Angra Mainyu's blog: Against the Kalam Cosmological Argument

William Lane Craig and other theists offer a number of arguments in support of the premises of the KCA, concluding that the universe has a cause. Then, they provide further arguments in support of the claim that the cause is God.

In the first section, I will show that a contradiction follows from William Lane Craig's position.

In the second section, I will address Craig's reply to the objection to the KCA that I raised in the first section of a previous argument against the KCA, which is the same I will raise in the first section of this argument.

In other sections, I will raise other objections to the KCA, as well as to the added conclusion – even assuming that the universe had a cause of its existence – that the cause is God.

b) I will focus on William Lane Craig's version of the KCA, given that that is the most common one.

c) Unless otherwise specified, I assume that a tensed theory of time is true. Craig and all other defenders of the KCA, to the best of my knowledge, defend the KCA in the context of a tensed theory.
I will, however, address a potential attempt to run the KCA on a tenseless theory, just for the sake of thoroughness. Section thirteen deals with that alternative.

d) On a terminological note, I will use the word “argument” loosely, to refer to both the formal argument, and the informal arguments used to support the premises of the formal argument. I think this is a common way of speaking, and context should prevent any ambiguity despite some notational abuse.

e) Before I go on, let me point out that I make no claim of novelty:

The Kalam Cosmological Argument has been around for considerable time, and I got some of the ideas I'm using in my arguments from many sources on the internet.

In other cases, I came up with the ideas for my arguments on my own; however, given for how long the KCA has been debated, I have no good reason to think that I'm the first one to come up those ideas, so I don't claim any novelty in that, either – I merely claim that the KCA provides no support for theism, and that this article shows that.

1) A contradiction follows from William Lane Craig's position

William Lane Craig and J. P. Sinclair[3]:

By an “event,” one means any change. Since any change takes time, there are no instantaneous events so defined. Neither could there be an infinitely slow event, since such an “event” would, in reality, be a changeless state. Therefore, any event will have a finite, nonzero duration.

William Lane Craig[4]

The reason I hold God to be timeless without the universe is that I think that an infinite regress of events is impossible, and, according to a relational theory of time, in the absence of any events time would not exist. The reason I hold God to be temporal since the beginning of the universe is that the creation of the universe brings God into a new relation, namely, co-existing with the universe, and such an extrinsic change alone (not to mention God’s exercise of causal power) is sufficient for a temporal relation.

William Lane Craig[5]

So if God is timeless, he is also unchanging, but it does not follow that He cannot change. I’d say that He can change and if He were to do so, He would cease to be timeless. And that’s exactly what I think He did.

God changes from timeless to temporal.

Any change is an event, so let E(0) be the event “God changes from being timeless to being temporal”.[6].

Now, if t=0 is the beginning of time, then E(0) is a change that ends precisely at t=0, since t=0 is the first time at which God is temporal.

Since every event has a finite, non-zero duration, E(0) has some duration e>0, and ends at t=0.

Then, there is a time interval of duration e prior to t=0.

That contradicts the hypothesis that t=0 is the beginning of time.

2) Craig's reply

After someone raised the issue on his website, Craig replied[7] to the objection I raised in section one of an earlier version of my argument – which is the same I've raised in section one of this article, though I provided a shorter explanation of my objection in the earlier version.

Craig replied that God's gaining knowledge of tensed facts (for instance) does not qualify as an event, since it's "instantaneous". [7]

First, his claim is false. He defined 'event' as 'any change', and those are obviously changes.

He did not define 'change' excluding 'instantaneous' changes, as one can easily see from the quotation from his book I posted earlier.

Second, as I also showed earlier, instantaneous changes entail a contradiction – regardless of whether Craig chooses not to call them 'changes' anymore.

That aside, let's continue analyzing Craig's reply to my objection:

William Lane Craig[7]

The reason I give for so restricting the range of “event” is that I’m talking about changes, and changes take time to occur.

First, Craig does not restrict the range of 'event' at all in his definition, and so he gave no reason for restricting the range at all. Instead, he defined 'event' as 'any change', and then argued from there, that any event will have a finite, non-zero duration. So, the 'restriction' is a consequence of his reasoning, not a stipulative definition.

