel were possible, then some other things would be possible, and a contradiction would follow.

Yet, the Hilbert Hotel, on its own, appears not to be contradictory. If so, clearly it does not entail a contradiction. So, Pruss appears to be using the Hilbert Hotel plus some criterion or criteria for metaphysical possibility, in order to derive a contradiction.

Yet, Pruss does not say what criteria he's using, or why he considers that criteria reliable, which obscures the matter considerably.

Still, apparently, Pruss is not using the 'conceivability without visualization' criterion, because that criterion seems to support the possibility of the Hilbert Hotel, but obviously not the possibility of a contradiction.

Also, he's apparently not using only a criterion that requires visualization, due to the infinities involved. Moreover, it seems that in order to establish the possibilities of each grim reaper, he's not even using a visualization criterion combined with other criteria, since he says that the grim reapers need not be physical entities, but might be non-physical entities with the specified causal powers, and even though the meaning of 'non-physical' is unclear, given usual examples, it seems plausible that they might not be visible.

So, even ruling out the 'conceivability without visualization' criterion for the sake of the argument, given that Pruss does not specify which criterion or criteria he is using, let alone defend them, we may point out the following:

1. It's not clear that if an infinite temporal regress were possible, it would be possible to make rooms like that. In particular, if metaphysical possibility reduced to causal possibility – as Pruss suggests elsewhere[10 ], though I'm not convinced -, there would seem to be no good reason to suspect that just because an infinite temporal regress is possible, there will be some entity with the power to bring about those rooms.

2. Even if the rooms were brought about, it's not clear that they would last for long enough for there to be infinitely many of them at any time.

3. Even if infinitely many rooms at once were possible, it's not clear that that would be a hotel. For instance, it might be possible that infinitely many rooms exist, yet the speed of light limits communication between them. In particular, for every room, only finitely many ones would be within its light cone. In that case, there would be infinitely many rooms, but they would not constitute a hotel, or anything that would work as required in this argument.

4. As suggested above, it's not clear that the rooms and/or the staff and/or anyone else would have the power to make grim reapers with the power to check whether Fred is alive from an arbitrarily large distance, and kill him instantly, or almost instantly.

5. Also, it's not clear that the staff or anyone else would have the power to make devices that properly measure arbitrarily short temporal intervals, etc.

6. In particular, it's not clear that all of those things would be possible together if an infinite temporal regress were possible.

Perhaps, Pruss is using a criterion or a set of criteria for assessing metaphysical possibility that is broad enough to allow him to establish that all of that would be possible if an infinite regress of events were possible. But the questions remain: which criterion or criteria is he using, and why should we accept them? Moreover, why should we reject the 'conceivability without visualization' criterion?

In any case, given the broadness of whatever criterion or criteria Pruss is using, we may reason as follows:

It seems clear that an infinite forward sequence of events {E(n)} is possible. That would not even require an actual infinity, but merely a potential one.

So, let's consider the following scenario – which we may call the 'Boundless Innocent Suffering' (BIS) scenario:

Let's start with some fixed year, which we may number '1'.

For n > 2, the event E(n) is as follows:

a. E(n) begins at the beginning of the year n!, and ends at the beginning of the year 1+2*n!

b. In the first year of E(n), 1 torture chamber with 1 sufridor in it (say, Bob(n)) is produced. Producing it does not need to take the whole year. It might take a second, a minute, a month, etc., but in any case, by the end of the first year, the torture chamber with Bob(n) in it is fully functional.

c. Since the torture chamber with Bob(n) in it is ready, and until the end of E(n), Bob(n) is burned alive from the waist down, allowed to regenerate in a few seconds, then burned alive again, and so on. So, this torture lasts for at least n! years.

So, for instance, Bob(3) is horribly tortured for at least 6 years, from the year 7 to the year 13, Bob (10^{1000000!!!!!!!}) is horribly tortured for at least ((10^{1000000!!!!!!!})!)years, from the year (1+((10^{1000000!!!!!!!})!)) to the year (1+2*((10^{1000000!!!!!!!})!)), and so on.

It seems clear to me that we can tell, beyond a reasonable doubt, that if the BIS scenario is possible, no 1-god or 2-god is necessary, but the construction seems to be similar to the one offered by Pruss in his scenario.

Granted, the previous scenario would only a problem for theism, but similar scenarios would also be a problem for other potentially necessary agents, even if not morally good ones, as long as they're defined as having a similar amount of power and some specific priority necessarily, instead of doing what's morally right.

For instance, a 3-god who essentially has some priority to – eventually – bring about that R does not obtain, for some R, would be ruled out by stipulating a scenario in which R happens repeatedly and for unbounded periods, as long as we can tell that R is possible for a certain period, and then extending it. That would seem to be no broader a criterion for metaphysical possibility than any criterion or set of criteria Pruss may be using.

All that said, I have to admit that the amount of suffering that actually exists in the world is much more than enough for me to conclude that there is no 1-god or 2-god. After years of reflecting on the matter, I don't find any theodicy remotely persuasive – let alone a 'mysterious reasons' argument -, but I suppose some of those who think otherwise might also say that the BIS scenario is compatible with a 1-god or a 2-god.

Still, it seems to me that the BIS scenario may well be too much even for most of those who reject arguments from suffering in the case of the real world, in particular because in the BIS scenario, there is no silver lining. BIS never ends, and the torture keeps getting longer and longer.So, while it's true that the suffering of each victim might end (that's not specified in the BIS scenario, so the torture might or might not continue after the stipulated period), for any natural number n and for any time t, there are more than n victims still to come in the future, each of which will be tortured for more than n years.

Leaving aside potential difficulties the criterion or criteria used by Pruss as a guide to metaphysical possibility and/or for theism, one may still point out that even if the Hotel with the reapers, mechanisms, etc., are possible, that would not entail that Fred cannot die unless he's killed by a reaper. Perhaps, for all we know, Fred's life extends through an interval [u,t₀] or (u,t₀] for some u prior to t₀, and the reapers would have no one to kill, resulting in no contradiction.

On that note, Pruss suggests[9] stipulating that there is nothing in the world that could kill Fred except for an individual grim reaper. Apparently, under that stipulation, Fred couldn't kill himself of die on his own of natural causes, either.

However, there seems to be no good reason to suspect that if an infinite temporal regress is possible, then it's possible that nothing but a grim reaper can possibly kill Fred in that scenario.

For that matter, we may suggest the following:

i. If a finite past is possible, then it would be possible that nothing but a grim reaper can possibly kill Fred. Then, if a finite past is possible, there would be no necessary 1-god, 2-god, or 3-god, and in particular all usual forms of theism would be false.

But since whether a finite past is possible has nothing to do with which entities could possibly kill Fred, for that matter we may suggest, in addition to i.

ii. If an infinite past is possible, then it would be possible that nothing but a grim reaper can possibly kill Fred. Then, if an infinite past is possible, there would be no necessary 1-god, 2-god, or 3-god, and in particular all usual forms of theism would be false.

From that, we may conclude that there is no necessary 1-god, 2-god, or 3-god, and in particular all usual forms of theism are false.

Of course, that wouldn't be a good argument against theism, since we would just be stipulating for no good reason whatsoever that nothing could possibly kill Fred in those cases. But Pruss' argument has the same problem – namely, the suggested stipulation would be unwarranted, and thus this 'grim reapers' argument would fail even if we granted all of the previous claims about the possibility of the hotel, the grim reapers, etc.

6.3. Grim placers and/or grim signalers.

In this subsection, I will address a variant of the argument from grim reapers, defended by Robert Koons [1 1 ], in which each grim reaper, or rather grim placer, checks whether there is some Fred particle at a specified location, and if there isn't, he places one at some specific location. Otherwise, he keeps the particle where it is.

According to Koons, his argument shows that time is not dense, and that there is no infinite past.

I disagree with that assessment, and furthermore, I will argue that some of his assumptions may be used, in combination with no less plausible ones, to make an argument against usual forms of philosophical monotheism.

6.3.1. Possibility of a grim placer.

Among other hypotheses, the argument assumes the following:

1. There is a region R of duration d in a possible world W, and a grim placer GP_d, such that GP_d has the intrinsic power and disposition to do as follows:

a. If there is no Fred particle at any distance y<d from a fixed plane P, then GP_d creates and places a Fred particle at a designated location exactly d meters from P.

b. Otherwise, GP_d keeps any Fred particle that is closer to plane P in its position.

It's not clear to me what criterion Koons is using, as a guide to metaphysical possibility, in order to assert that one such scenario is possible.

It seems to me that Koons probably isn't using a conceivability criterion like the one I suggest below, because such a criterion would seem to lead to the conclusion that there is no concrete being that exists necessarily, contradicting Koons' stance on that matter.

Also, it seems to me that we can't visualize the scenario, either. For instance, a requirement of the scenario is that the location of the particle is at exactly p meters from a certain plane. But it seems to me that we can't visualize anything with that kind of precision.

So, perhaps, Koons is using some other kind of conceivability criterion that is not broad enough to be a problem for Koons' position, but broader than a criterion that requires visualization.

But that raises the following issues: which criterion is that, and why should one accept that particular criterion as a good guide to metaphysical possibility?

It seems to me that the burden to explain and defend the criterion in question would be on those who make claims of metaphysical possibility based on it.

Still, in any case, intuitively, it seems to me that the hypothesis that one of the E(n) of BIS is no less plausibly possible than Koons' assumption above. So, I would be inclined to grant point 1. for the sake of the argument, but also assume that at least for some n₀, E(n₀) is possible.

Granted, it might still happen that Koons uses a criterion to assess metaphysical possibility that blocks all of the E(n), but allows assumption 1. However, it's hard to see what kind of criterion would have that effect, without being ad-hoc.

In any event, as before, I would say anyone using such a criterion would have the burden of stating it clearly and defending the claim that that criterion is a good guide to metaphysical possibility.

Still, alternatively, we may grant point 1. for the sake of the argument, without even assuming that any of the E(n) is possible, but assuming instead that the following scenario – which we may call the 'horror for eight minutes (HEM) scenario – is possible:

An entity with a mind, capability for suffering, regeneration, etc., similar to those of a sufridor, suffers horrible, tremendous pain – like being burned alive from the waist down, without any decrease in pain – for eight minutes.

Granted, someone might still reject the metaphysical possibility of HEM, while claiming that point 1, obtains but that also put an even heavier burden on the person making such a claim.

6.3.2. Compressibility of spacetime.

Another assumption of the argument – though this one is an assumption for a reductio – can be stated as follows:

2. If there is some object A with an intrinsic property Q in a region R of finite duration d in a possible world W, then:

a. There is a function f from the parts of R to the parts of some region R' of some possible world W', such that f is topology-preserving and compresses time and space by half. For instance, if the duration of R is d, the duration of R' is d/2

b. There is a counterpart A' of A and a counterpart Q' of Q, such that A' intrinsically has property Q' in R'.

Point 2. is used for a reductio against temporal density. Koons argues that 2. is reasonable under the assumption that time is dense.

If there is an intrinsic metric of time, it seems to me that we don't know whether some properties aren't compressible, whether some processes require at least some amount of time, etc., even if time is dense.

But let's say that that is not the case, and let's grant 2 for the sake of the argument.

Then, it seems to me that similarly, and regardless of whether time is dense, we may accept a principle of decompressibility of time, or DT, which is at least equally intuitive, and which we can state as follows:

2'. If there is some spatial and temporally bounded region R of duration d in a possible world W, then there is a duplicate R' of R in possible world W', which contains counterparts of every object in R with counterparts of its intrinsic properties, but expands time by a factor of two.

DT takes no stance on whether space is also expanded.

It may be argued that DT is in a sense stronger than Koons' principle, so a more tailored approach might be required for an atheistic argument, but if we assume that no properties are incompressible, no processes require a minimum amount of time, etc., and we accept 2. for that reason, it seems to me that it's equally plausible that a bounded region is possible temporally expanded by a factor of two.

But if one accepts DT plus E(n 0 ) of BIS, then there are possible duplicates of E(n 0 ) of arbitrarily long duration, provided that the properties of the torture chambers and the sufridores are intrinsic to the scenarios, which we may stipulate just as Koons stipulates that the properties of the reapers are intrinsic. Those duplicates wouldn't be exactly the other E(n), for n different from n₀, but the fact is that there would be arbitrarily long possible scenarios of sufridores getting tortured.

Alternatively, even without assuming that E(n 0 ) is possible, if the HEM scenario is possible, a relevantly similar result is achieved: namely, there would be arbitrarily long possible scenarios of sufridores or similar beings suffering horribly.

A potential objection to those scenarios of horrible extended suffering would be that, as time expands, so do the mental processes of the victims, which become slower, so they do not experience any increased suffering. However, given that the mind, capability for suffering, etc., of the victims is intrinsic to the individual scenarios – rather than, say, slower functioning minds -, it's not clear that this objection would succeed. It would depend on what counts as 'intrinsic', and that's unclear.

But let's say for the sake of the argument that all such minds would also become slower in that way, in the case of expansion of time, so this objection to the extended suffering scenarios described above is successful.

Even then, there are alternative ways of constructing similar scenarios. For instance, one such alternative can be constructed if the following premises are accepted:

Pa. For n=1, there is a possible scenario like HEM, which lasts for a minute.

Pb. Plausibly, if for some k, there is a possible scenario like HEM that lasts for k minutes, then there is another possible scenario like HEM, but which lasts for k+1 minutes.

How plausible are a. and b.?

Intuitively, I would say at least no less plausible than Koons' premises. Pa. seems quite clear, and Pb only requires finite additions (i.e., there is no assumption of a scenario in which one such being suffers forever).

Granted, someone might either reject Pa., or accept Pa but hold that, perhaps, there is some number K, such that for every k≤K, possibly, an entity of the relevant kind undergoes the kind of suffering described in the scenarios for k minutes, but necessarily, no such entity undergoes such suffering for K+1 minutes. That seems intuitively odd.

However, assuming that that kind of objection to the proposed scenarios of extended suffering succeeds, it seems plausible to me that the same kind of objection may successfully be raised to the principles proposed by Koons, since they're no more intuitively plausible than Pa and Pb.

Yet still, also assuming counterintuitively and for the sake of the argument that while all objections to the principles proposed by Koons fail and Pa is true, but Pb is not and there is such necessarily maximum number of minutes K, then we can still construct some scenarios that are very problematic for theism, especially when combined with Koons' principles. For instance, one such scenario can be constructed as follows:

All of space and time can be covered by non-overlapping spatiotemporal regions of equal size that are spatially cubic and have a fixed temporal duration K.

So, let's consider a possible world W at which there is a spatially cubic spatio-temporal region C(W) of finite size with one of those beings suffering for K minutes. We may consider then similar regions in other worlds, but spatio-temporally moved so that the regions are not overlapping (which seems obviously possible), and then apply infinitary patchwork, covering all of space and time at some world W'. While none of those entities suffers for more than K minutes at W', the fact is that all of time and space is covered by that kind of torment. We may also stipulate that there are no other agents spatially located in any of the regions, so that the whole of space and time is basically covered with horrible suffering and nothing else.

6.3.3. Infinitary patchwork.

A key principle of Koons' argument is what he calls "infinitary patchwork"[11] (or IP), and which can be put as follows:

Let's suppose the following conditions obtain:

IP(1): W = {W_n} is a countable series of possible worlds, and R={R_n}, is a countable series of regions of those worlds, such that for all n, R_n is a region of W_n.

IP(2): f is a function from R into the class[1 2 ] of spatio-temporal regions of some world W, such that f preserves the metric and topological structure of each of the R_n, and such that, if n≠m, then f(R_n) does not overlap f(R_m).

Then, there is a possible world W', and an isomorphism g from the spatio-temporal regions of W to the spatio-temporal regions of W', such that the following obtains:

IP(C): The part of W_n within R_n is exactly like the part of W' within g(f(R_n).

Let's grant IP for the sake of the argument.

Then, and as long as the minds of entities with intrinsic mental properties do not become slower as suggested in the previous subsection, it seems that from the assumption that E(n 0 ) is possible, plus the DT principle, a scenario relevantly similar to BIS follows at once, since for the reasons given in the previous subsection, there would be worlds W(n) and regions R(n) of those worlds with arbitrarily long periods of such terrible torment, and then one can send each of them to a world W via a function that preserves the topological and metric properties of each of them, and then patch them together into another possible world W' via infinitary patchwork.

Alternatively, given infinitary patchwork plus DT and the HEM scenario, it follows that there is a possible world where sufridores or similar beings suffer horrible pain – like being burned alive from the waist down – for arbitrarily long periods, and where that situation goes on forever.

Also, alternatively, if such minds would become slower, there are other scenarios that seem to work, as described in the previous subsection.

In my assessment, those conclusions would be a defeater for a claim that there is a necessary1-god, or a necessary 2-god, or generally for any usual form of theism.

Still, that's only a problem for usual variants of theism, but we still need to address the question of whether Koons' argument shows that time isn't dense.

It seems that even all of Koons' assumptions, plus the assumptions he uses in order to attempt a reductio, still do not present any problem for temporal density, as the following scenarios show:

First, let's consider the following scenario S₁:

1. There is a denumerable sequence of temporal intervals {I_n=[t_n+1,t_n)}, for all natural numbers n.

2. Each interval I_n has length 10^-n

3. During interval I_n, or at least during the last portion of it, there is a Fred particle at the designated position 10^-nmeters from the designated plane P. There is no other Fred particle during interval I_n

That scenario does not contain any grim placers, but it's a scenario that one could get by applying infinitary patchwork to each of the intervals.

Second, let's add grim placers; now, the scenario S₂is:

1. There is a denumerable sequence of temporal intervals {I_n=[t_n+1,t_n)}, for all natural numbers n.

2. Each interval I_n has length 10^-n

4. During interval I_n, there is a grim placer #n, GP_n.

That's a scenario containing infinitely many grim placers.

Each grim placer GP_n places the particle at the designated position, or the particle is there for another reason, so the grim placer has no job to do.

Someone might suggest that there is a problem if the intervals are open in the direction of the past, and closed in the direction of the future.

However, that wouldn't seem to be a problem, either, as the following scenario S₃ shows:

1. There is a sequence of temporal intervals {I_n=(t_n+1,t_n]}

2. Each interval I_n has length 10^-n

4. During interval I_n, there is a grim placer #n, GP_n.

Someone might add another condition to the definition of grim placers, demanding that they must act instantaneously, and suggesting that that would be a problem for each of the individual scenarios. However, in that case any problem in S 3wouldn't be related to the infinitary patchwork principle, but it would be a problem with each of the individual scenarios used for the patchwork. But then, that would not work as an argument against temporal density, which presupposes that the individual scenarios are all possible.

So, it seems that Koons' 'grim placers' argument does not work as an argument against temporal density, even leaving aside any atheistic parallel arguments. Similarly, they don't work as an argument against an infinite past, either, since similar counterexamples succeed.

6.3.4. Grim signalers.

Koons actually considers an objection like the one I just raised, and correctly points out that what is required is that some signals persist from one grim reaper, grim placer, or grim signaler, to the next.

So, he reformulates the argument without any particles, and replacing the grim placers with grim signalers. It's essential to a grim signaler to have the power of receiving a signal from a previous grim signaler, and to have the power to send a signal to a successor.

Koons considers a potential objection, based on the suggestion that the regions would overlap, and rejects it, positing adjoining non-overlapping intervals.

However, adjoining non-overlapping intervals aren't good enough. The power to send the signal to the next signaler is akin to the power to make the particle last into the next interval. That seems to defeat the argument, because the regions that are being patched would have to overlap and/or the properties of the signalers would not be intrinsic despite Koons' claims, so the principle of infinitary patchwork would not be applicable.

On the other hand, the atheistic parallel arguments I gave above do not have that problem.

6.4. Tristram Shandy.

Another one of Craig and Sinclair's arguments against an infinite past is based on the story of Tristram Shandy. [7 ]

Shandy is a man who writes his autobiography, at a rather slow pace: it takes Shandy a year to write the events of a single day.

According to Craig and Sinclair, we should reject an infinite past because it's obviously coherent to write an autobiography at that pace, but if Shandy had been writing from infinity, that would lead to absurdities.

However, what is obviously coherent is to write such an autobiography starting at a specific day.

On the other hand, to write an autobiography counting from infinity is logically impossible.[13]

To see why this is impossible, let's suppose otherwise, let's suppose the number of past years has the order type of the non-positive integers, and let's enumerate the past years in the following way: [14]

Last year is 0, the previous year is -1, and so on.

For instance, if this year is 2012, then 2011 is 0, 2010 is -1, 2009 is -2, and so on.

Now, let F be a function from the set of non-positive integers into itself such that for all non-negative integers r and n, F(-r) = -n if and only if -n is the most recent year Shandy wrote about during the year -r.

For instance, if, in the year -2000, Shandy wrote about a day in the year -300001 and about a day in the year -300000, then F(-2000) = -300000.

Given the rate at which Shandy writes, and given also that, when writing his autobiography, Shandy never writes about his future, we have the following conditions:

1. F(-r) ≤ -r.

2. F(-r-365) = F(-r) - 1.

By induction:

3. F(-r-2*365) = F(-r-365-365) = F(-r-365) - 1=F(-r) - 2

4. F(-r-k*365) = F(-r) - k, for all non-negative k.

So, in particular, taking r=0.

F(0) - k = F(-k*365) ≤ -k*365.

Hence, for every natural number k,

5. 364*k ≤ -F(0)

That's contradictory, as easily seen by taking (for instance) k = 1 + (F(0)*F(0)).

So, the Tristram Shandy scenario fails to show that infinitely many past years are impossible.

In other words, what's logically impossible is Tristram Shandy scenario itself, but that does not have anything to do with whether an infinite past is possible.

Craig and Sinclair acknowledge that the scenario is logically impossible, yet claim that because it seems "obviously" coherent to write one's autobiography at a rate of one day per year, it seems to them that the problem is the infinite past.

I have to confess that I find that reply puzzling. Clearly, the task of writing one's autobiography at a rate of one day per year 'from infinity' is logically impossible, and so not coherent. I honestly do not understand what else would be needed to reject the 'Tristram Shandy' scenario as an argument against an infinite past.