That is obvious in the quotation from his book I gave for context (due to copyright reasons, I may not post long parts of his book, but that part suffices to make that clear; of course, I invite readers to take a look at his book more closely in case of any doubt).

Second, that changes take time to occur is precisely one of my points, which I use to derive a contradiction on Craig's position.

Again, Craig actually claimed that changes take time to occur.

In fact, he claimed that there are no instantaneous events precisely because any change takes time, and he defined "event" as "any change".

So, I pointed out that the change – for instance – from a state S at which God does not know any tensed truths (because there aren't any tensed facts), to a state at which God knows some tensed truths (at t=0) is, well, a change, and changes take time to occur – as Craig stated -, from which a contradiction follows.

William Lane Craig[7]

Similarly, God’s coming to believe all tensed truths would not qualify as an event, since it, too, happens instantaneously.

But that is false. Since God's coming to believe at least one tensed truth is a change, then it follows – by his own definition – that it's an event.

In fact, by claiming that it's instantaneous, Craig is only contradicting his own claim that all changes take time. Once again, this follows from the previous quotation of his book.

Yet, in his reply to the objection I raised, Craig claims [7] that God's gaining knowledge of tensed facts is instantaneous, and therefore it's not a change in God in "this technical sense".

But there is no such "this technical sense" of "change" in Craig's KCA, since – as we can see in his book – Craig did not define "change" at all.

The only sense of 'change' is the usual sense of 'change' in English; in other words, he left 'change' undefined, used the usual concept in order to define "event" - as is apparent in the quote above -, and then argued from there – keeping in mind the usual meaning of 'change' -, that any change takes time.

Of course, God's change from not knowing any tensed truths to knowing at least some tensed truths is, well, a change in the usual sense of the word 'change' in English, and by Craig's own reasoning, we can conclude that it takes time, and thus derive a contradiction, as I did above.

So, in short, Craig did not define "events" as having zero duration. Neither did he define "change" as having a non-zero duration, or at all. Instead, he defined "event" as "any change", and assessed that events/changes have non-zero duration, as the previous quotation from his book shows (once again, I invite readers interested in more details can take a look at his book and see more context for themselves).

Yet, the changes I'm talking about are obviously changes in the usual sense of the word "change" in English – which is the one he was using in the context of the KCA -, and assuming that they have a non-zero duration, a contradiction follows as explained (I will later show that, in any case, a contradiction follows regardless of whether we assume that the changes take time or are instantaneous).

In addition to the above, Craig claims that there is no beginning or ending to those changes/events – which he describes as "events" in quotes – as – he claims, beginning to move or coming to exist do not have a beginning or ending [7]

However, there clearly would be a beginning point of the event, say, 'God changes from not knowing any tensed truths, to knowing at least one tensed truth', if such event/change made sense.

A beginning point would be a state without any changes occurring within that state, and the same for an endpoint. And so, in this particular case, the beginning point would be the only state at which God does not now any tensed truths. And the endpoint would be the first state at which God knows at least one tensed truth.

So, the claim that such changes have no beginning or ending are false. If such changes were possible, there clearly would have a beginning point and an endpoint. That follows from the description of the changes, as I just explained.

In addition to the previous claims, in his reply to my objection, Craig contends that in the second and third quotations, he was using "change" in a different sense from the sense in which he used the word in the context of the KCA, and that in those second and third quotations, he "merely" meant that God does not have the same properties in his timeless state as he does in his first temporal state[7].

But an analysis of his words show that he clearly did not merely meant that – that is only part of what he meant.

In fact, Craig said that God changed from timeless to temporal, and ceased to be timeless.

He did not say hat God changed from temporal to timeless, or that he ceased to be timeless – clearly, that would not have meant the same, and Craig himself does not accept the possibility of change from temporal to timeless.

So, when Craig said that God had changed – in the second and third quotations – he did not merely meant that God in his timeless state has different properties from God in his first temporal state.

The claim of a change is not only a claim that the properties differ, but there is also a direction: God has some properties in his timeless state, and changes and has some other properties in his first temporal state: it goes in one direction, not the other.

In other words, the change is from the timeless to the temporal state, not vice versa, so what he meant is not merely that God's properties in his timeless state are different from his properties in his first temporal state: change is not directionless.

So, that still is the usual sense of "change" in English, as he used in his book, in the Kalam Cosmological Argument, as far as one can tell from his statements.

So, in brief:

a) Craig's claim that he used 'change' in a technical sense in his book, is a false claim. He used it in the ordinary sense of the words.

b) Craig's claim that he used 'changed' to merely say that God has different properties in his timeless and first temporal states, is also false. Once again, he used 'changed' in the ordinary sense of the words in English.

c) The fact remains that a contradiction follows from Craig's position.

That aside, Craig also maintains[7] that in any case, one can change the definition of "event" in the second premise of the Kalam Cosmological Argument and clarify that the events in question are events of non-zero, finite, equal duration. Actually, if he did that, he would be withdrawing his claim that any change takes time, rather than merely clarifying his claims.

However, that is a side point.

The crucial point is that if we do that, or if we we make, for the sake of the argument, the false assumption that Craig said what he later claimed he had said, a contradiction still follows.

In fact, a contradiction can be derived without any assumptions about what Craig said, as the next section shows.

3) Still a contradiction

In this subsection:

a) By 'event' I mean the same as 'change'.

b) By 'P(2)' I mean the property of knowing at least one tensed truth.

c) By 'E(2)' I mean the event/change 'God changes from not having P(2) to having P(2) for the first time'.

d) By 'S' I mean the allegedly timeless state of God, at which God does not have P(2).

e) By 't=0' I mean the first temporal state of the world – and of God.

Note that, given Craig's account, E(2) exists. Craig may choose not to call it an 'event', or a 'change', but that is not my concern in this section. It's clearly an event/change in the usual sense of the word 'change' in English, so that's good enough.

While Craig seems to claim otherwise, the event/change E(2) has a beginning point, and it has an endpoint, both of which one can easily show:

The beginning point is the only state of the world at which God does not now any tensed truths. The endpoint is the first state of the world at which God knows at least one tensed truth.

So, we have a change/event from a beginning point, to an endpoint.

If E(2) has a duration e>0, then since E(2) finished at the initial temporal state T(0), there is a temporal interval of duration e>0, prior to T(0). But that is a contradiction, no matter how small e is.

If E(2) has a duration zero, then since the final point of E(2) - namely, the first state at which God has property P(2) - obtains at T(0), and the duration of E(2) is actually zero, then it seems that the initial point of E(2) - a state at which it is not the case that God has property P(2) - also obtains at T(0).

Note that the change is not said to take some small time, not even some kind of infinitesimal, but exactly zero. It can't be that it's some infinitesimal, either, because it ends at t=0, which is the absolute beginning of time.

Hence, at t=0, God has property P(2), and it is not the case that God has property P(2). But that is a contradiction.

Someone might suggest that E(2) does not have a zero duration, or a non-zero duration, but somehow 'duration' does not apply to it, because it's 'partly timeless'. I will address that in section 7.

Also, someone might object that the initial state of E(2) is not present at T(0), but at timeless state S, and the final state is present at T(0). However, if there is a change from some beginning point to some other endpoint, and the duration of such an event is actually zero, then both ends exist at the same time, and a contradiction follows. Duration is a measure of time, not of 'timelessness' - whatever that is.

So, the person who claims that the contradiction is somehow averted because one point is 'timeless', or something like that, would have the burden to explain what they mean by 'timeless' and how that would allow them to avert the contradiction...but that would clearly fail, since deriving the contradiction is unproblematic.

Still, and while the burden would be on the theist defender of the KCA, I will later take the initiative and show that the so-called 'timeless' state fails to be anything different from a first temporal state, but briefly, here I will point out that the actual situation would be one of an uncaused creator with a beginning at the first temporal state.

In other words, Craig description entails that there is a first state of the world – which would be a first temporal state -, an uncaused God, and then a second state of the world, and so on.