Incidentally, there is a contradictory scenario about the future that strikes me as similar to the 'Tristram Shandy' scenario:

Alice Shandy writes a novel starting in the year 2000, and the story is set in her future. She always writes about future days. Also, it takes Alice a year to account for what happens in one day in her novel, and she always writes her novel in sequence. In other words, she writes about what happens on some day d₁, and after she finishes writing about d₁, she moves to the day after d₁, without jumping to any later day.

Also, for any number n, Alice spends more than n years writing her novel.

The 'Alice Shandy' scenario is contradictory, but that does not warrant a conclusion that an unbounded future is metaphysically impossible.

Someone might insist that the task of writing a novel about the future, writing about consecutive days at a rate of one day per year, is obviously coherent, and so the fault must be with the idea of a future with an unbounded number of years, but it seems apparent to me that such a reply would be very mistaken.

The 'Tristram Shandy' scenario strikes me as similar, but in any case, I would say that we should in any case reject the 'Tristram Shandy' scenario because the task of writing one's biography at a rate of one day per year 'from infinity' is incoherent, and so the fact that assuming it's possible results in absurdities does not tell us anything about whether an infinite past in which the set of past years has the order type of the negative integers is metaphysically possible.

6.5. Orbits and parity.

Another argument against an infinite past defended by Craig and Sinclair[7 ] is based on orbits and the alleged parity of some numbers.

According to this argument, it's absurd that if Jupiter completes 2.5 orbits for each one Saturn completes, they would both have completed the same number of orbits, if they have been orbiting the Sun for an infinite number of years.

However, and leaving aside the fact that any planet, star, etc., only lasts for finitely many years in the actual world, the fact is that there appears to be no absurdity at all. As in the case of the Hilbert Hotel argument, the problem seems to be a confusion about the meaning of the words.

More specifically, that the number of orbits would be the same if they had been orbiting forever and there were an infinite past composed of denumerably many years merely means that there would be a bijection between the set of orbits completed by one of the planets, and the same set for the other planet, and that's as clear as the fact that, say, the set of natural numbers that are multiples of two has the same cardinality as the set of natural numbers that are multiples of five.

In addition to the previous argument, Craig and Sinclair also say that if a planet had been orbiting for eternity, the number of completed orbits would be both even and odd, and provide an unusual definition of 'even' and 'odd' that would apply to infinite cardinals, and under which infinite cardinals would turn out to be both even and odd.

However, that is not a problem, either, but rather, a consequence of the authors' unusual choice of definitions and the fact that there is a bijection between any two denumerable sets.

Of course, once again in reality planets don't last indefinitely, but that is not at all relevant.

6.6. Discrete time and infinite regress.

In addition to his 'grim reapers' argument, Alexander Pruss[9 ] gives another argument against infinite regress if time is discrete:

First, he argues that rigid discreteness is probably not an option, due to Zeno's Stadium argument, and relativistic considerations. I already commented on those matters earlier.

Then, he argues against infinite regress of events under Aristotelian discreteness, under the definition he suggests.[9]

So, Pruss reasoning is basically that if there were an infinite sequence of past events D(-n), for all natural n, such that D(-n) precedes D(-m) if n>m, then D(-n) could cause something at time 1/n, contradicting the hypothesis that time is discrete in the Aristotelian sense. According to Pruss, there is no reason to rule out all of those happening together.

But it seems to me that there may well be, and one possible such reason is precisely the fact that any consistent scenario in which time is discrete in the Aristotelian sense, and in which there is infinite temporal regress is a scenario in which it's not the case that the event D(-n) causes something at time 1/n.

In other words, what Pruss seems to be doing is going from the finite to the infinite case, including in the infinite case scenario some entity or entities with the causal power to bring about all of those things at time 1/n, and which exercise such powers successfully. But that's precisely not what happens in a consistent scenario in which time is discrete in the Aristotelian sense, and in which there is infinite temporal regress.

At this point, someone might ask questions like.

a. What would prevent the extension from the finite to the infinite case?

b. What would prevent those entities, if they exist, from exercising their powers?

I think that those would be the wrong questions, since it's not that something is preventing them from exercising powers. Rather, the problem is that one scenario is contradictory, but others aren't.

But purely for example, a consistent scenario in which time is discrete in the Aristotelian sense and in which there is infinite temporal regress and no entities with such powers may well be possible. Theists may believe otherwise as long as they believe in an all-powerful necessary entity or something like that, but I see no good reason to follow them on that.

For instance, the following scenario S₄ appears to be consistent:[1 4 ]

1. Time is discrete in the Aristotelian sense.

2. The set of years before some year – say, 0 – has the order type of the negative integers.

3. For any n > 10¹⁰⁰, there is no entity in the year -n with the power to bring about something in year 0, at time 1/n seconds (i.e., 1/n seconds after the year in question begins).

Granted, someone might add further conditions and reach a contradiction[1 4 ], but that's not the issue.

Also, someone might suggest that the 10¹⁰⁰restriction is arbitrary, but that would miss the point. For that matter, the following scenario S₅appears to be consistent as well:[1 4 ]

1. Time is discrete in the Aristotelian sense.

2. The set of years before some year – say, 0 – has the order type of the negative integers.

3. For any natural number n > 10¹³⁹⁸³, there is no entity in the year -n with the power to bring about something in year 0, at time 1/n (i.e., 1/n seconds after the year in question begins).

4. For any natural number n < 10¹⁰⁰⁰, there is an entity in the year -n with the power to bring about something in year 0, at time 1/n seconds.

On the other hand, the following scenario S₆ (for instance) would be impossible:

1. Time is discrete in the Aristotelian sense.

2. The set of years before some year – say, 0 – has the order type of the negative integers.

3. For any natural number n, there is an entity in the year -n with the infallible power to bring about something in year 0, at time 1/n seconds (i.e., 1/n seconds after the year in question begins).

So, we can construct consistent scenarios like S₄orS₅, as well as inconsistent ones like S₆, but that does not seem to tell us anything about whether an infinite past is possible if time is discrete in the Aristotelian sense.

In any event, I would say that constructing logically contradictory scenarios like the one proposed by Pruss above does not seem to tell us anything about time, as far as I can tell.

Incidentally, this argument, if it worked, would seem to provide a blueprint for essentially similar arguments against, say, infinitely many unembodied beings (like angels), or generally infinitely many objects that can be programmed to carry out a certain tasks in the future, etc., under the assumption that time is discrete in an Aristotelian sense.

For instance, a theist who accepts Pruss' reasoning might also argue as follows: let's say that God can create infinitely many angels {A(n)} in a finite past, before the year 2013. Then, each angel A(n) could be created with the task of doing something on, say, December 25, 2113, at noon GMT + 1/n second, and that would contradict that time is discrete in an Aristotelian sense.

There are, of course, non-theist variants, and these kind of arguments might be deployed against all other sorts of infinities, and maybe even against the possibility of infinitely many concrete objects.

In any case, I find the argument unpersuasive even under the assumption that time is discrete in an Aristotelian sense, for the reasons given above.

6.7. Scientific cosmology.

In addition to giving a priori arguments against an infinite past, Craig and Sinclair also claim that science supports the claim that the past is finite.

One of the arguments they use is based on what they call the "Standard Hot Big Bang Model". [6]

According to the authors, that model supports an origin that is an absolute origin ex-nihilo, and space and time themselves come into being at an initial singularity. But the fact is that a singularity in the mathematical model indicates that the equations don't properly describe some phenomena, not that there is some actual thing of infinite density – that would not even be defined.

Moreover, even that model entails an infinite past sequence of changes, since as we move farther back in time, the density of the universe tends to infinity, and so there are more than n consecutive changes in which the density of the universe decreases, for each n, even if the past in that model is metric-finite.

So, one of the models that they offer in support of his claims against an infinite past contradicts their stance on the possibility of actual infinities.

In any event, cosmologists already know that that model is insufficient to describe the early universe.

It's true that Craig and Sinclair also offer other scientific models in support of their claims, but they misuse them, since:

a. Even if our universe – in a limited sense of the word 'universe' - has a finite past, that would not rule out that there was time before the universe; Craig and Sinclair have not shown that that is not the case.

b. In fact, the question of whether the universe is past-finite, even in the narrower sense in which the word 'universe' is used in science, is still a matter of discussion among the experts in the field.

7. Some assorted comments.

This section is a bit of a side note, but I would like to address a few issues related to a number of contingency arguments, before addressing other arguments in greater detail.

7.1. The Big Contingent Conjunctive Fact (BCCF), and the BCCF*.

In his defense of an argument from contingency, Pruss [10] posits what he calls the "Big Contingent Conjunctive Fact" (BCCF), which is "the conjunction of all true contingent propositions, perhaps with logical redundancies removed", and defends the BCCF against Davey and Clifton's objection [16], based on a presumption of innocence – i.e., Pruss suggests that a conjunction should be presumed to make sense until proven nonsensical.

However, at least when it comes to unrestricted infinite conjunctions encompassing arbitrary classes of propositions, it seems to me that such presumption of innocence may not be warranted unless we have some procedure to construct them. Else, given the expressive power of propositions, paradoxes might be anywhere.

In any case, I will show that the BCCF makes no sense, assuming only that propositions – and not just sentences – can have subformulas – which Pruss seems to accept – and a principle we could call the "Subconjunctions Principle" (SCP), and which looks intuitively very plausible.

SCP: If C is a conjunction (i.e., one that makes sense), and P is a property, then the conjunction C(P) of all of the conjuncts of C which have property P is a conjunction (i.e., that makes sense) as well.

Since the BCCF is the conjunction of all contingently true propositions, we can use a slightly modified version Davey and Clifton's example and construct a conjunction BCCF(P) of all the conjuncts of the BCCF that do not contain themselves as proper subformulas.

But the BCCF(P) is just the conjunction of all contingently true propositions that do not contain themselves as proper subformulas, since a proposition R is a conjunct of the BCCF if and only if R is a contingently true proposition.

Let Q be the proposition, that BCCF(P) is true.

Since the BCCF(P) is contingently true because every single one of its conjuncts is, then Q is a contingently true proposition as well, and hence Q is a conjunct of the BCCF.

Does Q contain itself as a proper subformula?

Mirroring Pruss' explanation of Davey and Clifton's argument, we can see that either way, a contradiction follows:

If the answer is "no", then Q is a contingently true proposition that does not contain itself as a proper subformula. Hence, it's one of the conjuncts of the BCCF(P), and thus a proper subformula of itself, which contradicts the assumption that the answer is 'no'. Hence, the answer is 'yes'.

So, Q contains itself as a proper subformula, and the only way in which that can happen is that Q is a subformula of the BCCF(P).

But since Q is not a conjunction and the BCCF(P) is a conjunction, Q must be one of the conjuncts of the BCCF(P), and thus, Q is not a proper subformula of itself, a contradiction.

The conclusion is that the BCCF(P) makes no sense, and by the SCP, neither does the BCCF.

Someone might suggest that "logical redundancies removed" stipulation blocks the argument I just gave. But how does one remove something from something that makes no sense?

Pruss also offers an alternative to the BCCF, namely the BCCF*. Maybe the restrictions he imposes are sufficient, so the BCCF* makes sense, but it's not clear that it does.

7.2. Infinite causal chains.

As another brief note, I would like to make some comments about infinite causal chains.

Let's consider a simple principle (as an example):

CP(1): For every contingent being B, there is a cause of B's existence.

Would that principle be enough to conclude that there is a necessary being?

It seems not.

For example, it may be that some contingent being B(1) is caused by a contingent being B(2), which is caused by B(3), and so on, and there is no past time t at which none of the B(n) exists. In that case, all of the B(n) are caused, satisfying CP(1).

Someone might ask: but what about the whole chain? What about the being C(0) that is the chain {B(n)}, for all n?

A first difficulty is that it's not clear that the chain is a being, but leaving that aside, I would say that a causal explanation of C(0) is given by all of the B(n).

Someone might object to that suggestion and say that C(0) can't be the cause of C(0), because things, events, states of affairs, chains, etc., allegedly can't be self-caused, so – on this account – C(0) cannot cause C(0).

However, in my assessment, any apparent difficulty is the a result of terminological ambiguity, which disappears when we take a look at what is actually going on, namely that B(1) is caused by B(2), which is caused by B(3), and so on, giving a causal explanation for the chain {B(n)}.

So, whether we then say that the whole chain C(0) is self caused, causes itself, etc., seems to be a mere terminological issue, as far as I can tell, and regardless also of whether the word 'being' properly applies to the chain {B(n)}.

Still, there might more causes of {B(n)}, in a sense.

For example, it might be that, for all n, B(n) is caused but not fully caused by B(n+1), and also that B(1) is caused not only by B(2), but by a contingent being B(1,1), B(2) and B(1,1) are caused by a contingent being B(2,1), B(3) and B(2,1) are caused by a contingent being B(3,1), and so on, where the sets {B(n,1)} and {B(n)}, with n ranging over the natural numbers, are disjoint.

In that case, the chain C(0) may be said to be caused also by the chain C(1) consisting on the {B(n,1)}, for all natural numbers n, though in my assessment, that is again a terminological matter: what's actually going on is that B(1) is caused by B(2) and by B(1,1), that B(2) and B(1,1) are caused by B(2,1).

Also, someone might ask for the being C(1), consisting of the chain of all of the {B(n,1)}. But then, we may repeat the process.

That would result in a more complicated scenario, and the real case nay well be much more complicated still, but in any event, it seems to me that CP(1) can be satisfied by an infinite regress of causes.

However, if CP(1) is construed in a way that rules out such chains, I would be skeptical of it, since intuitively I find that an infinite causal regress with no past time at which none of the members of the causal chain existed may well be good enough as an explanation. If there were a time t prior to the existence of any of the B(n), the situation would be different, because in that case, the change from a state of affairs at which none of the B(n) exists, to a state of affairs at which infinitely many of them do, would intuitively call for an explanation. But as long as there is no past time t at which none of the B(n) existed, intuitively I see no problem.

Granted, someone might say that even if there is no such prior time, perhaps there is a causally effective timeless state at which none of them exists. I have serious doubts about the coherency of such suggestion, but even assuming it is coherent, I don't see any good reason to assume it obtains. So, intuitively, I would still say that an infinite causal chain without any past time at which none of the member of the chain existed, and also without any such timeless state, may well be a good explanation.

7.3 Morality and contingency.

Here, I would like to address a moral presented by Pruss[10] in support of a rather strong version of the Principle of Sufficient Reason (PSR) for contingently true propositions – in Pruss terminology, facts -, which can be stated as follows:

PSR(P,2): Necessarily, every contingently true proposition has an explanation.

According to this argument, if PSR(P,2) is not true, then then there might be no explanation [10] as to why it's not immoral to divert a trolley from a track where there are five people to one where there is only one person, but it is immoral to shoot an innocent person to save five (assuming those propositions are both true, for the sake of the argument).

However, even if those were examples of contingently true propositions, it seems to me that it's not the case that someone who does not take a stance on whether all contingently true propositions have explanations, ought to reject her own intuitions when they tell her that a particular contingently true proposition has an explanation – just as it is not the cast that someone who does not take a stance on whether all necessarily true propositions have explanations, ought to reject her own intuitions when they tell her that a particular necessarily true proposition has – or probably has – an explanation.

So, it seems to me that even if those were examples of contingently true propositions, someone might refrain from accepting that the PSR(P,2) and still have sufficient grounds for holding that there is an explanation as to why it's not immoral to divert a trolley from a track where there are five people to one where there is only one person, but it is immoral to shoot an innocent person to save five.

In any event, the fact is that if those propositions are true, they're not contingently true.

Someone might suggest that they're contingent, since for instance in a case in which diverting the trolley would also remotely activate a nuclear bomb that would destroy a city and kill a million people elsewhere – or something like that -, it would not be acceptable to divert it if one knows about that result, all other things equal.

However, that would not show that the propositions in question are contingent. Rather, that would be an instance of changing the scenario.

The scenarios mentioned above (i.e., trolley and shooting) have implicit conditions – or else, those clearly aren't moral truths.

In other words, if it's true that it's morally acceptable to divert a trolley from a track where there are five people to one where there is only one person, then what's true is not a general claim "for all x, if x is an instance of diverting a trolley from a track where there are five people to one where there is only one person, then x is morally acceptable", but rather, it's a claim that contains other, even if implicit, conditions.

So, the true claim (assuming it's true) is something like "For all x, if x is an instance of diverting a trolley from a track where there are five people to one where there is only one person under such-and-such extra conditions, then x is morally acceptable".

If that claim is true – i.e., if it's the case that for all x, under those specific conditions, the consequence obtains -, then it's necessary. Hence, the moral argument under analysis does not provide any support for the PSR(P,2).

7.4. Infinite conjunctions and cannonballs.

In this subsection, I'd like to consider what Pruss calls the "Hume-Edwards-Campbell Principle" (HECP)[10] . Pruss states the principle as follows:

Alexander Pruss[10]"For any proposition p such that one has explained every conjunct of a proposition, one might have thereby explained the whole."

As a counterexample, Pruss offers a scenario that, briefly, we can state as follows:

A cannonball is not in motion at noon, and it flies at any time between noon and one minute past noon. Let p_t be the proposition that reports the condition of the ball at t (momentum, etc.), for any time t in the open interval between noon and one minute past noon. Let p be the conjunction of all of the p_{t -}

According to Pruss[10], in a scenario like that, the following points obtain:

a. Each of the conjuncts p_tis explained of another conjunct p_t', for t' < t, plus the laws of nature and some conditions of the environment.

b. The conjunction p has not been explained unless one states that a cannon has been fired.

c. This is a case that is relevantly similar to any attempt at an explanation involving an infinite regress – even one that goes infinitely into the past -, in the context of cosmological arguments based on the Principle of Sufficient Reason.

However, the counterexample fails, for – at least – the following reasons.

First, we're not justified in applying Newton's laws or any other present-day model to arbitrarily small amounts of time, so this is a case in which we would not have a [proper] explanation of every one of the individual conjuncts. So, point a. is false, regardless of other considerations.

Second, let's assume for the sake of the argument that the universe is actually such that there are laws that we can correctly express with some formulas F that properly apply to any arbitrarily short period, and that we know the formulas in question.

Let's also leave aside issues such as whether we should talk of particles rather than cannonballs, when considering such brief periods.

Even then, Pruss' argument fails because if the process of the cannon's firing took place entirely during some interval (t₀, noon], then it seems that the ball is not at rest at noon, since – for instance – the energy has already been transferred to the cannonball at noon, and part of it even before noon.

So, the conclusion is that the firing of the cannon continued at least for some time after noon, and thus, for t sufficiently small, the individual conjunct p_tis not explained by a previous conjunct, plus the laws F and environmental conditions not including the firing of a cannon. That seems to block the cannonball argument, since Pruss' claim a. above is false, and regardless of other considerations.

Perhaps, someone might try to use the following variant:

The cannonball was fired before noon, and is not at rest at noon. But even then, all of the conjuncts, plus F, do not explain the flight of the cannonball in the open interval (noon, one minute past noon).

However, it seems to me that in that case, if each of the conjuncts is explained by F and a previous conjunct, the conjunction plausibly is explained by the conjuncts plus F, even though a more thorough explanation might also include the conditions of every other object in the universe at each time t in the given interval.

What is not explained by the conjuncts plus F is why the cannonball began to move in the first place, or F, but none of that is a part of the proposition to be explained, which is simply the conjunction of all of the p_t.

Granted, normally, we wouldn't accept such infinite regress as a good explanation if we asked why the cannonball was in flight in the open interval (12:00,12:01). However, it's also true that normally, we wouldn't accept the proposed explanations in the case of any of the individual conjuncts, either.

On that note, if we asked why a cannonball is in flight, we wouldn't normally accept the following reply as an adequate explanation:

The ball was in flight just one second before the moment at which you asked, and that ball one second before the moment at which you asked, plus the environmental conditions and some other objects, caused the ball to be in flight when you asked.

Regardless of issues such as whether we include some formulation of laws of nature explicitly, whether we understand the mathematical models as approximations reflecting the causal powers of substances, etc., the fact is that normally, we would not accept such an account as an adequate explanation of the fact in question.

Also, this is so independently of considerations such as the potential imprecision of expressions such as 'the moment at which you asked'.

The reason we would find the proposed explanation inadequate might be that the reply would not address the cause of a change from a state of affairs in which there is no ball in flight, to one in which there is one. In any event, and regardless of whether that is in fact the reason we would find the proposed explanation inadequate, the fact is that we would find the explanation inadequate in the case in which there is no infinite regress as well, so the problem here does not appear to be infinite regress.

The previous considerations do not seem to be a peculiarity of the cannonball example. For instance, let's consider another example.

Alice: Bob, why is there a big red balloon on the table?

Bob: The reason is that there was a big red balloon on the table one minute ago, and that balloon, plus the environmental conditions, laws of nature, etc., brought about that there is a balloon now on the table.

Intuitively, we would expect Alice to find the explanation offered by Bob woefully inadequate. Plausibly, that would probably be because Bob's answer would not address what Alice wanted to know, namely the ball got there in the first place. In other words, it's a change in a state of affairs, from a state at which there is no ball on the table, to a state at which there is one, which Alice wants an explanation of.

However, if for every time t in some interval (t₁,t₂), one has [adequately] explained why the ball was on the table at t in terms of some conditions at some earlier time t' in the interval (t₁,t₂) - conditions that might include laws of nature -, it may well be that one has explained why the ball was on the table during the interval (t₁,t₂). At least, I see no good reason to think otherwise.

Granted, intuitively I would say that why the ball was there has not been explained, but then, I would say the same for the individual conjuncts. So, if there is a problem here, it seems to me the problem is with the proposed explanations in the individual cases, and thus this line of argumentation does not provide any good reasons to reject the HECP.

7.5. Conjunctions, corners, and Inuits.

I will come back to the issue of explanations by infinite regress lat er, but first, I'd like to address another principle, which Pruss calls the "Hume-Edwards Principle" (HEP), and which he states as follows:

Alexander Pruss[9]"In explaining every conjunct of a proposition, one has explained the whole proposition."

I do not claim that the HEP is true, but I'd like to consider Pruss' arguments against it, because they lead to a number of interesting issues, in my assessment.

So, Pruss objects to the HEP by arguing that one wouldn't be able to explain why there are a hundred Inuit in a certain corner just by explaining why each of them is there, allegedly because there is a coincidence left to be explained.

However, the proposition that there are one hundred Inuit at such-and-such time and at such-and-such corner, is not a conjunction. But let's consider a conjunction:

C: Susan is an Inuit and is at corner X at time t (for some fixed X and t), and Tom is an Inuit and is at corner X at time t, and Jack is an Inuit and is at corner X at time t, and Mary is an Inuit and is at corner X at time t..., and so on.

Let's say that Alice gives Bob an [adequate] explanation of the fact that Susan is there at that time, and one of the fact that Tom is there at that time, etc.

Now, upon contemplating the fact that one hundred Inuits are there together, if the individual explanations do not make any mention to any coordination between them, then Bob might feel inclined to ask whether there was some previous agreement between them, which somehow was overlooked when presenting all of the individual explanations, etc.

However, let's suppose first that there wasn't such coordination.

Pruss seems to think that in that case, the individual explanations are or at least may be enough to explain the conjunction, but not in case there is some coordination between them.

So, let's suppose now that there was was previous coordination, and it was omitted in the case of the individual explanations.

Then, there are some alternatives, such as:

Hypothesis a. The [purported] explanations of some or all of the individual conjuncts given by Alice are inadequate, since they omit some important reason why the individual Inuits behave as they did, namely their coordination with the other Inuit in question.

Hypotheses a. is not a problem for the HEP, since in that case, some of the individual conjuncts have not been explained by Alice.

Hypothesis b: The explanations of the individual conjuncts given by Alice are individually adequate, and together, they explain the conjunction as well, even if there are more detailed explanations of the conjunction C.

Hypotheses b. is not a problem for the HEP, either.

In fact, there are also more detailed explanations of the individual conjuncts, for that matter, and that's at least usually the case for any explanation.

Hypothesis c:. The explanations of the individual conjuncts given by Alice are individually adequate, but together, they fail to explain the conjunction C.

Hypotheses c. would entail that the HEP is not true.

However, plausibly, there would still be an adequate explanation of the conjunction in terms of adequate explanations of the individual conjuncts.

For example, let's say that Alice gives an adequate explanation of why Susan was at corner X at time t which includes the fact that she had earlier agreed to meet Tom, Mary, Jack, etc., at that corner and at that time in order to, say, talk about Inuit history, the fact that she wanted to discuss Inuit history with them, and so on. Furthermore, let's say that Alice gives similar adequate explanations in the cases of Tom, Mary, etc.

Then, plausibly those adequate explanations in terms of the conjuncts do provide an adequate explanation of the conjunction. In light of that, someone might propose a principle that appears to be weaker than the HEP. Let's call it the 'Weaker HEP', or WHEP.

For every conjunction p such that p is explicable, and such that every individual conjunct q of p is explicable, there are explanations E_q of every individual conjunct q of p, such that all of the E_q together explain p.

In any case, it seems to me that there is a deeper issue at play here. I mentioned above adequate explanations. But it seems plausible to me, especially in light of the previous examples in this subsection and the previous one, that the issue of whether an explanation is adequate raises questions such as: Adequate for what purpose?

For instance, let's say Alice gives an account of why an individual Inuit, say Susan, is at corner X at time t, in terms of Susan's motivations that morning. Alice says that Susan wanted to use a hotspot at that corner to connect to the internet, and talk to her cousin who lives in Russia.

Let's say that Alice's account is true.

Bob might regard Alice's account as a satisfactory explanation. But he might not.

Bob might regard the account provided by Alice in the individual case as inadequate to explain why Susan is there, since the account in question fails to explain one or more of the following points:

a. Why Susan wants to talk to her cousin.

b. How Susan managed to get to the corner in question.

c. Why Susan would want to use a hotspot, instead of connecting from home (for instance).

d. Why Susan believes that the internet is an effective means of communicating with someone who lives in Russia.

e. Why Susan believes that there is a hotspot in that corner.

f. Why Susan believes that her laptop computer is an effective means of using that hotspot.

g. Why Susan exists in the first place.

h. Why Inuits exist in the first place.

And so on.

Is Bob mistaken in objecting in that fashion?

Some of Bob's objections would be prevented by a more detailed account, but the same goes for any potential objection in the case of the conjunction. On that note, Pruss says that in the case of the conjunction, there is a coincidence to be explained, and so he claims that for that reason, explanations of all of the individual conjuncts together wouldn't explain the conjunction. As a previous example shows, that is – at least – not true of all sets of explanations of the individual conjuncts, so regardless of whether the Inuit account shows that the HEP is false, it's unproblematic for the WHEP.

But moreover, if an account of the conjunction in terms of the individual conjuncts is inadequate just because it fails to explain the coincidence in the Inuit case, a question is: why would Alice's individual account of why Susan is there would not be inadequate also because it fails to explain a number of other facts?

In other words, why should Bob's objections be rejected, if they should?

In my view, and in light of the previous examples and considerations, whether an account offered as an explanation is indeed an adequate explanation depends not only on the content of the account in question, but on its context as well, including even issues such as what degree of precision has been requested, implicitly or explicitly. None of this seems to be a particular difficulty for explanations of conjunctions in terms of explanations of the individual conjuncts.

7.6. Unexplained contingent beings.

In this section, I will address the issue of whether we can rule out contingent beings that possibly exist without an explanation of their existence.

Let's assume that a non-deterministic interpretation of Quantum Mechanics is true – which, for all we know, might be the case. Then, even if bricks, cats, etc., don't pop up into existence at the actual world, it's only extremely improbable for that to happen, but it seems it's nomologically possible, given some improbable but nomologically possible particle behavior.

Granted, a theist might say that God would not allow that kind of thing, and so it's metaphysically impossible. Regardless of issues like the relation between nomological and metaphysical possibility, God's behavior is not something that we ought to assume beforehand in the context of a contingency argument, so for all we know (in this context, at least), that kind of thing might happen.

So, if a non-deterministic interpretation of QM is true, for all we know that there may be a possible world W where events that are extremely improbable, do happen.

Let's consider such a world W:

At W, bricks, cats, planes, etc., sometimes just pop into existence, despite their quantum improbability. Moreover, the people at that world still do experiments with particles and the like, and they get the same results as we get here.

However, on their planet, when people are not doing any experiments – i.e., never under controlled conditions – sometimes bricks, cats, planes, etc., just pop into existence.

Moreover, the behavior of particles does not have any causes different from the causes in our world. The same fields, etc., that exist in our world exist there, and just as in our world no one is directing the particles (for all we know, that may be the case, so let's stipulate so), no one is directing them in their world, either, but they just behave in a way that results in such bricks, cats, etc.

If I try to put myself in their situation, it seems clear to me that the events weren't explained in their world.

For instance, if those events begin to happen tomorrow, and some scientists offer as an explanation that we just happen to live in a world in which all of that happens even if it's extremely unlikely based on our experiments in controlled conditions, it's clear to me that those scientists would have failed to explain those events.

Someone might suggest that the preexisting conditions of the universe are a cause of those bricks, etc., and that that would explain them. But the fact would remain that the purported explanation would in practice amount to saying that the universe is just such that those things sometimes happen no matter how improbable, and that such a universe (or its previous states) counts as a preexisting condition and thus a cause that explains the existence of those things. It seems to me that that would not explain the events and things in question, even if it counts as a cause.

Alternatively, or in addition, someone might suggest that nothing is coming into existence in the proposed scenario, since the bricks, cats, etc., would be made out of preexisting particles, or new particles that result from energy, etc., so those are really not cases of contingent beings coming into existence without a causal explanation of their existence, but just transformations of things. However, in that case, it seems to me the usual examples for or against principles involving things that allegedly possibly exist without explanations fail to even address the matter, and arguably we may not even have clear examples in daily life of things that come into existence with causal explanations of their existence – though some philosophers would raise objections in the case of minds, etc.

I will not explore these scenarios in greater detail here, but in my assessment, the previous scenarios at least show that, for all we know, there may be possible worlds in which there is no explanation for the existence of some bricks, cats, planes, etc.

If possible worlds are a problem, we may drop them, and just consider the previous scenario as one that, while extremely improbable, might even actually happen, if a non-deterministic interpretation of QM is true. It's not something we should worry about, of course (it's too improbable to be a concern), but it seems to me it's enough to suggest that, for all we know, such scenario may be metaphysically possible.

7.7 Metaphysical necessity and causal necessity.

In the context of one of his contingency arguments, Pruss proposes a causal account of metaphysical necessity. [10]

According to this account, a state of affairs S is merely possible if there is something capable of originating a causal chain leading up to S, S is possible if S is actual or merely possible, and S if necessary if ¬S is impossible.

It seems to me that this causal account should be understood as implying that if there is [or probably there is or there was] something that is or was capable of starting a causal chain leading to ¬S, S is not metaphysically necessary. For instance, let's consider the state S: = In the twentieth century, Bill Clinton wins a Presidential election in the United States. Since that already happened, there is nothing that can bring about ¬S. But S is not metaphysically necessary.

That aside, if that account is true, it seems to me that the conceivability criterion, with our without visualization, would have to be set aside entirely, since what we can conceive of does not seem to be a good guide to the causal powers of actual entities, which we seem to learn mostly empirically.

Purely for example, even if we can conceive of or imagine ourselves being given a space suit and being teleported to Mars within two minutes, that does not seem to give us reasons to believe that some entity has the power to move objects faster than light within the Solar System.

Similarly, even if we can conceive of the BIS scenario, that does not seem to give us reasons to think that there are entities with the power to bring it about, or even to bring about a finite event, say, E(10 10000!!!!!!!!!!!!).

So, it seems to me that if this causal account of metaphysical modality in terms of causal modality is correct, our capability for conceiving scenarios are no guide to metaphysical necessity, possibility, etc.

That said, someone might raise the following objection:

Given that conceivability [perhaps, plus visualization; the specific objection may vary] is a good guide to metaphysical possibility, then if metaphysical possibility reduces to causal possibility, then conceivability [perhaps, plus visualization] is a good guide to causal possibility.

However, it seems very implausible to me that what we conceive of, with or without visualization, would be a good guide to what causal powers actually exist, because as pointed out above, we seem to learn about causal powers mostly empirically, and simply because I don't see any good reason to suspect that there is any connection between what we can conceive of, with or without visualization, and what actually can be brought about by some entity, except in the very limited sense in which, when we already know by empirical findings that some powers are possible, then we can conceive of some entity exercising such powers and bringing something about, but that does not seem to be what the conceivability criterion is about.

Perhaps, a theist might suggest that a, say, 1-god gave us a sense that allows us to track what is causally possible by means of visualization – for instance -, but it seems to me that would have to be argued for, and the burden would be on the claimant.

So, assuming that either visualization or conceivability without visualization is a good intuitive guide to metaphysical possibility, I would say that an account of metaphysical modality in terms of causal modality is probably incorrect.

On the other hand, if metaphysical possibility reduces to causal possibility, I would be very skeptical about any conceivability criterion, and moreover, personally I'd say that if metaphysical possibility reduces to causal possibility, chances are it reduces to nomological possibility as well – though I will not assume that in this essay, of course.

Intuitively, I find the conceivability criterion without visualization plausible, and the hypothesis that metaphysical possibility reduces to causal possibility implausible, but at least I would say skepticism is warranted.

In any case, the hypothesis that metaphysical possibility reduces to causal possibility would not be problematic for an infinite explanatory regress.

8. An argument from maximal contingent states of existence.

In a paper in which he proposes alternative paths to a necessary being[17], Joshua Rasmussen argues for the possibility of contingent states of existence that entail all contingent states of existence with which they are compatible. Those states would consist of some contingent objects' existing, and would be incompatible with the existence of any other contingent objects.

Then, he uses a causal principle, combined with the premise that there are possible maximal contingent states of existence, to derive the conclusion that there is a necessary concrete object.

I will assess his argument in this section, though I will address some evidence in greater detail later.

8.1. Possibility of maximal contingent states of existence.

In order to support the possibility of such maximal states, Rasmussen considers two different alternatives:

The first one would be a contingent object – which he calls 'Lonely' - that is maximally incompatible with other contingent objects. Also, that incompatibility is intrinsic, so if Lonely is possible, any duplicate [18] of Lonely at some other world[19 ] is also maximally incompatible with other concrete contingent objects.

It seems that Lonely can't be caused by another contingent concrete object that ceased to exist before Lonely comes into existence, either, so Lonely's incompatibility extends into the past if presentism is not true. In other words, Lonely, if possible, can't coexist with other contingent objects that previously existed, at least not if presentism is not true.

I'm skeptical about the possibility of Lonely, for the following reasons:

First, if we try to use the conceivability criterion, if we conceive of a scenario S in which a being B exists without including modal terms in the description of S, then it seems plausible that we can add a new being C without contradiction, which would indicate that B is not Lonely, at least if that's how the conceivability criterion works. For instance, assuming that unembodied physical beings (say, angels) are possible, why can't one add an angel without destroying B? [20 ]

If that's not how the conceivability criterion works and – say – visualization is relevant rather than whether the definition is in modal terms, then it seems that we can't visualize a scenario with a being B and which would rule out other contingent beings, so the criterion would be silent, but would provide no support for the possibility of Lonely.

So, it seems to me that either conceivability supports the impossibility of Lonely, or is silent.

Perhaps, someone might say that conceivability neither requires visualization nor does it require that the scenarios not be described in modal terms. But I'm not sure how to use the criterion then.

Leaving conceivability aside, I still do not see any good reasons to think Lonely is possible. I do not have any other intuitions suggesting it's possible or not. [21]

So, I would say that on intuitive grounds, skepticism about whether Lonely is possible is at least warranted.

Perhaps, someone might suggest a 'principle of innocence', according to which, unless one finds a contradiction, one should prima facie hold that a certain being probably is possible, even if it looks intuitively implausible.

However, in that case, we may for that matter consider (for instance) a concrete being that is incompatible with all personal beings, and then one that is incompatible with all non-personal beings, which would be a problem from arguments from contingency.

So, at least on intuitive grounds and in this context, skepticism about the possibility of Lonely is at least warranted. But there does not seem to be empirical support for Lonely, either.

Given that, it seems to me that skepticism is at least warranted.

Let's consider the second alternative that paper provides.

The author argues that if Lonely isn't possible, plausibly objects are generally compatible with each other, and then he proposes a scenario in which certain being called 'Big Blob' coexists with all contingent objects compatible with it.

The first issue is whether Big Blob is possible.

Big Blob, by definition, is a being that necessarily occupies all of space.

But let's say a being B₁ occupies all of space. If unembodied, self-aware, beings are possible, should we think it's not possible for there to be some powerful personal being B₂, who coexists with B₁ at world W, and who has the power to remove B₁ from any volume V of space of her choosing? [22]

A potential reply is that if B₁ is Big Blob, then B₁ necessarily occupies all of space, so if B₂ tried to remove B₁ from some volume V, the attempt would either have no effect, or else it would annihilate B₁, and the resulting being (if any being results) might still occupy most of space, but it would not be B₁ because the essence of B₁ is such that if B₁ exists, it must occupy all of space.

Without the assumption that essentialism is true, I would say Big Blob is intuitively implausible. But given that I'm assuming essentialism, I don't have any clear intuition one way or the other, so I would remain undecided on the possibility of Big Blob as well, on intuitive grounds.[23]

On the other hand, there seems to be nothing apart from intuitions that might be used to support the claim that Big Blob is possible.

So, given the above, I think skepticism about both the possibility of Lonely and of Big Blob remain at least warranted.

Even assuming that Big Blob is possible, it's still not clear to me that maximal contingent states of existence are so as well. For instance, if there is a state of existence containing some angels, is it always possible to add another one? [24 ]

8.2. The causal principle.

The causal principle in this argument can be stated as follows:

CP(R,1): Necessarily, normally, for all S such that S is a contingent state of existence, possibly S's obtaining, or that a duplicate of S obtains, is causally explained. [18]

Rasmussen considers a scenario in which a maximal contingent state of existence M contains infinitely many objects causing each other, etc., and points out that even if such causal chains are possible, it remains the case that no contingent concrete object could provide an external causal explanation of a maximal state M.

That is true, but then, it seems that in order to account for the epistemic possibility of such chains, the principle we should consider is the following one – which is equivalent to CP(R,1) if infinite causal chains like the one described above aren't metaphysically possible.

CP(Alt,2): Necessarily, normally, for all S such that S is a contingent state of existence, possibly S's obtaining, or that a duplicate of S obtains, is causally explained by a cause that is external to S. [18 ]

That principle has the problem that by means of considering bigger states of existence, we would keep removing causes from a causal account. By demanding that the causes be external, we would ignore all of the causes internal to the state, and that would bring up the question of whether we have removed them all, leaving no external cause left standing.

Also, it has the problem that it extends a principle not only from familiar cases to all actual cases, or cases in similar possible scenarios, but to all possible worlds. But that means that if Lonely is possible and existed at a world W, the only way that it would be normal at W – and at any time at W, it seems – that contingent concrete objects have causes would be that there is a necessary concrete object, which is improbable based on other pieces of evidence, and at the very least we ought not to assume beforehand.

As argued earlier, a principle like CP(Alt,2) is just one potential generalization from some of the evidence we have, to some (much) more general categories. Another potential generalization would be – for example:

CP(3): Actually, normally, concrete states of existence have causes.

CP(3) is more modest than CP(Alt,2) in some ways, and more demanding in some other ways.

It's more modest in that it does not extend the principle beyond the actual world, and in that it does not demand that the cause be external, so it does not remove causes from a causal account.

It's more demanding in that it does not limit the concrete states of existence to contingent ones.

But the principle CP(3) may well be satisfied in all cases without any necessary concrete objects. On the other hand, an uncaused concrete object would be an abnormality under CP(3).

Also, without a necessary concrete object, the state of existence C consisting in all contingent concrete objects' existing would not have any external causes, but that would simply be because we just put all of the causes within the state in question, which would be the same as the state T of all concrete objects' existing, and which does not have external causes regardless of whether or not there is a necessary concrete object.

In any case, for reasons I gave earlier, rather than trying to pick one principle or another, I would suggest assessing a larger body of evidence, which I will do later.

9. A mereological argument from contingency.

In this section, I will assess Koons' cosmological argument in support of the existence of a necessary cause, considering both the original formulation [25] and a later variant [26]. I will not address his arguments about the properties of such cause in this section, but I will do so later.

9.0. Notation and definitions:

I will use Koons' definitions, and a very similar notation, in particular:

x≤y: = x is a [mereological] part of y.

xOy (x overlaps y):= (xOy↔ⴺz(x≤y and z≤x)).

Ax: = x is actual.

▽x (x is wholly contingent): =(▽x↔Ax&∀y(y≤x→¬Ax)

x►y: = x is a cause of y.

9.1. Mereological principles.

9.1.1. Axiom 1: (x≤y↔∀z(zOx→zOy))

That seems intuitively plausible to me.

An interesting consequence of axiom 1 is that x is not a part of y, then there is some z that overlaps x but not y.

9.1.2. Axiom 4: (x≤y→(Ay→Ax))

A curious consequence of Axiom 4 seems to imply that (for instance), at least by any common usage of the terms, particles aren't parts of the Earth, since they keep decaying, but the Earth still exists.

While our language is imprecise, the word 'Earth' has a meaning, even if that meaning is imprecise to some extent, and the meaning is such that the Earth still exists if we remove a particle.

Someone might say that each time a particle ceases to exist, a new being comes into existence instead of the previous one, etc., and 'Earth' denotes all of those new beings, but that sounds rather unusual.

There is another problem, it seems:

Let's consider the state of affairs S₁ consisting of Napoleon thinking about Waterloo.

It seems plausible that possibly, Napoleon could have made different choices and could have never thought about Waterloo. If so, then, S₁ is not a part of Napoleon if axiom 4 holds.

If so, then by axiom 1, there is some concrete state of affairs z that overlaps the concrete state of affairs consisting in Napoleon thinking about Waterloo, but does not overlap Napoleon.

That sounds intuitively implausible to me.

9.1.3. Axiom 2: ⴺxF(x)→ⴺy∀z(zOy↔ⴺu(F(u)&uOz))

This axiom states that there are arbitrary mereological sums: if there is state of affairs of type F, then there is a mereological sum or aggregate of all the states of affairs of type F.

Given that F is an arbitrary type, that means (for instance) that there is a mereological sum of the supermassive black hole at the center of the Andromeda galaxy, Napoleon and Napoleon's mother (for instance).

In addition, since this is extended to any arbitrarily category, there is an aggregate of all contingent states of affairs, which is actually the aggregate of all states of affairs as well, regardless of whether there is a necessary state of affairs.

Intuitively, the axiom seems weird to me, and I see no good reason to accept it despite its counterintuitiveness, so I remain skeptical about it.

9.2. Causal principles

9.2.1. Axiom 6: (x►y)→¬(xOy):

This axiom, on its own and plausibly or in combination with axiom 2, eliminates causes from a causal account.

For instance, assuming axiom 2, let Let M(BHA, N) be the mereological sum of the supermassive black hole at the center of the Andromeda galaxy and Napoleon. A cause of M(BHA, N) is Napoleon's mother. While she's not a cause of all of the parts of the sum, she's a cause of one at least one of them, and so one of the causes of the sum too.

Now, let M(BHA, N, NM) be the mereological sum of the supermassive black hole at the center of the Andromeda galaxy, Napoleon, and Napoleon's mother.

If someone asked for a list of causes of Napoleon, his mother and the black hole in question, it seems to me that Napoleon's mother would be on the list, since she's a cause of Napoleon, and Napoleon is one of the things whose causes we're looking for.

Yet, the combination of mereological and causal axioms given so far implies that Napoleon's mother is not one of the causes when asking for causes of the sum M(BHA, N, NM), removing that cause from our causal account of the world.

Even on its own and without assuming or denying axiom 2, axiom 6 removes causes from a causal account, as the following example shows:

If we consider the state consisting in a house standing on a hill, it seems that the state has both external causes – like some stuff elsewhere in the Earth -, and some internal causes – like interactions between different parts of the house.

But axiom 6 removes all internal causes from a causal account, and only leaves the external causes left standing – of course, that is not related to the causal structure of the world, but with our account of it.

In particular, axiom 6 axiom has the potential for removing all causes from a causal account, regardless of whether there are any actual exceptions to causality going on; in other words, it tends to creates artificial exceptions.