However, accepting that would contradict the first premise of the KCA.
So, Craig claims that the first state is 'timeless' - whatever that might mean.

Yet, it's still a change, and it still has a beginning point and an endpoint, as explained above.

Denying that the first temporal state is actually temporal, but without actually denoting any difference, is what allows the derivation of a contradiction as before, since what actually would be happening is an ordinary event/change from the first to the second temporal state of the world, but with the defender of the KCA committed to a claim that that is not so.

Of course, showing that the so-called 'timeless' state is nothing but a first temporal state of the world blocks Craig's KCA on its own, without further arguing to a contradiction, but the argument given so far is simpler and sufficient.

4) The open interval variant

In order to derive a contradiction above, I assumed a first temporal state, and someone might suggest that Craig does not claim that.

In this section, will prove that Craig's arguments and claims in the context of the KCA (henceforth, Craig's arguments), entail that there is a first actual temporal state of the world.

I will prove this by contradiction, considering both the possibility that temporal units are instants, and the possibility that they are intervals which are not dividable into smaller ones. Considering such possibilities is enough, since infinitely dividable intervals aren't compatible with some of Craig's arguments, as I will show later.

I will not address the matter of whether there is any ontological difference between instants and non-dividable intervals as the units of time, or it's just a matter of notation. It's not necessary to settle that matter here, since the arguments I will give work regardless of that: if there is no ontological difference, then the argument that only considers instants suffices. Else, both arguments suffice.

a) Instants

If the units of time are instants, let's assume that there is a sequence of instants such that t(n+1) < t(n), for every n. We may take them such that there is no instant between t(n+1) and t(n), since Craig's position entails that time is discrete, which I will show later.

So let's define, for every natural n, the following actual events/changes:

E(n): = 'God comes to know that t(n+1) is past' (i.e., God changes from not knowing that t(n+1) is past to knowing that t(n+1) is past).

Clearly, those are infinitely many past actual events/changes; E(n+1) occurs before E(n).

That's incompatible with Craig's arguments.

Alternatively, we might – for instance -, take the events 'God comes to know that t(n) is present', for all n, reaching the same conclusion.

In any case, the conclusion is that if units of time are instants, Craig's arguments entail no infinitely many past actual events – not even of unequal length.

So, there is a t(0)=0, and a corresponding state of the world T(0).

Clearly, and reasoning in a similar manner, there is t(1), and T(1), the next instant and its corresponding state of the world, etc.

b) Intervals

If the temporal units are non-dividable intervals, then let's suppose there is no first non-dividable interval I(0). Constructing a sequence of non-dividable intervals I(n+1) < I(n) and the corresponding changes experienced by God, we immediately get an infinite past series of actual ordered events, which is incompatible with Craig's arguments.

Hence, if the units are non-dividable intervals, it follows from Craig's arguments that there is a first interval I(0), and a corresponding first temporal state of the world T(0). Similarly, there is I(1), T(1), etc.

5) A contradiction in the Big Bang Theory?

No, of course there is no contradiction in the Big Bang Theory.

However, I've encountered the objection that, allegedly, my reasoning to a contradiction proves too much, since it would make any change from a timeless state contradictory, and that would make the Big Bang Theory contradictory, since the initial singularity has been seen as timeless.

Now, the Big Bang is a hot, dense state of the universe that existed about 13.7 billion years ago. There is no point of infinite density (what would that even mean?), or actual singularity, or a 'timeless' state. We should not confuse a singularity in a mathematical model with reality.

Also, even if a model – like the one Craig mistakenly beliefs supports the KCA – adds an initial point – say, a time t=0 -, that should not be seen as existing in reality. Indeed, the model does not allow a way out of the singularity.

That said, let's consider the issue of the contradiction:

Even if we assume that there is an initial singularity of infinite density – whatever that might mean, but that's not even defined -, and that such singularity is timeless – whatever that might mean; also, not even defined -, the reasoning by which I derived a contradiction before doesn't work in this case.

In my reasoning, I define the following event/change:

By 'P(2)' I mean the property of knowing at least one tensed truth.