For instance, in the case of the category 'contingent states of affairs', clearly the procedure eliminates all causes from a causal account, since the mereological sum of all contingent states of affairs is the mereological sum of all states of affairs, so there are no external causes, and axiom 6 eliminates all internal ones. However, that does not tell us anything about the causal structure of the world.

I find this axiom very implausible when applied to states of affairs, on its own and even more so in combination with axiom 2.

9.2.2.Axiom 7: ∀x(▽x →ⴺy (y►x)).

Axiom 7 selects a category of states of affairs, namely wholly contingent ones, and states that any state of affairs in the category has a cause, which is to say an external cause in this context.

In combination with the previous axioms, it entails that there is a necessary state of affairs.

Koons says that the justification is empirical, because both by use of common sense and by use of science we keep finding causes of wholly contingent states of affairs.[27 ]

Yet, we also keep finding causes of states of affairs, or contingent states of affairs, not just wholly contingent ones.

Let M be the aggregate of all contingent states of affairs. Then, M is the aggregate of all states of affairs, because if any state S is necessary, the sum of S and a contingent state is contingent.

So, since M is the aggregate of all states of affairs, it has no causes assuming axiom 6.

Of course, M still has plenty of internal causes, but they're all removed from out causal account by axiom 6, because axiom 6 demands that a cause be external to the mereological sum.

Thus, the procedure of taking mereological sums, in combination with axiom 6, results in the elimination of all causes from our causal account, when it's applied to the category 'contingent states of affairs'.

This, of course, tells us nothing about the causal structure of the world.

Yet, for all we know a priori, there may well not be any necessary states of affairs. And empirical evidence does not seem to change that.

So, we have good reasons to reject axiom 7, namely that for all we know, it may well be that the category 'wholly contingent states of affairs' is the same as the category 'states of affairs', and if so, by removing all internal causes, we would have no cause left standing.

9.2.3. Axiom 8: Normally, (▽x →ⴺy (y►x)).

Axiom 8 is proposed by Koons[26 ] as an alternative to axiom 7.

Given axiom 6, accepting axiom 8 would lead us to conclude that every wholly contingent state has an external cause, unless a positive reason can be given to exclude some particular state.

But it seems to me that there is a good reason, as explained above – namely, it may well be that the category 'wholly contingent states of affairs' is the same as the category 'states of affairs', and if so the mereological sum of all wholly contingent states of affairs has no external causes, simply because that would be the same as the mereological sum of all states of affairs, and then all of the causes would be internal.

Axiom 8 would be one of many possible generalizations from usual cases to arbitrary categories. An alternative generalization would be:

CP(Alt,8): Normally, any state of affairs has a cause. (not necessarily an external one)

That principle may well be satisfied if there are no uncaused beings, but an uncaused being would be an abnormality.

However, in any event, those generalizations are just that: extrapolations from some evidence that we have – including intuitions about familiar cases – to general categories.

So, for the reasons I gave earlier, rather than trying to pick one generalization or another, I would suggest taking a look at a larger body of evidence[4]; which I will do later.

10. Three more causal principles, and more contingency arguments.

In this section, I will consider three more causal principles, proposed by Joshua Rasmussen[17].

CP(R,3): ∀T(T is a type of contingent concrete object → ¬◊ (the obtaining of the state of affairs there being at least one member of T is causally explained by a member of T).

However, even if the state of affairs there being at least one member of T is not explained by any particular member of T, it seems to me it may well be causally explained by infinite regress involving members of T. That actually looks like a plausible assessment of the evidence to me, which is a matter I will address in greater detail later.

Whether that would also imply that that there is at least one contingent concrete object is metaphysically necessary would depend on whether metaphysical necessity reduces to causal necessity, a suggestion I addressed earlier, and which I personally don't find convincing.

Let's assess another principle:

CP(R,4): ∀T(T is a type of contingent concrete object → ◊ (the obtaining of the state of affairs there being at least one member of T is causally explained))

It's clear that assuming CP(R,3), CP(R,4) would lead directly to a necessary concrete object (e.g., by applying CP(R,4) to the type 'contingent concrete objects'), if one rejects causal explanations involving infinite regress, but I find them intuitively good enough, whereas I do not find a necessary being intuitively good enough as an explanation.

However, if we stipulate that an infinite causal regress does not count as an explanation in CP(R,4), then the principle appears implausible to me.

The author points out that there are philosophers who find CP(R,4) intuitively plausible by considering examples such as armchairs, and similar cases.

That's true, but I'll point out that those familiar examples do not extend infinitely into the past, and further, it seems that also some philosophers find one or more of the following points intuitively plausible:

1. For every concrete object that exists, it possibly does not exist, and so the category 'contingent concrete object' is the same as the category 'concrete object'.

2. Moreover, the criterion of conceivability without visualization is a good guide to metaphysical possibility, which supports 1.

2. Every concrete object that actually exists has at least a cause.

3. A causal explanation including infinite regress, is good enough, whereas one proposing a necessary cause isn't; I will analyze the explanatory power of two competing hypotheses later.

In any case, in order to assess the matter, and for reasons I gave earlier , I would suggest not trying to pick one principle or another, but taking a look at a greater body of relevant evidence, which I will do later.

To end this section, let's consider another causal principle proposed in the same paper, which can be stated as follows:

CP(R,5): ∀T(T is a type of contingent concrete object → ◊ (the obtaining of the state of affairs there being exactly n members of T has a causal explanation)); n >0.

The reply is similar to the reply to the reply in the case of CP(R,4).

A variant of the explanation by infinite regress also works similarly: for instance, if all concrete objects are contingent and the total number of present and past actual concrete objects is z – for some cardinal z -, then the explanation as to why there are z in total would be that at any time t, there were z(t), and that was brought about by, say, z(<t), the ones that existed previously, and so on, and the total number sum is z, counting each thing once of course. If time is discrete, we may introduce a countable sequence instead, etc.

11. An argument from the exemplification of properties.

In this section, I will address another contingency argument, based on the exemplification of some properties, defended by Joshua Rasmussen. [28]

I will introduce a definition, for the purposes of abbreviation:

Definition: An intrinsic property P is a B-property if and only if P can begin to be exemplified, and can be exemplified by something that has a cause.

Notation: 'B(P)' means that P is a B-property, and 'CCP' means the property of being a contingent concrete particular – if that is a property at all.

Given that notation, the causal principle states:

CP(R,6): Normally, if B(P), then there can be a cause of P's beginning to be exemplified.

Rasmussen defends that principle, and also argues that being a contingent concrete particular is a B-property. Before I address the causal principle, I will address the claim that being a contingent concrete particular is a B-property.

11.1. Properties and existence. Contingency.

Let's consider some existential claims first.

O1: Obama exists.

It seems to me that O1 does not ascribe any properties to Obama. O1 does not seem to describe Obama. Rather, it seems to me that, O1 tells us how the world is – namely, it contains Obama.

O2: It is metaphysically possible that Obama exists, and it is metaphysically possible that Obama does not exist.

As in the case of O1, in my view O2 does not seem to ascribe any properties to Obama. O2 does not describe Obama is. It tells us something about some ways in which it is possible for the world to be.

O3: Obama is a contingent being.

O3 means that Obama exists, and it's possible that Obama does not exist.

But O3 is also not ascribing properties to Obama, as in the cases of O1 and O2, and for the same reasons, in my assessment.

So, I would say that being contingent, or existing contingently, is not a property of Obama, and for the same reasons, it's not a property of any other being, either.

But then, it seems to me that being a contingent, concrete particular is not a property of beings, either, just as being a concrete particular that exists is not a property of beings.

But if being a contingent, concrete particular is not a property of beings, in particular it's not a B-property, then that seems to block this path to a necessary concrete being.

A variant of this path may use 'predicate' instead of 'property', but it seems plausible to me that being contingent is not a predicate, for essentially the same reasons explained above, namely that to say that some entity exists and/or possibly exists and possibly does not exist, etc., seems not to describe the entity in question. If anything, it seems to describe how the world is, or possibly would be.

11.2. A beginning of time.

In order to assess another part of this case for a necessary being, let's assume for the sake of the argument – and in this subsection only – that being a contingent, concrete particular is a property of beings, and further that it's an intrinsic property.

Under those assumptions, a question is whether CCP can begin to be exemplified. It seems to me that under that assumption, and leaving aside 'empty time' without any concrete particulars – which appears impossible to me -, the conclusion that CCP can begin to be exemplified requires the following extra hypothesis:

EH(Time): Either there is a necessary concrete being, or possibly, time has a beginning.

It's clear to me that we have no epistemic obligation in this context to accept beforehand that if it's impossible that time has a beginning, then there is a necessary concrete object.

So, it seems to me that a relevant issue here is whether we should accept that possibly, time has a beginning.

The paper suggests that we can imagine an initial singularity, particles coming into existence, etc.

However, a singularity in a mathematical model means that the equations break down, not that there is some infinitely dense object – that's not even well-defined. Even leaving that aside, it's not clear in which sense we would be able to imagine that time possibly has a beginning.

Does imagination require visualization?

If so, it seems to me we can't[2 8 ] do that.

Perhaps, someone might say we can partially visualize a beginning of time, even if not one with a singularity or particles. However, visualizing a scenario and stipulating that there is no previous time does not seem to amount to visualizing a beginning of time, and I've not been able to find any way of visualizing it.

If visualization is not required for imagination in this context, then can't we similarly imagine that there is no concrete object, entailing no necessary concrete object exists? [30 ]

Alternatively, also if visualization isn't required, can't we imagine that time begins, and at the beginning there is a single personal being C₁, creator of all of those particles, etc., and then imagine a different beginning, with a different creator C₂?

If C₁ and C₂ are both possible, then it seems to me that no concrete being is necessary.

So, let's say that visualization is required. Then, for the aforementioned reasons, it seems to me that the criterion provides no support for the view that possibly, time has a beginning.

Science does not seem to settle the matter in the actual case, either.

So, unless another argument establishes that possibly, time has a beginning, it seems to me that we are justified in remaining skeptical about that – either that, or plausibly we're justified in using the conceivability without visualization criterion to conclude that there is no necessary concrete object, but let's leave this alternative aside for now.

There are some philosophical arguments that, if successful, would establish the possibility of a temporal beginning, though they all seem to go further than that, since they aim to establish the impossibility that time has no beginning. However, in my assessment, they all fail. I addressed some of the most common arguments in support of that conclusion earlier.

11.3. The causal principle.

The principle is:

CP(R,6): Normally, if B(P), then there can be a cause of P's beginning to be exemplified.

That's one generalization from some familiar cases to arbitrary categories, among many potential generalizations.

For the reasons I gave earlier, I would suggest taking a look at a greater body of evidence instead of trying to apply some generalization as the correct one. I will take a look at such evidence in the next section, but first, I'd like to point out that if one accepted that time possibly has a beginning, and also this causal principle, one may reason as follows:

First, for the reasons given above, it seems that there is no property of being a contingent, concrete particular, blocking the use of CCP in CP(R,6).

Second, the following plausibly are properties:

a. Self-awareness – the property of being self-aware.

b. Consciousness – the property of being conscious.

c. Intelligence – the property of being intelligent.

d. The property of having subjective experience.

e. The property of having a mind.

Under the assumption that time possibly has a beginning, then it seems plausible that any of those properties can also begin to be exemplified, so unless there is a specific reason why they would be exceptions to CP(R,6), it seems the beginning of their exemplification possibly has a cause.

At this point, someone might say that none of those properties can begin to be exemplified if there is a necessary timeless, intelligent, self-aware, etc., agent. However, the claimaint should coherently explain what she means by 'timeless', and why one should suspect that there might be such being, even if 'timeless agent' is coherent. If that burden isn't met, it seems it remains plausible that those properties can begin to be identified.

Similar considerations, but applying CP(R,6) to properties like 'having a non-zero volume', 'having a spatial location', etc., would also lead to the conclusion that the exemplification of such properties also has some cause, unless a specific reason against that is given.

So, given all of the above, and under the assumption that possibly, time has a beginning plus CP(R,6), a probable conclusion would appear to be that there is no necessarily uncaused concrete being that exists necessarily. Then, a plausible conclusion would be that there probably is no necessary concrete being.

However, I think that an approach like that, in addition to the problematic assumption that time possibly has a beginning, also has the weakness of trying to apply one specific principles, like CP(R,6), instead of looking at a broader body of evidence.

So, as I said, I'd rather take a look at a broader body of evidence, which I will do in the next section.

12. A proposed assessment of the evidence.

In this section, I will present two potential hypotheses, and consider a reasonable amount of evidence for or against them, using 'evidence' in broad sense, including a priori intuitions.

On a terminological note, in this section, by 'space' I mean to include all spatial dimensions that exist. In particular, I'm not talking about our particular universe, in case there are more – a matter on which I take no stance.

That aside, the hypothesis are:

Hypothesis 0:

1. Every concrete being is metaphysically contingent.

2. Actually, every concrete being is at least a partially caused.

3. No concrete being or beings that actually exists or existed has or ever had the causal power to bring about that there are no concrete beings.

4. Concrete beings have powers (and liabilities, if we wish to distinguish them) such that, if one of those beings is destroyed, other beings are formed in its place, and there are specific beings that are formed in some specific being-destroying events.

For instance, it particle of type A collides with particle of type B and they're both destroyed, their causal powers and liabilities are such (for instance) that only particles of types C, D, or F can be formed, and at least some of them do.

5. There is no beginning of time, in the sense that:

a. If there are finite temporal intervals, then for every finite temporal interval I, there is a previous finite temporal interval J such that J does not overlap I.

b. If there are temporal instants, for every instant t, there is a previous one t'.

In particular, hypothesis 0 takes no stance on whether concrete beings are always or sometimes fully caused, on whether time is dense or discrete – or, if discrete, on whether it's rigidly discrete -, or on whether time has an intrinsic metric.

Hypothesis NB:

There is a concrete being O such that O is uncaused, and it's metaphysically necessary that O exists. O is a cause of the existence of every contingent concrete being. There are possible contingent concrete beings that only O can bring about.

Before I go on, I would like to address a number of difficulties when assessing these matters.

First, different people seem to have different intuitions, even about what is a priori plausible.

In my assessment, that may well be, perhaps to a considerable extent, because even those intuitions are the result of our experiences, what we have encountered so far, etc.

Still, regardless of the causes of the interpersonal differences in intuitions, the fact remains that different people seem to have different intuitions on a number of these matters, and while, perhaps, given sufficient empirical evidence and time for reflection, in the future people's intuitions will converge when it comes to the issue of contingency arguments, it seems to me that we're a long way from that point yet.

Second, there is an enormous amount of empirical evidence that may well be relevant. That means that even when we take into consideration an ample body of evidence, it may well be that we left relevant evidence aside. Moreover, in this essay, I will select some of the evidence that I find the most relevant, rather than going on for hundreds of pages.

Still, I do think that the approach of looking at a larger body of evidence instead of trying to apply one or another principle is generally a better approach, as we're more likely to include relevant evidence that otherwise may well be missed.

Third, and to some extent related to the first point, it's not clear whether some pieces of evidence – including different intuitions – are relevant, and if so, how much. On that note, we may cite the case of conceivability with our without visualization, etc.

For instance, if metaphysical possibility reduces to causal possibility, then it seems to me that what we intuitively find conceivable, with or without visualization, are no guides at all, though I acknowledge that's also disputable.

On the other hand, if metaphysical possibility does not reduce to causal possibility – which seems more plausible to me -, conceivability may well play a role, but it's also unclear how they should be used. In my assessment, conceivability without visualization plausibly is an acceptable guide, at least in many cases, but I recognize that many others have different views.

Fourth, of course the previous two hypotheses aren't exhaustive, and some pieces of evidence might support some other theory better.

With all that said, I will take a look at a what I think is a reasonably broad body of evidence in this context, much of which is usually used in the context of contingency arguments, and explain my assessments, acknowledging that other people make very different ones.

12.1. Uniformity and simplicity.

It seems to me that under hypothesis 0, the world is much more uniform than under NB, since hypothesis 0, every concrete being exists contingently, and is at least partially causally explained.

In particular, with regard to modality, there are no concrete beings that exist necessarily, so there is no the modal structure of the world seems is more uniform.

Also, and with regard to causation, hypothesis 0 does not entail any anomaly in the causal structure of the world: every concrete being and/or concrete state of affairs has a cause.

What about the state of affairs M consisting in all concrete objects' existing, having relations between them, instantiating properties, etc.?

Clearly, M does not have any external causes, but of course, it has plenty of causes; it's just that they're all internal ones. There seems to be no actual exception or anomaly in the causal structure of the world at play. The fact that there are no external causes of M is merely the result of the definition, but all of the causes are still there. It's just that we're defining a state that contains all of them, so we've put all of the causes together when considering them, and we've not left any causes outside. It seems to be a matter of notation, but the causal structure of the world contains no exceptions.

On the other hand, hypothesis NB does contain a concrete being O without any causes at all, or – if one prefers – a state of affairs with no causes at all – the state consisting in O's existing.

So, NB contains an actual anomaly in the causal structure of the world, whereas hypothesis 0 is uniform in that regard.

Also, on hypothesis 0, all concrete beings have limited powers and they have some liabilities, and so on. In addition, there is no special temporal point, no beginning of time.

Granted, NB makes no claim as to whether time has a beginning, and also has fewer conditions than hypothesis 0 on powers and liabilities of concrete beings in general, but on the other hand it contains a special being, and some specific claims about the powers of that special being.

All in all, in my intuitive assessment, if we can assign a prior probability to such hypotheses at all, the prior probability of hypothesis 0 is no less than the prior probability of NB.

12.2. Conceivability without visualization.

In my assessment, the conceivability criterion does not require visualization, for the reasons I gave earlier. Moreover, it seems to me that the conceivability criterion supports the conclusion that NB is false, for the following reasons:

a. We may posit a scenario S in which there are no concrete beings, and find no contradiction.

b. We may posit a scenario S' in which there are no personal beings, and find no contradiction.

c. We may posit a scenario S'' in which space does not exist, and find no contradiction, etc.

Intuitively, I would find those scenarios plausibly possible.

In particular, intuitively, it seems to me that that there are no concrete beings is possible regardless of what actually exists.

On that note, it seems to me that that's very different from cases like, say, 'water is H₂O'. In a case like that – and assuming that it's metaphysically necessary that water is H₂O -, we can tell a priori and by our intuitive grasp of the term 'water' that necessarily, water if ABC if and only if actually, water is ABC – whatever ABC is, and even if we do not know that water is H₂O. So, we know that for some XYZ, whether it's possible that water is XYZ depends on what actually obtains, but that is not my intuition when it comes to assessing hypotheses like 'there are no concrete beings', in which intuitively I would say that that no concrete being exists appears possible regardless of what beings actually exist, what properties they have, etc.

So, intuitively, I would say that the conceivability without visualization criterion supports the conclusion that NB is not true, and generally that neither is any hypothesis that posits that a concrete being exists necessarily.

At this point, a potential objection to my assessment using the conceivability criterion would be that we may also posit that a concrete being exists necessarily, and find no contradiction.

However, I think that the objection fails, just as the objection to the unicorns example fails, because plausibly either the scenarios we may justifiably take into account when applying the conceivability criterion shouldn't contain modal terms in their definition, or at least scenarios not containing modal terms take precedence over those that do.

Also, based on all of that and my intuitions about other scenarios, I will tentatively propose the following partial account of metaphysical possibility for scenarios:

A scenario S described in non-modal terms is [metaphysically] possible if an only if:

a. For every object B such that B exists in S, if B is identified by a term that, by its meaning, entails that some of the properties and/or relations of the referent must be the actual properties and/or relations, then S respects those fixed properties and/or relations.

This applies both to names of particulars, like 'Julius Cesar', or to words denoting kinds, like 'water', if any word like that fixes some of the properties and/or relations to be the actual ones. It also applies to any other word that fixes the referents in such a fashion, if there are any other such words.

b. S is not internally contradictory.

Granted, scenarios that involve modal terms in their descriptions aren't covered, and that would require considerably more work, so the above is just a sketchy partial account, which seems account for the intuitions of at least some of us.

That aside, another potential objection to the use of conceivability without visualization as a criterion against the existence of a necessary concrete being (or personal being, etc.) would be that, perhaps, there is a hidden contradiction in scenarios in which there are no concrete beings, no personal beings, etc., which would seem to imply that there is a successful ontological argument for the existence of concrete beings at least, or of at least one personal beings.

However, that potential objection appears weak to me as well, especially given that no one has been able to a find a contradiction, despite the fact that many people have tried for a long time; of course, I tried as well, to no avail.

On that note, it seems that if we can't find a contradiction for a long time, that seems to give us good reasons to think that a statement is not contradictory, unless we have good reasons to remain skeptical in a specific case. Otherwise, it's seems hard to see how we could properly assess that there probably is no contradiction in, say, Zermelo-Fraenkel set theory, number theory, finite field theory, and so on.

To put it in a different way: if we reject the objection from potential hidden contradictions in usual mathematical theories, even involving complex sets of axioms, why should we accept this objection when it comes to what seems to be a much simpler statement, which merely denies the existence of concrete beings?

Perhaps, someone has a good answer, but I've not been able to find it. All that said, I recognize that many philosophers have different intuitions, and/or may reject conceivability without visualization as a guide to metaphysical possibility for other reasons. So, I will assess other potential criteria; in particular, in the next subsection, I will consider a visualization criterion. [3 1 ]

12.3. Conceivability plus visualization.

As I mentioned earlier, I'm skeptical about the view that visualization plays a role in assessing metaphysical possibility, so if conceivability without visualization is not a good guide to metaphysical possibility, then I think it's plausible that neither is conceivability plus visualization (or just 'visualization' for short), for the reasons I gave in a previous section.

However, there are philosophers who accept the visualization criterion but not the conceivability without visualization, so in this subsection, I will analyze some cases using the visualization criterion.

So, using only visualization, it seems to me that there isn't much we could tell:

First, it seems that we can't visualize unembodied minds, or their non-existence, so the visualization criterion is silent about whether they're possible, contingent, etc.

Second, we can visualize scenarios in which space exists. Moreover, we cannot visualize any scenario in which space does not exist. So, this criterion does not support the contingency of space.

On that note, it's interesting that even if we are able to visualize a volume of space with some properties that are different from the ones we found around us, for all we know that might be a parallel universe, so that kind of visualization would not support the contingency of space, either.

Furthermore, if the visualization criterion were used also as a guide to metaphysical necessity, it would support that space necessarily exists, which would be a problem for hypothesis 0 if also space is a being.

However, it seems to me this criterion is usually used as a guide to possibility, not to necessity.

Third, we can visualize a finite volume of space without any objects that would be big enough for us to see if they were there, and which wouldn't be invisible.

However, we cannot visualize a finite volume of space in a way that rules out that there are objects that are too small for us to see, or perhaps otherwise invisible objects.

Moreover, even in the case of visible objects, a finite volume of space without those objects would not entail that the objects in question do not exist elsewhere.

Fourth, in the case of objects with parts that we can see, we can visualize them breaking into parts, so it seems visualization supports contingency in that case.

12.4. Continuity.

According to this criterion, if some scenario is possible, then analogous scenarios that are more or less extended in space and/or time without any limiting lines are possible as well. The rationale behind this is that any line would be arbitrary.

This criterion, if accepted, may be used in an argument in support of the view that any particle is contingent if it exists, as follows:

Since it's possible that a finite volume of space is devoid of objects of volume greater than, say, one cubic meter, then the same is true for any smaller volumes. Also, by extension, it's possible that all of 3-dimensional space be empty, and thus no particle is necessary.

However, it's not clear that an argument like that succeeds in ruling out necessary particles, for the following reasons:

i. If a maximal connected 3-dimensional region of space it empty, that does not seem to entail that there aren't any other 3-dimensional regions, regions, some of which are not empty. Whether an extension from a finite volume of empty space to all 3-dimensional regions of space is doable by the continuity criterion depends on how exactly the criterion is construed.

Plausibly, we may consider different versions of the continuity criterion – more precisely, different continuity criteria -, some of which would extend to all 3-dimensional regions of space, and some of which do not extend.

ii. In any case, it seems to me that zero-volume particles might escape the argument above, if such particles possible.

Still, depending on the way continuity is constructed, that might provide evidence against necessary particles, if accepted.

That aside, this criterion, if accepted of course, would also work against a number of potential agential candidates to necessary beings, as the following examples show:

1. We know that a being with a mind like that of a two-years-old human kid suffering horribly for a brief period is possible, so by the continuity criterion, it's possible that such a being suffers for eternity, ruling out a necessary 1-god, or a necessary 2-god.

While not needed to rule out a necessary 1-god, or a necessary 2-god, we may also add an arbitrarily large number of such beings suffering for eternity, or even add an infinite torturer – resulting in something like the Malo scenario -, or one infinite torturer per victim, etc.

2. We know that at least one very ugly object is possible, and then by continuity, that ugliness possibly extends across time and all across 3-dimensional space with as many ugly objects of that kind as we wish. That would be evidence against a necessary 3-god who essentially appreciates beauty and rejects ugliness.

There are potential objections, though. For instance:

2.a. A potential objection would be that that is only an extension to 3-dimensional space, but there may still be other dimensions, or spaceless objects.

However, even if there are other dimensions and/or spaceless objects, it seems plausible to me that a necessary 3-god who essentially appreciates beauty and rejects ugliness would not create a 3-dimensional space filled with ugliness all across time, given her appreciation for beauty and rejection of ugliness.

2.b. Another potential objection would be that, perhaps, the continuity criterion only shows that it's possible that there is a maximal connected 3-dimensional region of space of arbitrary large volume that is filled with ugly objects all across time, but that does not extend to an infinite volume and/or does not rule out that there are also other, parallel 3-dimensional regions with beauty in them.

However, even if any of that is true – which depends on how exactly the continuity criterion is construed -, it remains plausible to me that a 3-god who essentially appreciates beauty and rejects ugliness probably would not create such an eternally ugly region.

2.c. A third potential objection would be that, perhaps, the 3-god in question has moral reasons to behave in such a fashion, for instance if she's contingently morally good and decides to punish some other entities for eternity, placing them in an ugly Hell, and assuming that such entities appreciate beauty as well.

However, it's intuitively clear to me that a morally good 3-god would not engage in infinite punishment.

That said, the case against a necessary 3-god who essentially appreciates beauty and rejects ugliness based on the continuity criterion may be inconclusive, unlike the case against a 1-god or a 2-god. But still, if the continuity criterion is accepted, the previous construction seems to provide enough evidence to conclude that very probably, there is no necessary 3-god who essentially appreciates beauty and rejects ugliness.

3. In a similar fashion, a warranted conclusion would be that very probably, there is no necessary 3-god who essentially appreciates ugliness and rejects beauty.

4. More generally, if B is a [proposed] necessary 3-god who essentially has the priority to – eventually – bring about that R does not obtain, for some R that we can visualize for brief periods and in finite volumes, then by continuity, R possibly happen for eternity, plausibly ruling out B as a candidate to a necessary being.

If required – perhaps, for some potential 3-gods -, by continuity, R also possibly happens in arbitrarily large finite volumes of space, or even in an infinitely large 3-dimensional volume.

That would not be strong evidence against NB – since there would be plenty of other candidates left -, but at least it would rule out some of the most commonly proposed candidates, including any usual form of monotheism, and a good number of others.

In addition to all of that, this criterion or a similar reasoning, if accepted, seems to provide support for point 5. of hypothesis 0, namely that time has no beginning, since it's possible that an event happens before another event, and it seems any line would be arbitrary if any future line is, unless an argument against an infinite past succeeded. In my assessment, they do not succeed; I replied to some of those arguments earlier.

As I mentioned earlier, in my assessment the conceivability without visualization criterion plausibly works and rules out NB, or at least makes it very improbable, but assuming that that is not the case for some reason and the conceivability without visualization criterion fails despite its being so intuitive to me, I would be rather reluctant to accept any criterion based on intuitions about what's plausibly possible, rather than actual evidence of possibility. It seems to me I would have to know why conceivability without visualization fails, assuming it does, in order to properly assess the plausibility of the continuity criterion, or other such criteria.

So, in particular, I wouldn't find the arguments based on continuity given above persuasive, under the assumption that the conceivability without visualization criterion fails to show that NB is not true, or at least very probably not true. [3 2 ]

Still, it's a complex issue, and maybe others consider continuity a good guide to metaphysical possibility, even if they reject conceivability without visualization. If they're correct, then the arguments provided in this subsection would provide at least some evidence against NB – and, in particular, against theism -, and some evidence in support of hypothesis 0.

12.5. Agents and complex physical brains.

A relevant question is whether our evidence supports the conclusion that actually, agents depend on complex physical objects – which we may call 'brains', to give them a name -, and if so, to what extent.

This matter is relevant to the issue of at hand, because evidence supporting that conclusion would be evidence against a necessary uncaused agent, which would also be evidence against NB, since it would affect a number of the potential candidates to the necessary being in NB, even though not all of them.

Perhaps, someone might still suggest that maybe a necessary agent might have a complex physical brain that exists necessarily. However, even in that case, it seems to me that the agent would plausibly have causes in the particles that make up that brain – or in whatever it is that makes it up – so that would plausibly not be an uncaused agent.

In my assessment, the evidence strongly supports the conclusion that actually, agents depend on complex brains.

This is not something we could tell a priori, but an empirical finding.

For example, for all we can tell a priori, we might have found that:

1. People who die communicate telepathically with the living, telling the living that they still exist, and providing evidence by moving objects whenever they say they will, answering questions only they knew as far as we could tell, etc.

2. Some spells that allow people to apparently swap bodies – as in movies, or TV shows – seem to work fine, even after repeated testing for centuries.

3. There is no correlation between the development of the brain or of any other part of the body, and the development of the mind, and in particular no detectable change in the brains in the case of body-swapping spells.

4. Similarly, brain damage never results in character changes, memory loss, or generally loss of cognitive functions.

5. A few beings apparently can possess people or non-human animals at will, and/or appear to us in many different forms, and/or communicate telepathically even when they're not apparently in any body.

In my assessment, that would have been very strong evidence against the hypothesis that actually, agents depend on complex brains. There are other possibilities, of course. However, that is not what we found. Among other things, we found that:

6. There is a tight correlation between the development of brain and mind, in humans and other animals. In my assessment, in any agent that we can tell beyond a reasonable doubt exists, we can also tell that there is that correlation.

7. Similarly, damage to the brain results in damage to the mind, and loss of brain function results in loss of cognitive functions, and even changes in someone's personality, etc.

Also, in particular, slow but significant deterioration of the brain, by aging or illness, results in similar deterioration of the mind, with progressive loss of memories, ability to reason, etc.

Granted, many people believe that there is evidence from near death experiences and/or out of body experiences that supports the opposite conclusion. In my assessment, when carefully analyzed, there is no evidence providing non-negligible support for that conclusion.

So, I recognize that an in-depth analysis of the evidence is beyond the scope of this essay, but in my assessment, empirical evidence strongly supports the hypothesis that actually, agents depend on complex brains, and I don't think any philosophical arguments against that conclusion succeed, either, though that is also a complicated matter.

If that assessment is correct, then it seems to me that that is strong evidence against any uncaused necessary agent.

12.6. Particles and contingency.

In addition to different conceivability criteria, we may assess whether empirical evidence supports the hypothesis that particles are contingent.

On one hand, it seems that we keep finding particles, and they are contingent.

But on the other hand, someone might wonder whether the evidence might have gone in a different direction, supporting the hypothesis that they're necessary.

While I do not know what evidence might have made a hypothesis that some particles are necessary probable, I can think of some scenarios that would seem to at least be more favorable to that hypothesis than what we found.

For example, let's say that we had found the following – which we couldn't rule out a priori:

1. We are unable to destroy atoms, no matter what we do.

2. Theories that posit that atoms existed forever and will exist forever, and posit nothing that can destroy them, always make correct predictions. On the other hand, any similarly simple theory that posits otherwise makes many incorrect predictions, to the best of our knowledge.

Would that have been evidence in favor of the hypothesis that some particles are metaphysically necessary?

Personally, I wouldn't say that it would be strong evidence, but it seems to me it would have been at least some evidence, though of course not much if we can rule out necessary particles on a priori grounds beyond a reasonable doubt.

12.7. Causality.

In support of point 2. of hypotheses 0, I would say that we keep finding causes of at least nearly every being that we find.

A potential objection to this would be space (or spacetime), if space (or spacetime) is a being.

Still, if, say, space is a being, it may be that a cause, and even a full cause of space's existing at t is that it existed at some time u < t, and so on. I will address the matter of regress below.

12.8. Causal limitations and liabilities.

It seems that beings we encountered so far can be classified at least in nearly all cases into types of beings with some limited powers and liabilities. In particular, when a being of a certain type is destroyed in a certain way, some specific beings are formed, etc.

As before, this is not something we could tell a priori.

For instance, for all we could tell a priori, we might have found that some particles annihilate each other without any detectable trace, and that the theories that posit no trace at all correctly predict observations, whereas similarly simple theories that posited otherwise do not.

So, there seems to be at least some empirical support for point 4. of hypothesis 0.

12.9. Explanatory intuitions.

The matter of explanations is one in which, in my experience, intuitions vary widely.

Still, I will explain my assessment in this subsection, comparing hypothesis 0 vs. NB, when it comes to the explanation of the proposition P, which states that there are concrete beings.

12.9.1. Explanatory intuitions without necessary beings.

If hypothesis 0 is correct, then the following obtains:

First, P is causally necessary, in the sense that there actually isn't, and never was a being with the power to bring about ¬P.

Second, if metaphysical necessity reduces to causal necessity – which I doubt -, then P is also metaphysically necessary. If not, then P may or may not be metaphysically contingent.

Third, if P is metaphysically contingent, then if we accept possible worlds, there is a possible world at which P does not obtain, but that world is not causally accessible from the actual world.

Fourth, regardless of whether P is metaphysically contingent or necessary, it seems to me that there is a causal explanation of P in terms of the P_t, for all times t, where P_t states that at t, P obtains.

On this account, the explanation of any P_tis that for some t'<t, P_t
'is true, and given the causal powers and liabilities of the beings at t', that entails that P_t obtains.

Someone might object to that kind of explanatory regress as an explanation of P, but intuitively, I do not see the difficulty. At least, I would say any intuitions about familiar scenarios – which are scenarios that don't extend infinitely into the past – actually having explanations and/or causes would be satisfied, and the account by infinite regress given above seems to be good enough to me, when it comes to P.

In particular, intuitively, I would say that hypothesis 0 does far better than hypothesis NB in that regard, though I recognize other people have very different intuitions.

But let's take a closer look at NB and its purported explanatory power:

12.9.2. Explanatory intuitions and necessary beings.

For the reasons given earlier, in my assessment, hypothesis 0 provides a causal explanation of the existence of concrete objects that is good enough, and has no causal or modal anomalies, whereas NB contains both kinds of anomalies.

In this subsection, I will address the issue of the explanatory power of hypothesis NB – or other, similar hypotheses that posit necessary concreta.

On that note, if someone claims that some being must exist, I find myself wondering 'Why must it exist?', and if the reply is that it must exist because of the necessity of its own nature or something along those lines, I find the answer puzzling.

But to illustrate my take on these matters more clearly, I'll introduce a principle used by William Lane Craig in his defense of an argument from contingency:

EP(1): Anything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. [33 ]

I find that puzzling, for the following reasons:

First, even assuming essentialism, it seems to me that the nature of a being would consist in some properties, but that seems to have nothing to do with whether the being in question exists, since existence is not a property – which is also why I consider purported properties defined in terms that entail necessary existence problematic as well.

Second, leaving that aside, if necessity were a property of beings, I would still wonder: why is the nature of that being such that it necessarily exists?

So, the assumption that necessity is or may be a property won't help in my case. I would still find myself asking the question as to why that being must exist, whereas I find the explanation I mentioned above under hypothesis 0 intuitively good enough.

Moreover, intuitively I find the claim that some concrete being must exist to be in much greater need of an explanation than the claim that such concrete being does exist.

So, even a hypothesis that posits a contingent entity as a first cause would be, in my assessment, and while explanatorily worse than something like hypothesis 0 all other thing equal, still better than a hypothesis that posits a necessary one and leaves the fact that the entity in question necessarily exists or must exist without an explanation.

That said, someone might raise the following issue:

But what about numbers, propositions, or the laws of logic? Isn't an adequate explanation of their existence the necessity of their own nature?

I do not see how those would be beings, but in any case, let's consider for instance a paradigmatic case like the case of the Law of Excluded Middle (LEM), in order to assess the matter.

It seems to me that we can tell, just by the meaning of the words, that for any proposition Q, the proposition (Q v ¬Q) is true, regardless of what Q is.

Yet, that seems to be true independently of any ontological claims, and I don't know why I should accept an ontological claim that the LEM exists.

In fact, a claim like that is even hard for me to grasp. Similar points can be made for, say, claims about propositions, or numbers.

Granted, we're usually warranted in saying that, for instance, there are infinitely many prime numbers. But that does not look to me like an ontological claim. Rather, my impression is that what we're saying is that there are infinitely many prime numbers in the set of natural numbers. But of course there aren't infinitely many prime numbers in, say, the set {1, 3, 5}. When we say that there are infinitely many primes, it seems to me that we (usually) implicitly pick the natural numbers as our domain of discourse, but that's all. As far as I can tell, we're not asserting that some objects exist, other than in the sense that they exist in the set of natural numbers, but without making ontological claims.

Similarly, there are necessarily true propositions (for instance) in the category of all propositions.

However, the question of whether such sets or categories exist, as an ontological claim, appears equally puzzling to me. It strikes me as conflating the territory (in non-philosophical but hopefully clear enough terms, what's 'out there', including minds with some thoughts, etc.) with abstractions based on the territory, our intuitions, experiences, etc. [3 4 ]

That aside, I recognize many other people, theists and non-theists alike, have a very different view on these matters, and it's a complicated matter. But still, even assuming that the LEM, numbers, etc., are beings and necessarily exist, a claim that the explanation as to why those beings exist, or why they must exist, is 'the necessity of their own nature' would remain just as puzzling to me.

Similarly, a claim that they exist because they must exist would make me wonder: 'But why must they exist?' Intuitively, I would still keep looking for an explanation.

So, given all of the above, I find hypothesis 0 to be much more satisfying, in terms of explanations, than hypothesis NB.

As I mentioned, I recognize that other people have very different intuitions on the matter.

12.10. Foundations and intuitions.

Some philosophers may also have an intuition that contingent beings cannot exist without a metaphysically necessary concrete being, and some might offer as an analogy – for example -, a house, which needs a foundation to stand.

However, I do not have that intuition, nor do I find that example, or other potential examples, analogous at all.

For instance, a house needs a foundation because of how some concrete beings interact, given their causal powers, etc. On the other hand, a spaceship built in orbit and not designed to land wouldn't need such a foundation. But in any case, I do not find that example or any other similar examples related to the issue of a whether there is a concrete being that exists necessarily.

On hypothesis 0, concrete beings are all contingent, but none has the causal power to destroy them all. I do not see any intuitive difficulty here.

12.11. Overall assessment.

Given all of the previous subsections, in my assessment, hypotheses 0 is considerably more probable than hypothesis NB, even if I leave aside the conceivability without visualization criterion. But I recognize that the matter is complex, and other people have different intuitions.

In the rest of this essay, and unless otherwise specified, I will assume for the sake of the argument that there is indeed a necessary concrete being, and assess theistic arguments in favor of the claims that such being is an agent, has infinite or maximal power, moral goodness, knowledge, etc.

13. Candidates to necessary concrete beings. General considerations.

In the previous sections, I've focused for the most part on arguments that intend to establish that a necessary concrete being exists, and raised a number of objections.

From now on, and unless otherwise specified, I will assume for the sake of the argument that there is a necessary concrete being, and raise objections to arguments in support of the claim that that being is God, under some common definition of the term 'God'. In particular, I will assume that the criterion of conceivability without visualization fails, and that the partial account of metaphysical possibility suggested above is mistaken.

Part of my strategy[35] involves presenting different non-theistic hypotheses, including some candidates to necessary beings, and then assessing theistic objections and arguments, actual or potential, also comparing non-theistic potential replies with theistic ones.

So, let's introduce the hypotheses in question:

Hypothesis 1:

Space, including all spatial dimensions (as many as they turn out to be), is a necessary being, and necessarily, space has some necessary causal properties that we may call 'laws of nature', and we may approximate by some mathematical models.

Particles aren't necessary.

I will call the necessary space, with its necessary properties '1-megaverse'.

Hypothesis 1 takes no stance on whether there are parallel universes in the 1-megaverse, how many dimensions there are, whether space is infinite, and similar issues. It also takes no stance on whether the 1-megaverse is deterministic, causally or otherwise.

Hypothesis 2:

Spacetime, including all spatial dimensions (as many as they turn out to be), is a necessary being, and necessarily, space has some necessary causal properties that we may call 'laws of nature', and we may approximate by some mathematical models.

Individual particles aren't necessary, but causal powers of spacetime are such that if particles are destroyed, then others are formed instead (photons count as particles here). Also, the laws are such that necessarily, there are some particles.

I will call the necessary spacetime, with its necessary properties '2-megaverse'.

Hypothesis 2 takes no stance on whether there are parallel universes in the 2-megaverse, how many dimensions there are, whether spacetime is infinite, and similar issues. It also takes no stance on whether the 2-megaverse is deterministic, causally or otherwise.

Hypothesis 3:

Some basic particles that we've not found yet are necessary beings, and either space or spacetime is a necessary being too.

I will call space (or spacetime), plus the necessary particles, '3-megaverse', though I make no claims that they would be some sort of mereological sum: I'm merely considering them together for the purposes of evaluating the hypothesis.

Hypothesis 3 takes no stance on whether there are parallel universes in the 3-megaverse, how many dimensions there are, and similar issues. It also takes no stance on whether the 3-megaverse is deterministic, causally or otherwise.

To be clear, I'm not suggesting that a non-theist who believes that there is a necessary concrete being ought to believe that one of the hypotheses above or a similar one is correct. There are more options, including agnosticism about what kind of concrete being or beings are necessary. I'm just introducing these candidates as potential examples.

14. Some theistic objections, and rebuttals.

In this section, I will assess several potential theistic objections to some of all of the previous hypotheses.

In particular, I will in a number of cases construct non-theistic replies that mirror a potential theistic argument, but have a non-theistic conclusion. In this context, I do not mean to claim that the non-theistic conclusion obtains, but only to show some of the problems of some potential theistic arguments, which are illustrated by non-theistic parallels.

14.1. Objection 1.

For any particle P, it is conceivable that P does not exist, or ceases to exist, so all particles plausibly are contingent. So, hypothesis 3 is plausibly false.

Reply:

If visualization is required for conceivability – but why?-, then there are subatomic particles we can't [2 9 ]visualize, except in the sense that we can of course visualize something and stipulate that that something represents the particle, but for that matter we can make such a representation of anything disappear.

It's true that we can already check that many particles are contingent, but hypothesis 3 posits that some particles we haven't discovered yet.

On the other hand, if conceivability does not require visualization and it's enough to stipulate that a given particle does not exist or ceases to exist and find no contradiction, then it seems we can similarly conceive of the non-existence of any given personal being by stipulating that she does not exist and finding no contradiction.

Rejoinder:

a. We can visualize empty space, which also gives us grounds to think that no particle is necessary.

b. Based on our experience with particles so far, we can tell that probably, all particles are contingent.

Reply:

a. We can't visualize any spatial volume in a way that would rule out that it contains particles that are too small for us to visualize, of course.

Moreover, even if we managed to visualize a finite volume of empty space, the necessary particles might be elsewhere, for all we know.

b. Based on our experience with intelligent beings, personal beings, self-aware beings, beings with complex minds, etc., we can tell that probably, they're all contingent.

Rejoinder.

a. We can visualize a finite volume of space that is devoid of any objects of a size that we could visualize. Then, by a continuity criterion, since any lines would be arbitrary, we should conclude that it's possible that all of 3-dimensional space be empty of any object of a positive, finite size.
Hence, both hypothesis 2 and hypothesis 3 are false.

Reply:

As I argued earlier, it's not entirely clear to me that that argument against necessary particles succeeds.

However, even granting that such a criterion works against necessary particles and rules out both hypothesis 2 and hypothesis 3, it seems that that criterion rules out theism as well.