By 'E(2)' I mean the event/change 'God changes from not having P(2) to having P(2) for the first time'.

That assumes that there is a first temporal state at which God has property P(2), namely T(0)

As I showed earlier, in the previous section, I'm justified in assuming that there is such a T(0) in order to derive a contradiction from Craig's position because that follows from Craig's own position.

Someone might try to define an event 'the universe changes from timeless to temporal', and argue that the change has duration zero, because it begins at the timeless state, and has already ended at any time 1/n, for any natural n.

However, in that case, the change/event does not have an endpoint. It's fuzzy. Being 'temporal' is not a state of the universe, but a beginningless sets of states, for all t>0. Without an endpoint, the reasoning by which I derived a contradiction is blocked.

6) Continuous time and continuous changes

Another objection that might be raised would also hold that my argument to a contradiction, if correct, would prove too much. The objection would go as follows:

Let's assume that time is continuous, and so are changes in the universe.

That might or might not be true, but it is not contradictory.

So, let's pick any specific point in time, say t(3), and lets define the following event:

E(t(3)): The universe changes from its state S(t(3)) at t(3), to no longer being at state S(t(3)).

Now, what's the duration of E(t(3))?

Since the changes of the universe are continuous and happen all the time, then E(t(3)) has already happened at (t(3) + 1/n seconds), for all natural numbers n. Hence, the duration of E(t(3)) is literally zero. Since E(t(3)) begins at t(3), and its duration is literally zero, its endpoint is also present at t(3). So, at t(3), it is not the case that the universe is at state E(t(3)). That is a contradiction. So, this reasoning must be flawed, since it would derive a contradiction from continuous time plus continuous changes, but continuous time plus continuous changes is not contradictory.

However, there is no endpoint in this case. In fact, 'no longer being at state S(t(3))' is not actually a state of the universe, but a beginningless set of ordered states.

So, E(t(3)) is a sort of a fuzzy event. If we can say that the duration is zero because there are states S(t), with t>t(3), and arbitrarily close in time to S(t(3)), then fact is that there would be no initial point and end point at the same time, since there is no endpoint of the fuzzy event, and so that does not result in a contradiction.

7) Timeless change?

Perhaps, Craig or someone else might then claim that the change I use to derive a contradiction – and it is a change, in the usual sense of the word 'change' in English – does not have either a zero duration, or a non-zero duration, but somehow it's a timeless or partially timeless change, and somehow for that so-called 'reason' one shouldn't speak of duration of them.

But if they did that, I would first point out that Craig claimed that the first cause is – at least in his timeless state, 'sans the universe' -, changeless.[9]

How could then that change be 'timeless' or 'partially timeless'? What would that even mean?

Also, Craig claims now that the changes I'm talking about are 'instantaneous'.

What does Craig even mean, then, by 'instantaneous', if not 'having a zero duration'?

But let's leave the matter of what he meant by that aside.

Essentially, the crucial point is that Craig applies the label 'timeless' to name a scenario that actually should be characterized as God's existing at t=0, with a temporal beginning but without a cause, and then creating the universe at the next temporal instant.

By calling the state in question 'timeless' - instead of 't=0' -, Craig is denying that the state is temporal, from the description of the state and Craig's arguments in the context of the KCA, one can see that it has all of the features of an initial temporal state; in other words, it would be an initial temporal state, which would change into a second temporal state, and that change of course takes time.

So, in particular, Craig's creator, if he existed, would in fact be an entity that has a beginning in the first temporal state of the world, but no cause, contradicting the first premise of the KCA.

I will show this in the next two subsections:

7.1) Discrete time

In this subsection, I will prove that Craig's arguments entail that time is discrete, in the following sense:

a) If the units of time are instants, then for every two times t and u such that t < u, there are only finitely many instants in time between the two. Models may contain infinitely many ones, but there are only finitely many actual instants.

b) If the units of time are intervals, then for every temporal interval [a,b], there is some non-negative integer N(a,b), such that [a,b] cannot be divided into more than N(a,b) smaller consecutive temporal subintervals.