14.2. Objection 2.

If particles are contingent, plausible it's possible that they all cease to exist. So, hypothesis 2 is plausibly false.

Reply:

That would simply deny hypothesis 2.

While I find a concrete being that exists necessarily intuitively implausible, assuming that such a being exists, I do not see any further counterintuitiveness in a theory that holds that necessarily, that being brings about some contingent particles.

14.3. Objection 3.

Theistic hypotheses are simpler, and probabilistic considerations favor them over non-theistic ones, both in terms of prior probability and more importantly posterior probability.

Reply:

While I disagree with that assessment, a discussion of such probabilistic arguments would be beyond the scope of this essay.

14.4. Objection 4.

It's conceivable that the universe may have different laws, so it would be a different universe. Hence, plausibly, hypotheses 1, 2 and 3 are false, since space, or spacetime, aren't necessary.

Reply:

Actually, hypotheses 1, 2 and 3 are all compatible with the existence, in addition to our universe, of parallel universes which behave in a different manner from the way our universe behaves.

They would all exist in the megaverse.

For instance, some multiverse models in actual scientific cosmology posit parallel universes with some local laws different from those of our universe, while more general laws hold in all of the multiverse. Something similar might happen under hypotheses 1, 2 or 3.

Also, none of the hypotheses in question requires that our universe necessarily is brought about, either. The megaversal laws do not need to be causally deterministic.

14.5. Objection 5.

If space plus some laws is conceivable, then space – all of it – with different laws is also conceivable, and so hypotheses 1, 2 and 3 are plausibly all false, because a different megaverse is conceivable.

Reply:

If conceivability requires visualization, even if only partial, plausibly we can't conceive of a scenario incompatible with hypotheses 1, 2 or 3, since any partially visualized scenario might happen in a universe parallel to our own, but still in the megaverse of one of those hypothesis.

If conceivability does not require visualization, then, for any personal entity, we may stipulate that she does not exist, and find no contradiction. Alternatively, we may posit that the most powerful agent is not morally good and find no contradiction, and so on.

Rejoinder:

Since it's possible that a finite volume of space is devoid of objects of volume greater than, say, one cubic meter, then the same is true for any smaller volumes, by a continuity criterion. Also, by continuity, it's possible that all of 3-dimensional space be empty, ruling out hypotheses 2 and 3.

Similarly, it's possible that all of 3-dimensional space is filled with a copy of some object, say a ball. But that would seem incompatible with hypothesis 1 and 2, which hold that space has some necessary laws, since it seems it's possible that 3-dimensional space be filled with pretty much anything.

Reply:

First, even if a maximal connected region of 3-dimensional space is possibly filled with pretty much anything, or empty, whether a continuity criterion entails that all of 3-dimensional space is possibly like that depends on how continuity is constructed.

Second, in any event, even if this argument based on the continuity criterion actually rules out hypotheses 1, 2, and 3, an argument based on that criterion also rules out theism.

14.6. Objection 6.

All the parts of necessary beings are necessary. But hypotheses 1 and 2 would entail necessary beings (namely, the 1-megaverse and 2-megaverse) with contingent parts (i.e., the particles), so they're false.

Reply:

Assuming something like Koons' axiom 4, then it's true that a necessary being could only have necessary parts.

That axiom seems pretty dubious to me, as I've argued earlier, but in any case, that is not a problem for hypotheses 1 or 2: assuming that axiom, it simply wouldn't be the case that particles are parts of the 1-megaverse or 2-megaverse. That does not seem to be particularly odd, since we may plausibly understand the particles as contained in space or spacetime, rather than being parts of it.

14.7. Objection 7.

We can asses by empirical evidence (daily experiences, science, etc.) that probably, any partially or wholly physical beings are contingent. Since space, a universe, multiverse, etc., are at least partially physical, that gives us good reasons to think that any of those beings is probably contingent.

Reply:

Similarly, we may say that we can assess by empirical evidence (daily experiences, science, etc.) that probably, any concrete being is physical, or at least partially physical. Hence, since a necessary concrete being (which here we grant exists) is a concrete being, we have good reasons to think that any such being is probably physical, or at least partially physical.

Rejoinder:

Actually, personal beings and other beings with minds aren't even partially physical. Our bodies aren't parts of us, and we're wholly non-physical.

Reply:

First, that would have to be argued for, and the burden would be on the claimant.

Second, if that were the case, then we would be able to tell by our daily experiences that very probably, any wholly non-physical being is contingent. In fact, it seems to me we would be able to tell that, for every wholly non-physical being we can tell for sure exists, we've been able to establish, beyond a reasonable doubt, that the being in question is contingent, whereas we've not been able to establish the same result to the same degree of confidence in the case of space.

Third, non-physical or physical, we can tell by empirical evidence that probably, every agent depends on complex brains, as mentioned earlier. On the other hand, we do not have any similar evidence supporting the view that every physical thing depends on an agent.

14.8. Objection 8.

Explanations of contingent facts, states, situations, etc., are either scientific, or in terms of the actions of an agent. However, to the best of our knowledge, science only posits contingent causes, so hypotheses 1, 2 and 3 are probably false, and the necessary being that causally explains contingent ones is plausibly an agent.

Reply:

Even if we accept classifying explanations in agential and non-agential, calling the latter 'scientific' is a misnomer at best, and potentially confusing.

For instance, let's suppose scientists find a number of mammoth fossils together and in certain positions, and explain the finding by positing that a mammoth got stuck in tar, others tried to help her out, and they all got stuck and died. That's a perfectly good scientific explanation in the ordinary sense of the expression 'scientific explanation', though apparently, it would not count as 'scientific' under the proposed terminology. This matter is not crucial to the objection, but the potential for confusion is a problem for that proposed terminology.

That aside, and more importantly in this context, science does not take a stance about whether the beings it posits are contingent. In particular, for example science does not hold that space (as many dimensions as actually exist) is contingent.

14.9. Objection 9.

We can tell by empirical evidence (daily experiences, science, etc.) that probably, essentially temporal beings are contingent. Since space, a universe, multiverse, etc., are essentially temporal, that gives us good reasons to think that any such being probably is contingent, and a necessary concrete being is timeless.

Reply:

The word 'timeless' is not a colloquial term, except perhaps in the sense that, say, a painting is timeless, which is not relevant in this context.

So, it seems to me that it's a technical term, and I think it's fair to ask: what does 'timeless' mean?

An answer stating that X is timeless (by definition) if and only if X does not stand in temporal relations – or something along those lines – would not seem to give us any way of grasping the meaning of 'timeless'.

Perhaps, someone might point to propositions, numbers, laws of logic, etc., say that those are timeless beings, and suggest that we should grasp the meaning of the word 'timeless' intuitively, guided by those examples.

However – and leaving aside the issue of whether abstracta are beings -, if she later suggested that, say, a timeless 1-god exists, that would look to me like pointing at cars, motorcycles, trains, planes, bicycles, etc., and say 'those are bluts', and then suggest that the number 5 or the rules of chess may be bluts. Personally, I would still be puzzled, wondering what 'blut' (or 'timeless') might mean.

Still, I recognize that there is a lot more to be said about timelessness, so let's assume that the concept of a timeless agent is coherent, for the sake of the argument. The fact that I've not been able to grasp what 'timeless' means complicates the matters to some extent, but going by usual claims about what beings are temporal as a guide, a reply mirroring objection 9 would be as follows:

We can tell by empirical evidence (daily experiences, science, etc.) that probably, concrete beings are essentially temporal. Hence, since a necessary concrete being (which we here assume exists) is a concrete being, it's probably essentially temporal.

14.10. Objection 10.

Let's introduce a definition:

A being X is essentially spatial if and only if it is essential to X to have at least one spatial property, like spatial location, or non-zero volume. For instance, the Sun is essentially spatial, because it is essential to to the Sun to have a spatial location. The Sun's coordinates in space are contingent properties, but the property of having a spatial location is essential (i.e., the location isn't fixed, and needn't be for the purposes of the definition).

Now, we can tell by empirical evidence (daily experiences, science, etc.) that probably, essentially spatial beings are contingent. That gives us good reasons to think that space, spacetime, etc., are contingent.

Reply:

We may mirror that objection by saying that we can tell by empirical evidence (daily experiences, science, etc.) that probably, concrete beings are essentially spatial. Hence, since a necessary concrete being (which we here assume exists) is a concrete being, we have good reasons to think it is essentially spatial.

14.11. Objection 11.

If we accept Koons' axioms, or similar ones, we can tell that the cosmos, universe, etc., are contingent, so hypothesis 1, 2 and 3 are false.

Reply:

As argued above, it seems to me that skepticism about some of those axioms is at least warranted.

Leaving that aside, and granting Koons' axioms for the sake of the argument, at most we could tell that the cosmos, the universe, etc., are contingent in the sense in which Koons uses the terms 'cosmos', 'universe', etc.

On the other hand, those axioms appear compatible with any of the hypotheses 1, 2, and 3, and hence with the necessity of the 1-megaverse, 2-megaverse or 3-megaverse.

14.12. Objection 12.

Non-theistic hypotheses about a necessary universe, megaverse, etc., imply or at least suggest a multiverse where everything that can physically happen, does happen. That would make our intuitions about the future so unreliable that we wouldn't even be able to tell that the future will resemble the past at all.

Reply:

Actually, hypotheses 1, 2, and 3 suggest no such thing, and they're non-theistic. They don't even have a commitment to parallel universes, though they have no commitments against them, either.

Moreover, a claim that in a multiverse like that our intuitions about the future would be unreliable appears unwarranted as well. Their reliability would depend on issues like how some deterministic or probabilistic laws are, etc.

14.13. Objection 13.

The constants of the universe are finely tuned for intelligent life. Regardless of whether there are more dimensions, etc. Hypotheses 1, 2, and 3 can't explain that.

Reply:

While arguments to design are beyond the scope of this essay, assuming that there is such thing as fine-tuning[36], I will make the following point:

If any hypotheses like 1, 2, and 3 is true, then there is a necessary being with certain causal powers and dispositions, which already has the finely-tuned constants, since we live in it.

On the other hand, a theistic hypothesis posits an extra being with certain specific psychological makeup, which includes a propensity to create intelligent life. If the propensity is not included explicitly, it's allegedly entailed by some other properties.

At any rate, the matter would have to be addressed in terms of probabilistic arguments, considering many factors.

14.14. Objection 14.

Non-theistic hypotheses about a necessary megaverse, etc., are epistemically disastrous, regardless of whether they hold that everything that can physically happen, happen.

Without an agential creator, we wouldn't even know whether the laws of nature are such that everything will change tomorrow and everything we think we know will turn out to be mistaken; further, if the universe changes radically, we will all die, or perhaps suffer greatly.

Reply:

With that criterion, we may as well say that if there is an intelligent necessary agent of great power, she might make everything change tomorrow, etc.
Rejoinder:

We can plausibly infer some of the psychological properties of a necessary agent from what we know about minds. She would plausibly want an ordered universe.

Reply:

We can plausibly infer some of the properties of space, time, etc., from what we observe, and things do not change overnight radically. In fact, science has being doing that for quite some time already, and even before modern science, we could already tell some (many) of the properties. There is no chaos.

Rejoinder:

All that order in space, time, etc., is only the way things have been up till now. If the necessary cause is not an agent, we have no good reason to think that that won't radically change tomorrow, resulting in chaos.

Reply:

With that criterion, someone might similarly say that what we know about minds is only the way things have been up till know, and that we have no good reason to think that minds won't radically change tomorrow, wanting chaos.

In reality of course I do believe we have good reasons to expect that minds won't radically change like that, but the point here is that the same seems to apply to non-agential objects.

15. Basic attributes of a necessary cause.

After deriving the existence of a necessary cause from the premises of his cosmological argument, Koons concludes that there is at least one necessary being, and makes some arguments regarding the fundamental properties of that being. I will grant for the sake of the argument that a necessary state of affairs includes a necessary being, and assess some of Koons' arguments.

15.1. Notation.

Koons calls the necessary being 'God', and the fundamental properties "basic attributes" or "attributes".

I will call the properties in question 'basic attributes', but I will not call that being, or beings, 'God', since the term might make the matter less clear.

15.2. More alternative hypotheses.

In order to assess some of Koons' arguments, I will introduce some new non-theistic hypotheses about a necessary being, which are more specific sub-hypotheses of hypothesis 1 and hypothesis 3.

Hypothesis 1.1: Hypothesis 1 is true. Space has infinite volume essentially, as a basic attribute. Also, space is a unity, and has no parts.

Hypothesis 3.1: Hypothesis 3 is true. Space has infinite volume essentially, as a basic attribute. Also, space is a unity, and has no parts. For each of the necessary particles P, it's necessary that P has some spatial location, but which exact location P has, is a contingent property, and P's being in a specific location has at least one cause in the necessary causal powers of space.

Hypothesis 1.2: Hypothesis 1 is true. Space and time are rigidly discrete. There is a basic unit of time, and a basic unit of volume.

Before considering Koons' arguments, I will address a potential objection to two of the previous hypotheses:

Objection:

Anything that has a size, has a part of finite size. If space is infinite, it has a part of finite volume.

Reply:

The claim that anything that has a size, has a part of finite size does not appear warranted, and the burden seems to be on the claimant.

Rejoinder:

When we look at space, study it, etc., we often consider finite volumes only. That suggests that those are parts of space.

Reply:

That's a matter of convenience, not a matter of ontology.

For that matter, if Yahweh existed, Christian philosophers would often be focusing on a limited amount of his knowledge. All of that is to be expected, given our cognitive limitations, but it does not have ontological implications.

15.3. Aggregates and necessity.

Koons argues that the necessary cause cannot be what he calls a "mere aggregate", allegedly because if it were an aggregate, it would have contingent parts.

That does not seem intuitively plausible to me.

For instance, if there is a necessary agent, for all we know, there may be many necessary agents. [37 ] Together, those many beings would not seem to make up a unity, but an aggregate if we accept that there are arbitrary mereological sums, as Koons seems to.

I suppose that someone might suggest that if they all exist necessarily, they do not qualify as an aggregate, but I don't see why not.

In any case, aggregate or not, it seems to me that, for all we know, even accepting Koons' axioms, there might be many beings with different agendas, if they're agents at all, or a combination of agents and non-agential necessary beings, etc.

15.4. Basic attributes, necessity and measurability.

A key claim in Koons' paper seems to be that any measurable property takes part of the structure of a continuous spectrum, and – according to Koons -, it's reasonable to make an assumption that we may state as follows:

MA(K,1): For every property P and for every being B, if P is the property of having some determinable D to degree x and B has property P, then there is some y such that B possibly has D to degree x+y, or x-y.

From that, it follows that no attribute or property that is measurable in Koons' terminology, can be had essentially or necessarily.

On the other hand, Koons accepts that it's possible to have properties that involve whole integers essentially.

In the following subsections, I will take a closer look at MA(K,1) and some of its consequences.

15.4.1. Measurability and abstracta.

For every real number x, there is a subset of the set of real numbers S(x) such that S(x) has Lebesgue measure x, and it seems that that would be an essential property of the being S(x), if S(x) were a being. Hence, it seems to me that if MA(K,1) is true, then a correct ontology does not include such usual mathematical objects.

I suppose someone may include those objects in an ontology and then restrict MA(K,1) to concreta, but it's unclear to me why there would be a difference between concrete and abstract objects in this regard, if abstracta were beings.

Since I wouldn't include abstracta in an ontology, that is not a problem for MA(K,1) in my view, but the matter may be relevant for those who do include abstracta.

15.4.2. Intuitions and measurability.

Leaving abstracta aside, a question if whether MA(K,1) is intuitively plausible.

Indeed, it seems Koons' argumentation in support of MA(K,1) relies entirely upon the alleged a priori intuitive plausibility of the principle that somehow continuous spectra are such that if an entity has some determinable D to degree x, it possibly has D to degree x+y, or x-y.

Personally, I would say that if I drop the assumption of essentialism, MA(K,1) appears intuitively plausible. [38] However, under the assumption of essentialism, it's not at all clear to me that MA(K,1) is true, or even plausibly true.

Actually, I have to admit that I don't have any intuitions one way or another about whether some being B possibly has some property P to degree x essentially.

I would say that least on intuitive grounds (i.e., if we have nothing else), it seems reasonable to remain undecided on the matter, neither asserting nor denying MA(K,1).

In addition to that, if we're assessing the matter intuitively, it seems to me that the intuitions that allegedly would support MA(K,1) are some sort of conceivability without visualization intuitions which plausibly also support that there is no necessary concrete being. And even assuming that there is a necessary concrete being, those intuitions seem to support the possibility of the Malo scenario, BIS scenario, etc.

15.4.3. Daily experiences, science, and measurability. Mental properties.

In addition to the aforementioned intuitions, we may assess whether MA(K,1) is supported by other pieces of evidence, such as what we observe in daily life, in science, etc. [39].

On that note, it seems that ordinary objects do seem to have properties to different degrees contingently, but on the other hand, they do not seem to have properties to an infinite degree, when it makes sense to have them to an infinite degree.

So, while an object that has a property to some determinable degree x essentially would be different from what we observe in daily life, the same would be true of an object that had a property to some infinite degree, when such an infinite degree makes sense.

Ordinary objects aside, we may also take a look at science: do things discovered by science support MA(K,1), or its negation?

Many things discovered by science seem to be in line with MA(K,1).

However, in a good number of cases in modern physics, it seems to me that the answer is that the objects in question plausibly do not respect MA(K,1) - i.e., MA(K,1) is probably false -, at least if certain properties are part of the continuous spectrum.

For instance, the electric charge of an electron seems not to change at all, and given essentialism[3 8 ], it seems plausible that it has that property essentially. To be clear, here I'm assessing evidence from science (I assessed a priori intuitions earlier), and the empirical evidence seems to support the hypothesis that having a certain charge probably is essential to the electron, as we've not found any exceptions yet, and the scientific theories positing that such charge does not change seem to make correct predictions of observations. [40 ]

On the other hand, if those properties aren't part of a continuous spectrum, but there is a basic unit (e.g., of electric charge), and the properties in question can only be had in whole multiples of that basic unit, that would not be a difficulty for MA(K,1), but that would bring up another difficulty for the theistic case, which I will address in the next subsection.

So, based on our present-day evidence and knowledge, it seems to me that skepticism about MA(K,1) remains warranted.

Leaving those properties aside for now, another body of evidence that may be relevant to the issue of what properties a necessary concrete being might have, is the evidence involving some mental properties.

On that note, in our daily experience, mental properties that can be had to different degrees, like intelligence, knowledge, moral goodness, or preferences for certain objects, etc., [41]seem to be contingent properties, but also are not had to an infinite degree, assuming it makes sense to say that an entity has one of such properties to an infinite degree.

For instance, if Bob – a human being – is morally good, it seems that it's a contingent matter how morally good he is, and he's not infinitely morally good, even assuming it makes sense to say that someone is infinitely morally good. If to say that someone is infinitely morally good means (say) that he or she never does anything immoral, and always tries to do something morally praiseworthy, then that is also not what we find. The same goes for other mental properties, and for other animals with minds.

So, the evidence that we have so far would seem to suggest that any entity with mental properties is likely to have the kind of property considered above to finite degrees – regardless of whether we can assign a number to it -, and contingently, if it has such a property at all.

If so, it seems to me that even if there is an agential necessary being, it's more likely that she too has those properties contingently if she has them.

To be clear, I'm not saying that the evidence is so strong that we're not warranted in remaining also skeptical about the conclusion that she would instantiate the properties in question contingently, but merely that that fits the evidence from other agents better than an alternative.

15.4.4. Discrete time, space, charge, etc.

As I argued in a previous subsection, if properties such as charge, magnetic momentum, etc., can only be had in whole numbers of minimum units, then some evidence from modern physics is not a problem for MA(K,1).

Here, I'd like to mention the epistemic possibility that that is in fact the case, and that also space and time are discrete, and there is a minimum unit of time and of volume.

If that is the case, then using numbers other than whole integers to describe volumes, durations, charge, etc., is an imprecision, or a matter of convenience, or both, but it has no ontological relevance. Ontologically speaking, if those properties are only had in whole numbers of basic units, they all avoid MA(K,1), even if MA(K,1) is true, given that Koons makes an exception to such properties, which would count as immeasurable.

15.4.5. Probabilistic assessments.

Perhaps, someone might suggest that even without assuming that MA(K,1) is true, if B is a being and P is a property that can be had to degree x, for any real number x, or to an infinite degree, it would be more probable than B has P essentially to an infinite degree.

Let's consider two different hypothesis:

a. B essentially has property P to an infinite degree.

b. There is some real number x, such that B has property x to degree x.

In my assessment, there is no way of telling a priori, for all B and P, whether a. is more or less probable than b.

It seems to me that that depends on other properties of B, what P is, etc., and sometimes – or many times – we may not even have a way of making an a priori probabilistic assessment.

15.5. Spatial and temporal location.

Koons' argues that the first cause cannot be essentially located in time or space, not even in the whole of space or time, because allegedly in that case, the first cause would have parts that have measurable attributes.

Yet, the conclusion appears unwarranted even granting MA(K,1) for the sake of the argument, for the following reasons:

First, according to hypothesis 1.1, space is a unity and has no parts, so space would not have any parts of finite size. Similar considerations apply in the case of time; for instance, perhaps hypothesis 2 is true, and spacetime is a unity.

The same is true of hypothesis 3.1.

Second, in the case of hypothesis 3.1, each necessary particle P would be essentially located in space and time (or spacetime, etc.) in the sense that, necessarily, P would have some spatiotemporal location.

However, P would not have any specific location in space or time essentially. So, since the specific location would be a contingent property, there would seem to be no violation of MA(K,1).

On the other hand, if MA(K,1) is construed as entailing that being essentially located in space and time but not in a specific place is also impossible, then I would say that MA(K,1) is almost certainly false, considering usual examples. For instance, it seems clear to me that, say, a mosquito, a virus or planet Earth is essentially located in space and time, even though not in any specific location, assuming essentialism.

Third, if there are are basic, minimum units of space and of time, then it seems space and time avoid MA(K,1) altogether – it's a 'whole integers' case -, even if MA(K,1) is true.

Thus, it appears that Koons is implying that space and time are not necessarily rigidly discrete.

In my assessment, taking no stance on the matter seems epistemically acceptable given our present degree of knowledge – for some of us, at least.

15.6. Personhood and degrees.

This subsection is a bit of a side note, but I'd like to address an issue related to personhood.

In his paper, Koons claims that while MA(K,1) is true, properties involving finite whole integers count as immeasurable and can be had essentially. As an example, he mentions the property of "existing as three persons".

Existence isn't a property in my assessment, and in any case, a being that is three persons doesn't make sense to me. But that's not the matter I'd like to tackle here. The matter I'd like to address is whether personhood is a degreed property. Koons seems to assume that it isn't.

That may be a usual view, but is a view that I would like to challenge in this subsection.

To do that, I will present both a developmental and an evolutionary argument. Also, I will drop the assumption of essentialism for the rest of this subsection. [42]

15.6.1. Development.

Let's consider first Komodo dragonhood – i.e., the property of being a Komodo dragon -, and the following scenario:

A female Komodo dragon is in a zoo.

There are no males and no artificial fertilization, so she reproduces by means of parthenogenesis. She produces some ova. Each of those individual cells[43] is not a Komodo dragon. However, one of those ova undergoes a process that eventually results in an adult male Komodo dragon.

Assuming that Komodo dragonhood is not measurable, it seems to me that if time is continuous, there are two temporal intervals (t₁, t₂) and [t₂, t₃), or (t₁, t₂] and (t₂, t₃), such that there is no entity that is a Komodo dragon at all in the first interval, but there is one that is a Komodo dragon in the second. [44]

If time isn't continuous, we may go from the ovum to the adult dragon, say, one Planck time at a time, and so there is a time t₄such that, at t₄, there is no Komodo dragon, but at t₄plus one Planck time, there is an entity that is fully a Komodo dragon.

Either way, that result appears extremely implausible, since the change from ovum to Komodo dragon is gradual, not in leaps. Even in the Planck time case, the steps are very short.

So, it seems to me that, plausibly, Komodo dragonhood can be had to different degrees.

Let's now consider personhood, i.e., the property of being a person.

A human embryo is plausibly not a person. [45]

Yet, it may undergo a process that eventually results in a person.

The conclusion seems to be as in the case of the Komodo dragon.

A somewhat similar scenario, which avoids the issue of whether an embryo is a person but is considerably more tentative, would be as follows:

In a distant future, some genetically modified humans reproduce via parthenogenesis.

Now, a human ovum is not a person. But in some cases, human ova undergo processes that result in a person.

The conclusion is the same in this case too.

Granted, reproductive parthenogenesis in mammals seems to be a problem, but given thousands or even millions of years of advances in biotechnology – including genetic engineering -, it may well be doable.

Granted, also, someone might suggest or claim that personhood begins when a soul enters a body, and it happens instantaneously or something like that. But we needn't assume that.

15.6.2. Evolution.

The second argument for the claim that personhood can be had to different degrees is evolutionary.

As before, let's begin with Komodo dragonhood.

Komodo dragons, like humans, evolved form unicellular organisms that weren't Komodo dragons.

But there appears to be no entity that was fully a Komodo dragon, but hatched from eggs that were laid by an entity that was not at all a Komodo dragon. Biological evolution is gradual and even quite slow by our daily standards, even when it happens at what biologists may call a very fast pace.

That supports also the view that Komodo dragonhood is a degreed property.

The same gradualism happened in the evolution of other animals, including humans.

To be clear, I do not claim that only individuals of our species are persons. Maybe, say, Homo Erectus were persons too – or maybe they were persons to some degree.

The point I'm trying to get at here is that whatever properties humans normally have, including mental properties, it seems very probable that some of our ancestors normally had those properties to a different degree.

Given that, it seems very probable that personhood can be had to different degrees.

Granted, theists might claim that, say, the first persons to be born on Earth were born to parents who were not persons by means of a miracle, or that some entities that were non-essentially non-persons were transformed into persons by God, etc.

However, we don't have an epistemic obligation to assume that, and as a non-theist assessing the evidence from evolution, plus the evidence from development, it seems to me that personhood is a property that can be had in degrees, even if that view is not usually held.

16. Power, agency, knowledge and moral goodness.

In this section, I will consider some paths from a necessary being to God presented by Joshua Rasmussen[46], and raise some difficulties for those paths.

I will grant for the sake of the argument not only that there is a necessary concrete being N, but also that the obtaining of at least some states of affairs can only be causally explained by N.

16.1. Terminology.

I will follow the paper's terminology, basically:

A gridscape S is a state of affairs consisting in some objects, the x's, instantiating some intrinsic properties or relations P's.

A wholly contingent gridscape is one in which all of the P's are instantiated not necessarily by the x's.

16.2. Libertarian freedom.

The path to volitional agency is based on a distinction between agent causation and causation by non-agents. According to that distinction, beings cause things by being in a certain way, or by means of exercising volitional agency, and the exercise of that agency isn't logically determined by the way they are. [47]

I would say that skepticism about that is at least warranted [48], and the burden to show a libertarian account of freedom is the correct understanding of freedom would seem to be on the claimant.

That aside, it seems to me that even showing that a libertarian account of freedom is the correct account of freedom would not suffice to clear this path to agency, even if some other assumptions are granted.

For instance, and regardless of any other considerations, the path to agency seem to be blocked by some potential beings, like a non-agential necessary concrete being, N – perhaps space, as in hypothesis 1, but N may be something else – that deterministically brings about certain kind of complex beings that are agents, and then those agents act non-deterministically based on different volitions. Those agents needn't be as intelligent as humans – e.g., maybe much less complexity than a human brain might suffice for volitional agency to start.

Also, those agents would not exist necessarily: they would be brought about necessarily, but they would come into existence and eventually cease to exist. That alternative does not seem to result in any consistency problems, even assuming a libertarian account of freedom. [49]

Perhaps, someone might argue that libertarian freedom requires souls, but that would require a separate argument. Moreover, even that would not be enough, it seems to me, since that would not rule out souls that are brought about by deterministic non-agential causes alone. [49]

16.3. Degreed properties.

This paper uses a premise similar to MA(K,1), which I addressed earlier.

There is a difference, though: Rasmussen' makes no exception for whole numbers. [50]

It seems to me that skepticism about that premise is justified, since the same reasons given earlier apply here as well, just leaving the parts about whole numbers aside.

16.4. The causal principle.

The causal principle used in all of these paths to different theistic properties is:

CP(R,7): For every wholly contingent gridscape S, it is possible that S's obtaining is causally explained.

As explained in the paper, the principle should be understood as follows:

a. A causal explanation does not have to be sufficient to bring about its effect.

b. Every property or relation in S is causally explained, considering a).

c. One of the explanatory causes is a concrete object or an event that is not in S. If it's an event, it may involve an object in S.

As Rasmussen points out, the principle is more modest than a number of other principles.

However, while it's true that other theist philosophers have used stronger principles, condition c) requires an external cause, and that's still is a condition that may block infinite regress in many scenarios, and seems to have the potential to erase all causes from a causal account, for all we know, as in some cases I analyzed earlier in this essay.

While here I'm assuming for the sake of the argument that N exists, that does not require assuming that a principle that removes causes from a causal account in that fashion is true.

On the other hand, if we assume not only that N exists, but that that is a conclusion reached by means of one of the usual principles defended by theists, assuming CP(R,7) seems adequate.

16.5. Infinite power.

The paper shows two paths to infinite power. The first one relies upon a principle similar to MA(K,1). I addressed that matter earlier.

The second path does not require MA(K,1), and is based on a principle that can be stated as follows:

CP(R,8): For every wholly contingent gridscape G, there is another possible wholly contingent gridscape G', such that the power required to bring about G' is greater than the power required to bring about G.

Briefly, my assessment is as follows:

1. The principle in question looks more intuitive to me than its negation, but not enough for me to be convinced. Moreover, my assessment of the principle is based on the same kind of intuitions that tell me that for every being, there is a more powerful possible one, or that it's possible for the being in question not to exist, etc. But those intuitions seem to be very problematic if N exists, which I'm granting in this section for the sake of the argument.

Also, personally, I find the Malo scenario, or the BIS scenario, no less intuitively plausible.

2. Granting CP(R,8), this path to infinite power seems to remain blocked in my view, because it seems to me that we're warranted in remaining skeptical about the possibility of a maximal wholly contingent gridscape, for similar reasons to the reasons given earlier, in the context of assessing the possibility of contingent states of existence that are maximal with respect to contingent concrete objects. However, if there are no such maximal gridscapes, the following might happen:

N does not have the power to bring about any being but K(1), K(2),...K(n), for some fixed natural number n, and some fixed beings K(j).

While N does not have the power to bring about arbitrarily difficult gridscapes, N can bring about some of the K(j), and they have the power to bring about some other beings. Some of those other beings have the power to bring about more powerful beings, and so on, so that for every wholly contingent gridscape G, there is a possible contingent being C(G) with the power to bring it about, and that being can be brought about by a causal chain started by N, but N can't guarantee that C(G) or G will be brought about, or anything even close to that.

Under that scenario, even if for every possible wholly contingent gridscape G there is possible wholly contingent gridscape G' such that G' is more difficult to bring about than G and N is a cause of G', it seems to me it would not be adequate to say that N is infinitely powerful.

On a related note, even the causal power to be one of the causes of any metaphysically possible state of affairs might end up being pretty limited, and then describing an object like N as having infinite power might be misleading in my assessment.

For example, it seems to me that time[51] may be relative in a way such that it's actually impossible for every actual being to transmit information faster than the speed of light, within the universe at least.

But then, if time is relative in that fashion, let's say that there are astronauts on Mars, and one of them asks N to, say, establish a communication between her (i.e., the astronaut) and her loved ones on Earth, with no more than a, say, five seconds delay (or five minutes, for that matter). Then, it seems N does not have the means to grant the request, even if N is aware of the request and wants to grant it.

But if that is the case, then it's clear to me that no being has any power remotely like that ascribed to God by any of the predominant religions and/or in the context of philosophy of religion.

In that scenario, saying that N has infinite power would be misleading in my assessment, even if N necessarily is one of the causes of any metaphysically possible state of affairs.

16.6. Agency.

In addition to the matter of agent causation vs. non-agential causation – which I addressed earlier -, the path to agency relies on the assessment that having the property to bring about some states according to some probability function F is not an essential property.

That assessment is based on considerations similar to those used in the case of degreed properties, and I would say that skepticism about that assessment is justified, for similar reasons as in the case of degreed properties.

16.7. Infinite knowledge.

The path to infinite knowledge relies on considerations similar to those given in support of the claim that N has infinite power, plus the conclusion that N is an agent, so the points I raised earlier apply in this case as well.

16.8. Infinite goodness.

Rasmussen also offers a path to infinite goodness, and he also explains several of the difficulties very clearly. I will not raise any of those objections here, though.

Instead, I will raise a very different kind of difficulty. [52]

Briefly, the idea is to raise the issue of potential alien minds, and assess the consequences.

This kind of objection is not specific to the theistic arguments presented in the paper under consideration. Moreover, in my assessment, the objections I will raise in this subsection present a significant difficulty for many other theistic views and arguments as well – or potential ones -, such as – purely for example – any argument intended to establish that a being with maximal knowledge and freedom would be morally perfect – or at least morally good -, or that there is a maximally great entity – where 'greatness' is partially defined in moral terms –, etc., since those arguments and views would have to address the issue of minds like the ones I will outline, and similarly many other potential alien minds.

So, in the next subsections, I will present scenarios that, in my assessment, we're not justified in deeming impossible or even probably impossible[53], and then consider objections to them, and to my assessments based on them.

16.8.1. The problem of [potential] alien minds.

First, let's consider the following scenario:

On a distant planet in another galaxy, some intelligent, self-aware, social beings evolved, but they evolved from different unicellular organisms, and they evolved in an ancestral environment that was quite different from our human ancestral environment, and even their present-day environment is quite different from ours.

For example, many of the organic molecules that were common in their ancestral environment were unusual or non-existent in ours, and vice versa, and the same goes for their and our present-day environments respectively. Also, for instance, the spectrum of their star is different from that of the Sun, etc.

In particular – and more relevantly here -, they also evolved in a considerably different social environment.

These aliens – let's call them 'zurkovians', to give them a name -, have an average IQ far higher than that of humans. They have something similar to human color vision, and there are objects that they perceive in a way similar to the way humans perceive red objects.[54] Some other objects are perceived by them in a way similar to the way humans perceive green objects. However, the electromagnetic frequencies associated with those perceptions are very different from those associated with similar perceptions in humans. In fact, the zurkovian visible spectrum is not even the same as the human visible spectrum. [55]

So, zurkovians have a different visual system, including different eyes and brain.

In particular, red traffic lights and green traffic lights here on Earth are the same zurkovian-color, or z-color. On the other hand, on their planet, zurkovians have signals that they perceive differently, while humans would not be able to tell the difference with human eyes. So, whatever zurkovians perceive in a way similar to the way we perceive red (z-red for short) is not the same as red, z-green is not the same as green, etc.

Zurkovians also have something like a sense of smell, and there are some things on their planet that would normally cause in them perceptions and/or sensations similar to those we humans have when we smell some things on Earth[56], but associated with very different chemical compositions.

Also, zurkovians have something like our sense of beauty, but associated with considerable different objects, shapes, etc. In particular, a rose would be perceived differently by them[5 6 ], and they would no doubt qualify a beautiful rose as z-ugly.

Moreover, if they were shown something (say, an image on a computer screen) that looks to them more or less like a beautiful rose looks to us (e.g., a similar mental image), they would still classify the image as z-ugly, as their psychological makeup is quite different.[58]

There are some similarities in their attraction to some kind of symmetric shapes, but that's as far as the similarities go, in terms of beauty vs. z-beauty.

Similarly, zurkovians have something similar to a moral sense, and reactions similar to how humans (who aren't psychopaths, etc.) react when making moral assessments; in other words, they have feelings similar to guilt, feelings similar to how we humans often feel when we become aware that we have a moral obligation, etc., and generally something like our moral motivations, but associated with different behaviors, including different agents carrying them out – though there are some similarities.

In particular, zurkovians are motivated by their z-moral assessments more or less as humans are motivated by moral assessments.

It seems to me that zurkovians are not only conceivable, but moreover, given what we know about evolution and how minds are adapted to their environments, we shouldn't rule out scenarios more or less similar to that. Maybe that won't happen, but we do not know enough about exobiology to rule them out – though in this context, all that is needed is that some of us are justified in not ruling them out.

Additionally, we may consider scenarios with different aliens who evolved elsewhere, and who do not have anything even similar to a moral sense.

Purely for example, it seems to me that aliens with an average IQ greater than that of humans but who aren't social beings may have evolved from something more or less similar to, say, octopuses, or generally from non-social or mostly non-social organisms, on one of the many planets in one of the – at least – many billions of galaxies in our universe.

So, let's consider the following scenario:

Kitonians evolved on yet another planet, in the same galaxy as the zurkovians. On average, they have higher IQ than humans, though not nearly as high as that of zurkovians.

Kitonians are not social beings, and do not have anything that resembles our moral sense, or any of the feelings normally associated with it in humans.

In particular, they do not make any judgments similar to moral judgments, do not experience feelings such as guilt, or how we humans may feel when we become aware that we have a moral obligation, etc.

Also, in particular, there are significant differences in what humans and kitonians value, and how they value.

For instance, we humans value some entities, actions, etc., because of moral issues. We also value some entities, actions, etc., for other reasons (e.g., I may value the ice-cream in the refrigerator because I like it, but that's not related moral issues).

Kitonians too value some entities, actions, etc. However, like octopuses, they never value anything because of moral issues, since they simply do not have morality, or anything that resembles morality.

Moreover, normal kitonians do have some shared species-wide value function – say, V(K) -, in addition to some individual values that they may get during their development, and which vary from individual to individual. However, the V(K) are in many ways very different from what humans value.

So, in short, kitonians don't care at all about moral good or evil, but they care about other things.

As in the case of the zurkovians, I do not see any good reason to conclude that kitonians aren't possible, or even that something similar to them isn't actual.

Some interesting questions (in my view) would be:

a. Would the zurkovians be moral agents?

b. What about kitonians?

c. Would it be proper to call kitonians 'evil' because they do not care about morality, but something else, or would they be non-moral agents, like octopuses, even if far more intelligent?

In any case, it seems to me that these agents would be intelligent, free agents who would not care about morality one way or another. Someone might suggest that they wouldn't be free, but I see no reason to suspect so.

Zurkovians would seem to care about z-morality, whereas kitonians would not care about anything that resembles morality.

Of course, there are plenty more potential aliens.

My point here is that, when assessing the potential psychological (i.e., mental) makeup of a [potential] necessary agential creator, it seems to me we can't rule out beforehand a mind with propensities far removed from those of humans, or of any primates who evolved on Earth.

If that is correct, then that seems to be a very serious difficulty for any argument to moral goodness, moral perfection, etc., especially if it's meant to be persuasive to people who are being rational but aren't already theists, and are also looking at a large body of evidence, including evidence from present-day science.

In the next subsections, I will consider some potential objections to my scenarios and assessments.

16.8.1.1. Theism and alien minds.

Objection:

You're assuming non-theism, because if theism is true, that kind of beings are impossible, at least with respect to morality, and perhaps beauty.

Reply:

First, I'm not assuming non-theism, but I'm not assuming theism, either.

I'm just making an assessment about what might happen, based on what we know about the world around us, including the evolution of minds. I do not need to assume that the process is not guided, but just refrain from assuming it is guided. [59]

Second, if theism entails such bold claims about exobiology[60], I would say that the problem is for theism, or more precisely for the justification of theistic belief, since we don't seem to have any means at this point to assess whether there are some aliens similar to the zurkovians, or the kitonians.

Granted, a theist might claim that the justification is precisely theism, or some other pieces of evidence (including intuitions) that allegedly justify their theistic belief.

I disagree, but in any case, when assessing arguments for theism, we are surely justified in not assuming theism, and without that assumption, it seems to me that for all we know, something similar to those aliens may well be possible, or even actual.

16.8.1.2. Objective morality and alien minds.

Objection:

If something like zurkovians (or maybe even kitonians) were possible, there would be no objective morality. But we can tell that there is objective morality, since, say, the Holocaust was immoral. Hence, zurkovians, or anything like them, are impossible.

Reply:

First, I see no good reason to believe that statements like 'the Holocaust was immoral' entail any bold claims about exobiology, and in my assessment, whoever makes that claim would have the burden to make their case. Indeed, it would be very odd if our daily assessments about moral right and wrong committed us to claims about what kind of intelligent living organisms inhabit other planets, if any of them does.

But for instance, let's consider the color case:

What may have evolved on other planets has nothing to do with whether, say, Joe ignored a red traffic light. That the traffic light was not z-red is irrelevant.

Similarly, it seems to me that some roses and some paintings are beautiful, regardless of what may happen or may have happened in other planets, or what normal zurkovians would say about them if they saw them, and even regardless of whether those roses and/or paintings are z-beautiful, z-ugly, or z-something-in-between.

But then, also similarly, it seems to me that the Holocaust was immoral, regardless of what evolved elsewhere in the universe, or whether it was z-immoral. For that matter, perhaps, humans aren't z-moral beings, so nothing we can do is z-right or z-wrong, but that seems unimportant when it comes to making moral assessments.

Granted, someone might claim that in the case of beauty and/or in the moral case, what happens on other galaxies is relevant, and so the cases above are not all relevantly similar.

But that seems very counterintuitive to me.

For instance, let's say that in the distance future, humans or very intelligent people who evolved from humans (via genetic engineering, etc.) make contact with aliens similar to zurkovians.

Should those people then conclude that, say, Pol Pot did not do anything immoral, if they ponder the matter?

I find that extremely implausible.

Generally, it would seem very odd to me that any sort of first contact would warrant or even provide any support for the metaethical hypothesis that there are no moral truths, or that we have no moral knowledge, etc., regardless of what the psychological makeup of the extraterrestrials in question turns out to be.

Second, and with respect to the claim of objectiveness, I would say the following:

If Joe is accused of crossing on a red traffic light, using a usual, intuitive grasp of the terms as they're colloquially used, I would say that there is an objective fact of the matter as to whether he did cross on a red traffic light, regardless of the result of any philosophical discussion on whether the relation between color perception and the human mind and/or eyes implies that color properties are mind-dependent in some technical sense.

In any case, mind-independent or not, Joe crossed on a red traffic light (or didn't, but let's say he did), and if someone claims that the traffic light wasn't red, she's making a false claim.

But similarly, as long as the same holds for morality (e.g., many of the actions of Pol Pot were evil, and if anyone claims otherwise, she's making a false claim), that seems to suffice in this context.

16.8.1.3. Human moral knowledge and alien minds.

Objection:

If something like zurkovians (or maybe some of the other aliens) were possible, we would have no moral knowledge. For instance, how would we know that humans got the right morality, and zurkovians got the wrong one? Why would humans be the special ones? Why should we assume that they got it wrong?

But we can tell that the Holocaust was immoral. Hence, zurkovians, or anything like them, are impossible.

Reply:

The reply is similar to the reply to the previous objection, but briefly:

First, as above, I do not see any good reason to think that moral knowledge has anything to do with what may have evolved on distant planets.

Second, we have knowledge about color, and if there are zurkovians, they have knowledge about z-color. Similarly, we have knowledge about beauty, and if there are zurkovians, it seems to me that they have knowledge about z-beauty.

Why would moral knowledge be any different?

It seems to me that the burden would be on the claimant; as for me, I make no claim that humans are somehow an exception.

In any case, even if for whatever reason zurkovians or similar social beings turn out to be impossible, something like kitonians or other non-social beings would still pose a similar problem in the context of assessing the character of N, assuming that N is an agent.

16.8.1.4. Morality and some different alien minds.

Objection:

Even if something like zurkovians is possible or even actual, that would not imply that they have some zurkovian morality, or "z-morality" instead of morality, even if their minds are very different from ours. Rather, zurkovians would simply have a moral sense that tells them what's morally right or wrong for zurkovians to do, and they would have no knowledge about what's morally wrong, good, etc. for humans to do, and similarly our knowledge would be about humans.

What's morally good, bad, etc., for an agent to do depends on a number of other, non-moral mental properties of the agent, in addition to the relations she's in.

Reply:

That is an interesting objection.

However, if correct, it would create a different sort of problem for theistic arguments: if entities with very different mental makeup could be moral agents that may do immoral or morally good things that we wouldn't be able to understand as such, then it seems to me that whether a necessary creator would be morally good or bad would be inscrutable, since we would have no way of assessing how she would behave if she were morally good, or how she would behave if she were morally bad.

For instance, if this objection is correct and zurkovians (or something like them) exist, then for all we know, it may be that it's not morally wrong for zurkovians to invade the planet inhabited by the kitonians, kill them off and get the planet's resources for themselves – or just invade Earth and do the same to humans.

In other words, if moral language is such that even alien minds like zurkovians would have morality and a moral sense – rather than z-morality and a z-moral sense -, then we're not in a position to assess what kind of behavior a morally good or morally bad entity would exhibit, as long as the entity in question has a mind considerable different from that of humans, and we do not know that an agential creator would have a mind similar to that of humans in the relevant sense.

That aside, even if any sufficiently intelligent social beings would have intuitions similar to our moral intuitions (i.e., no z-morality, and no different moral intuitions), including perhaps even similar psychological reactions (e.g., guilt), that would not resolve the problem of aliens who do not care about morality at all, like kitonians.

16.8.1.5. Alien minds without morality or anything like it.

Objection:

Even if kitonians are possible, the necessary being N plausibly would have moral goodness to an infinitely positive degree, but V(K) to an infinite negative degree, or not at all.
Reply:

Assuming that having moral goodness to an infinite degree makes sense, then the problem is that, for all we know, N might have V(K) to an infinite degree, and thus not care about morality at all.

Granted, I've not specified what V(K) actually is, but that's not required. On the contrary, the (epistemic) possibility of many different such V(K), and generally many different alien minds, only seems to compound the problem of potential alien minds.

Rejoinder:

We already know that moral goodness is a metaphysically possible property, but we do not know that it's metaphysically possible that a being with an IQ greater than the average human IQ possibly does not care about morality at all, but has some value function V(K).

Reply:

Yet, it seems clear to me that we're not justified in ruling out something like V(K).

For instance, I don't see any good reasons that would allow us to rule out a scenario like the one I suggested earlier, namely that in one of the (at least) many billions of galaxies in our universe, some non-social beings with an average IQ higher than that of humans may have evolved from something similar to octopuses. Octopuses are merely an example, of course. There are different ways in which, for all we know, non-social beings with an IQ higher than that of humans might evolve, and which we have no good reasons to rule out, in my assessment.

In any case, even a weaker claim would suffice as a reply to this rejoinder, namely that at least, some of us are justified in refraining from reaching that conclusion about exobiology – though I doubt anyone is.

Conclusion.

After considering several arguments from contingency, and taking a look at a broad amount of evidence, in my assessment it's probable that there is no necessary concrete being.

Assuming there is necessary concrete being, though, in my assessment, we're justified in not concluding that it's an agent.

Furthermore, even assuming that there is a necessary agent, it seems to me that we're at least justified in not concluding that the agent in question is morally good.[61]

Notes and references.

[1] It seems to me that in order to look for contradictions when testing metaphysical possibility, we should take into account potential cases in which the semantics of a term fixes the referent to be the actual referent.

For instance, my impression is that we can tell by conceptual analysis that in any possible scenario 'water is ABC' is true if and only if 'water is ABC' is actually true. We do not need to know that water is H₂O in order to reach that conclusion, but rather, we are (potentially) able to reach that conclusion only by our grasp of the meaning of the word 'water'.

If so, while a scenario in which water is not H₂O is not strictly logically impossible (e.g., we may consistently stipulate that science got it wrong), there is a contradiction once we factor in that water is actually H₂O.

That said, the issue of whether necessarily, water is H₂O, is disputed as well, but if it's not, then I would still say that fixed referents ought to be taken into consideration when assessing metaphysical possibility, even if that particular example does not work.

If no referent is fixed in that manner, then it's not clear to me that there is any metaphysical modality that is different from strict logical modality (or, if there is any difference, strict logical modality plus analytical equivalences), which would seem to even more clearly indicate that there is no metaphysically necessary being. Of course, I will not assume that in this essay.

[2] It is true that the scenarios are not completely specified, but that does not appear to be a problem. In fact, it seems to me we can hardly ever completely specify a scenario.

[3] Here, I'm just using the word 'can' in an ordinary sense, which I think is clear enough given context, so this shouldn't cause confusion. If there is any difficulty, for the purposes of the matter at hand, it's enough to say that we have not fully visualized and will not fully visualize those objects.

[4] Granted, a non-theist who believes that unembodied intelligent beings are possible may well not have a problem with those alternatives, but they seem to be a problem for most forms of theism.

[4] The evidence may well include intuitions, and if we use 'intuition' in a broad sense, arguably it always does.

[5] The reply to the Kalam Cosmological Argument can be read here, or download from here (in .html format), or from here (in .pdf format).

[6] That would be debatable on presentism, which is precisely the theory of time that Craig defends. But let's grant for the sake of the argument that no actual infinity entails no infinite past, even on presentism.

[7] William Lane Craig and J.P. Sinclair, "The Kalam Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6.

[8] Greater infinities would not make a relevant difference, so one may assume a larger infinity for that matter, and essentially the same counterarguments would work just as well.

[9] Sources:

http://prosblogion.ektopos.com/archives/2009/10/from-grim-reape.html

http://alexanderpruss.blogspot.com/2009/10/from-grim-reaper-paradox-to-kalaam.html

More details on the definition of Aristotelian discreteness suggested by Pruss: http://prosblogion.ektopos.com/archives/2009/10/from-grim-reape.html#comment-107238

While Pruss' does not seem to explicitly say that, under Aristotelian discreteness, it's necessary that there are only finitely many moments or intervals between two given times.

However, it's clear in context that his conception of time that is discrete in an Aristotelian sense rules out that time is possibly dense. On that note, he gives an argument against infinite regress assuming that time is Aristotelian discrete, and in which he concludes that the mere possibility of temporal density would contradict the assumption that time is discrete in an Aristotelian sense.

[10] Source: Alexander Pruss, in "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6.

Pruss' defense of Leibnizian arguments can be found in the following page: https://bearspace.baylor.edu/Alexander_Pruss/www/papers/LCA.html

[11] Sources: Koons, R. C. (2012), A New Kalam Argument: Revenge of the Grim Reaper. Noûs. doi: 10.1111/j.1468-0068.2012.00858.x

http://www.robkoons.net/media/83c9b25c56d629ffffff810fffffd524.pdf

[12] Koons uses the word "set", but it's not entirely clear to me that that would be a set.

For instance, for all I know, there might be a possible world W with physical structures of cardinality x, for any cardinal x. If so, the class of spatio-temporal regions of W would appear not to be a set.

So, I prefer to use the word 'class'. In any case, this is a side issue.

[13] Josh Dever, in "Worlds Apart", Taiwanese Journal for Philosophy and History of Science, 10 (1998), pointed out that the scenario is contradictory.

This was also pointed out by Graham Oppy, in "Arguing about Gods", Cambridge University Press (2006).

[14] I'm stipulating 1 year = 365 days and ignoring leap years, for the sake of simplicity; a more complicated proof would include leap years, but it's clear that the contradiction does not depend on whether we take into consideration leap years.

Also, the assumption that the set of past years has the order type of the non-positive integers is acceptable in this context, since that is the main hypothesis that Craig claims ought to be rejected due to the Tristram Shandy argument, and since in any case, I intend to show that the 'Tristram Shandy' argument does not show that such a past is impossible.

[15] As usual, the scenario isn't completely specified, so someone might argue that it's more accurate to say it's a type or category of scenario, but calling them 'scenario' seems to be pretty standard. In any case, that they're not fully specified shouldn't cause any confusion, as that's normally the case.

[16] Davey, K. and Clifton, R. (2001) "Insufficient reason in the ‘new cosmological argument".

Religious Studies 37, 485–90.

[17] Rasmussen, Joshua. “From States of Affairs to a Necessary Being,” Philosophical Studies (2010).

http://www.nd.edu/~jrasmus1/research.html

In my assessment, Rasmussen's paper contains some of the most clever arguments in support of the existence of a necessary being, but I think they ultimately don't succeed.

[18] A duplicate of B is another object D(B) with the same intrinsic properties as B. As Rasmussen explains in his paper, characterizing intrinsic properties is difficult.

Personally, I would say that may be a problem, but I won't address the matter in this essay.

[19] In the context of the paper under analysis, to exist necessarily is by definition to exist at every possible world, so I'm using possible worlds in my reply as well. However, that is not crucial. If a similar argument were made without using possible worlds, one could also reply similarly, though part of the reply would need to be reformulated to some extent.

[20] I would suggest that some theists too might find Lonely implausible, for the following reason:

If, at W, one contingent being B exists, and no other contingent being exists, why can't God add an angel, without destroying B?

The assumption of essentialism makes the issue obscure to me, though.

[21] If I dropped the assumption that essentialism is true, it would seem intuitively very plausible to me that Lonely isn't possible.

[22] I would suggest that some theists too might find Big Blob implausible. If, at W, some being B exists and occupies all of space, why can't God remove it from some volume V, without destroying B?

The assumption of essentialism makes the issue obscure to me, though.

[23] Of course, I'm leaving aside space itself, which may well be a being and in a sense necessarily occupies all of space. But that isn't the sense relevant in this context, and it wouldn't help the case for a maximal contingent state of existence, at least not in this context.

[24] My original intuition on this matter was that for every possible state of affairs, if unembodied beings are possible, one more probably could be added. But in ex-apologist's blog, Joshua Rasmussen gave interesting reasons in support of the alternative conclusion, namely that no more angels could be added. As a result, I remain undecided – as usual, under the assumption of essentialism; else, I would say that one more could be added.

Incidentally, a maximal state like that might be odd for some theists as well: Is is possible for there to be so many angels that God can't create one more without destroying one of them first?

[25] Koons, Robert, "A new look at the cosmological argument", American Philosophical Quarterly 34: 193–211. (1997) http://www.arn.org/authors/koons.html

[26] Koons, "Defeasible Reasoning, Special Pleading and the Cosmological Argument"

http://www.arn.org/docs/koons/rk_defeasible.htm

[27] Koons seems to assume at this point that a number of states of affairs we encounter in science are wholly contingent, ruling out necessary basic particles, necessary space, etc. He does make arguments against the necessity of such beings later, though, but I do not find them persuasive, for reasons I will give later.

[28] A New Argument for a Necessary Being, Australasian Journal of Philosophy (2011).

http://www.nd.edu/~jrasmus1/research.html

[29] When I say we can't visualize some kind of particle (for instance), I'm not making a modal claim of metaphysical impossibility. I'm just using the word 'can' in what is at least one of its ordinary senses, and which I think is clear enough given context, so this shouldn't cause confusion.

In any case, it would be enough to say that we've never visualized and never will visualize such-and-such objects, etc.

[30] Moreover, the Malo and BIS scenarios seem intuitively conceivable as well.

Granted, that's only a problem for theistic necessary beings, but still, if a certain criterion as a guide to metaphysical possibility is used in the context of an argument for theism, it seems to me that such consequences may reasonably be pointed out.

[31] Someone may want to further distinguish between different types of conceivability that don't require visualization. Given my take on the matter, I don't think that that's required, but I recognize it's another potential approach.

[32] I would still think that the amount and kind of actual suffering in the world – for instance – is enough for us to rule out the existence of a 1-god or a 2-god but that's another matter, and I will not argue for that in this essay.

What I'm getting at in in this context is that if conceivability without visualization does not work as a good guide to possibility despite its being so intuitive to me, I would be hesitant to accept the continuity principle, and so in particular, I wouldn't find an argument from suffering and/or moral evil based on it to be an improvement over an argument from actual suffering and/or evil, as an argument against a claim that a 1-god or a 2-god exists necessarily.

[33] Craig, William Lane, "Reasonable Faith, Christian Truth and Apologetics", Third Edition. Publisher: Crossway.

In this context, Craig seems to use the terms 'being' and 'thing' interchangeably.

[34] Our actual mental states are part of the territory too, though maybe 'in here' would be more descriptive than 'out there' in this case.

For example, if Alice is thinking about the number 5, that's a being with certain properties, in the territory.

On the other hand, let's say that we come up with a hypothetical scenario, say the BIS scenario.

Then, in my view:

1. We can have knowledge about the scenario in question, make true (or false) claims about what happens in it, and so on.

For instance, if I claim that in the BIS scenario, no being is in pain, that's a false claim. On the other hand, if I say that in the BIS scenario, there are eventually more than 8397994 concrete beings, that's a true claim.

2. When we talk about the BIS scenario, we're not talking about actual mental states.

For instance, even if all of the people who ever thought about the BIS scenario were to die, that would not change the fact that in the BIS scenario, there are eventually more than 8397994 concrete beings.

3. In general, there is no 'BIS scenario' in the territory.

So, it seems to me that we have knowledge about an abstract, hypothetical scenario, but when we talk about things that happen, exist, etc., in that scenario, we're not talking about the territory, but about an abstraction more or less loosely based on it, our intuitions, experiences, etc.

4. The BIS scenario belongs in the category 'strictly logically consistent scenarios', but if someone included the BIS scenario in an ontology, I would find that puzzling, as I would find an ontological claim that the category of strictly logically consistent scenarios exists, and so on.

I concede that this is a very complicated matter, and many other people have very different takes on it, though, but in my assessment, to include abstracta in an ontology is a mistake.

That does not entail that claims like '1 + 1= 2' are somehow false; that claim is true, as is the claim that in the BIS scenario, there are eventually more than 8397994 concrete beings, but neither claim requires an ontological claim of existence of abstracta, whether it's numbers or the BIS scenario, in my view.

[35] Different arguments from contingency use different causal or explanatory principles, so perhaps one might want to introduce more non-theistic hypotheses, tailored to those different principles.

However, I prefer to introduce some rather general hypotheses, and then compare them with theistic alternatives to see how they fare. I will introduce some more specific hypotheses when I think that's useful as a means of handling some specific theistic arguments.

At any rate, the non-theistic alternatives I'm suggesting are only part of my strategy, and I will challenge some theistic arguments on different grounds as well.

[36] There are issues such as how one goes about assessing what range of fundamental constants counts as 'narrow', but that's beyond the scope of this essay too.

[37] I'm talking about different beings, rather than a being that is three persons, assuming that it's coherent for a being to be three persons, or to exist as three persons. Personally, I concede I can't make sense of a being that is three persons.

[38] The assumption of essentialism may be causing problems here, but dropping that assumption would probably be much more of a problem for the theist, since (for example):

a. Essences are commonly used in theistic arguments, including contingency arguments.

b. God is usually claimed to have an essence, and so is each human on theism, etc.

c. In particular, nearly all versions of Christianity seem to maintain that the creator is essentially a trinity, etc.

Since essentialism seems to be frequently accepted, I'm granting it for the sake of the argument – at least, in nearly all of this essay.

[39] Our intuitions, even if 'a priori', are not only the consequence of innate predispositions, but are also informed by our experience, in my view.

However, I do not think that that causes problems for my assessment of the evidence.

In any event, we may assess all the evidence together if we so choose, and the result does not seem to be more supportive of Koons' arguments from a necessary cause to some specific kind of being.

[40] Incidentally, that the charge would not change is not something we could tell a priori, and for all we knew a priori, the empirical evidence might have turned out different from what it is.

But as it turned out, the charge seems not to change.

Granted, that a property does not change in a lot of cases does not entail that it cannot change, but it seems to provide at least some empirical evidence in support of the theory that the property in question is essential, under the assumption that essentialism is true.

[41] Regardless of whether we can properly assign a number to those degrees, it seems clear that those properties can be had to different degrees.

[42] I'm not assuming here that essentialism is false, either. I'm just dropping the assumption that it's true. I will leave aside the issue of whether the case I'm making provides evidence against essentialism.

[43] We may as well start with a cell at any earlier stage. This is not crucial to my argument.

[44] There probably is a semantic difficulty as well:

The words that we use to describe the world around us do not seem to be precise enough for there to be, say, a first nanosecond at which there is a Komodo dragon, or even a fully formed Komodo dragon (or a dog, or a human being, or a person, etc.), regardless of ontological matters.

However, raising semantic problems would seem to be of no help for the ontological view that a property is immeasurable, in my view, so there is no need to go any further on that.

[45] Granted, most Christians believe otherwise, but we needn't assume that here.

In any case, we may as well start with an unfertilized ovum and make the argument in that fashion, arguing that there probably is no 'first instant' at which there is a person. Incidentally. fertilization is a gradual process as well, so 'moment of conception' replies won't block my argument.

[46] Rasmussen, Joshua, "From a Necessary Being to God".

International Journal of Philosophy of Religion 66.1: 1-13. (2009).

[47] It's not clear to me whether the paper distinguishes here between causal determinism and determinism in general. It's not important to my reply, though, since the path to agency in any case assumes that some kind of libertarian account of freedom is the correct account of freedom, which is all I need in this part of my reply.

[48] My position is that libertarians have a mistaken account of freedom, and that the semantics of terms like 'freedom', 'free will', etc., do not rule out determinism, causal or otherwise.

But it's beyond the scope of this essay to make that case, and I'm not going to assume that they're mistaken. Instead, I will say that if a theist claimed that a correct account of freedom is libertarian freedom, the burden would seem to be on her.

[49] Probabilistic assessments of this matter are beyond the scope of this essay, so I'll just state that my position is that theistic hypotheses are less probable than most non-theistic ones, and even than some rather ad-hoc ones, in terms of prior probabilities if we can properly assign priors – given conditions like omniscience -, and especially final probabilities – given conditions like moral perfection omnipotence and omniscience, or at least moral perfection plus great knowledge and power.

[50] The premise looks incompatible to me with having the property of being three persons, if that's a property and makes sense. But then again, I can't make of a being that is three persons, anyway.

[51] If metaphysical time is not physical time, then my scenario is about metaphysical time.

Incidentally, a claim that time is actually not relative and only physical time is, looks to me like a claim that some of our observations are illusory. They might be so, but the claim would seem to need defending, in my assessment.

[52] The source of some of the main ideas on which I base some my arguments in this subsection is an anonymous poster whose user name at www.freeratio.org is 'Bomb#20', so he deserves the credit for them. To be clear, though, I don't claim that the points I'm making reflect his views, since I'm also using a number of my own ideas – and I don't know whether he agrees with those -, and also I might have misunderstood some of his views, so any errors here are on my part.

On a related note, I replied to a number of metaethical arguments for theism in another essay, in which I also used some of his ideas.

[53] As a justification for rejecting arguments for infinite moral goodness in this context, it is enough that some of us are justified in not concluding that the scenarios I will present are impossible, or probably impossible.

However, in my assessment, a stronger claim holds, namely that a person who is moderately familiar with biological evolution and the scale of the universe shouldn't conclude that they're impossible, or probably so. Granted, many theists may well dispute that, and it's a matter of assessing the evidence and discussing the matter, but that would be beyond the scope of this essay, so I'm just introducing the issue.

[54] I'm assuming that different human individuals have similar perceptions and mental experiences, and in particular, that there is no inverted color spectrum.

That assumption seems quite probable to me, but in any case, that is not crucial to my argument, and the scenarios may be suitable modified if needed.

[55] As we know from animals on Earth, a star with a spectrum different from that of the Sun is not required for different lifeforms to have different visible spectra, as a result of the evolutionary process. The condition that their star's spectrum is different is merely to stress the differences between the respective ancestral environments.

[56] There probably is more variation among humans in the case of smell than in the case of color, but I'm talking approximately and on average.

Also, a difference in the way that different lifeforms perceive smell does not require different prevalence of organic molecules in their environment, etc., so that condition is merely for the purpose of stressing the differences between the different ancestral environments.

[57] In other words, the mental image they would get if they looked at a rose would not be the image we humans get when we look at it. They would see different degrees of detail, different coloration, etc.

[58] On that note, it's quite plausible that the sense of vision of Neanderthals was very similar to that of modern humans, but their sense of, say, Neanderthal-beauty was at least in some respects significantly different from our sense of beauty.

For instance, the mental image that they got when looking at another Neanderthal was plausibly not very different from the mental image that we would get. But plausibly, many faces that were Neanderthal-beautiful were not beautiful, and vice versa.

So, there are such differences, and that's an example from a species that is very closely related to our species, or a subspecies of our same species, depending on how one classifies them.

The sense of S-beauty of a very different species S may well be far more distant from our sense of beauty than the Neanderthal sense of Neanderthal-beauty was, so we may reasonably stipulate that the zurkovians' sense of z-beauty is very different from our sense of beauty.

Also, there may well be considerably greater differences between the senses of beauty of different humans, even under normal conditions – much greater than the differences in normal color vision, for example. If so, someone might argue that that may well have significant consequences for a philosophical analysis of beauty. However, there is no need to address the matter here.

Alternatively, or additionally, someone might argue that things may be beautiful to some agent or to some other agent, but that there is nothing like 'Neanderthal-beautiful', except in the sense of something that would be beautiful to all Neanderthals, or to all normal Neanderthals, etc., and similarly in the case of humans, things may be beautiful to some human or another human, etc.

However, there is no need to address those matters here, either. I used beauty as an example because I think it might clarify some of the difficulties for theistic arguments for moral goodness I'm getting at. However, if it causes any difficulties, we might as well remove any reference to beauty in the scenario about zurkovians and the argumentation based on it, and the problem of potential alien minds in the moral case is not affected.

[59] While I think that there are sufficient reasons for believing that no entity is guiding the process, regardless of whether there is some deistic creator that started it, I don't need to claim that in this context.

[60] Personally, while I don't think theism is compatible with the existence of zurkovians, kitonians, etc., for that matter, I don't think it's compatible with the existence of humans, either, since in my assessment a 1-god or a 2-god would never create anything remotely resembling our universe, given their power, knowledge and moral goodness. But I'm not making an argument to that conclusion here, or assuming that that is the case. My arguments in this context are independent of that assessment.

[61] Personally, I would say that we ought to conclude that there is no 1-god or 2-god, given the suffering in our world (for instance). But that would require a very different argument, and it's beyond the scope of this essay.

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Monday, August 6, 2012

A Reply To Theistic Arguments from Contingency (v 5.3)

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