I will give proofs by contradiction in both cases.

a) Instants:

Let's assume, that God exists, a tensed theory of time is true, and that there are infinitely many actual instants between times t and u, where t < u.

Then either there is an increasing sequence, or a decreasing one.

Let's say there is an increasing sequence, for all natural n:

t < t(n) < t(n+1) < u

Let's consider the following sequences of actual events/changes.

G(n): God changes from not knowing that t(n) is present, to knowing that t(n) is present.

Note that those are actual changes in God's mind.

While it's true that those are not changes of equal duration (if they even have a duration), that is orthogonal to the matter at hand, which is the fact is that those are all actual changes experienced by God's mind.

Since at time u or later, every single one of those changes G(n) has occurred (i.e, for all n, G(n) has occurred), then the number of ordered actual changes in God's mind that are in the sequence is ℵ_0.

Now, the events {G(n)} would be a case of an actual infinity, according to Craig's position, since the events are actual [1], and Craig's arguments are incompatible with an actual infinity, and in particular with infinitely many actual events, one after then next.

For instance:

William Lane Craig: [8]

The second premise states that an infinite temporal regress of events is an actual infinite.

The point seems obvious enough, for if there has been a sequence composed of an infinite number of events stretching back into the past, then the set of all events in the series would be an actually infinite set.

Clearly, that does not depend on the length of the events, as long as they're actual changes in the world.

William Lane Craig:[8]

So when we say that the number of past events is infinite, we mean that prior to today, ℵ₀ events have elapsed.

Once again, that does not depend on the length of the events. And Craig goes on to claim that ℵ₀ events are impossible.

William Lane Craig:[8]

Because the series of past events is an actual infinite, all the absurdities attending the

existence of an actual infinite apply to it. For example, if the series of past events is actually

infinite, then the number of events that have occurred up to the present is no greater than

the number that have occurred at any point in the past.

While Craig was talking about events of equal length, that is not relevant to whether or not they're actually infinite; indeed, if the previous paragraph actually showed any absurdity, that would be so regardless of whether the events are of equal length.

The case of a decreasing sequence is essentially the same.

So, if the temporal units are instants, Craig's arguments entail that time is discrete.

b) Intervals

Let's consider, then, the case of intervals, not instants.

Let us assume that for an interval [a,b], there is a strictly increasing sequence m(n), for all n, such that for every n, [a,b] can be divided into m(n) different actual, smaller intervals, one before the next.

So, for each n, let's divide [a,b] on m(n) intervals I(1,n)<I(2,n)< ...<I(m(n),n), where '<' denotes the 'earlier than' relation.

Then, let us consider, for every n, and for every k in {1, 2, ...m(n)}, the following distinct, actual events/changes:

J(k,n): God changes from not knowing that I(k,n) is present to knowing that I(k,n) is present.

The crucial question is:

How many distinct actual events/changes happened in the world during the temporal interval [a,b]?

In yet other words, assuming that there weren't more distinct actual events/changes than any cardinality – else, we're through -, what is the cardinality of the set of distinct actual changes that happened in the world during the temporal interval [a,b]?

If the answer is that the number is finite, then let p(0) be that number.

Then, we may consider the distinct actual changes J(k,m(p(0)+3)) (for instance), for all k in {1, 2, ..., m(p(0)+3)}, reaching a contradiction.

So, the number of actual changes in [a,b] is at least ℵ₀.

However, that's incompatible with Craig's arguments.

Hence, if the temporal units are intervals, Craig's arguments entail that time is discrete.

An immediate corollary is that every interval that is dividable into smaller subintervals, is dividable into finitely many smaller subintervals such that each of them is not, in turn, dividable into any smaller subintervals.

To see this, let [a,b] be an interval that is dividable into smaller subinterval. Then, there is a natural number N(a,b), such that [a,b] cannot be divided into more than N(a,b) smaller subintervals. Let's divide [a,b] into the maximum number of subintervals into which [a,b] can be divided. Then, each of those subintervals is non-dividable into smaller ones.

7.2) No ontological difference – God vs. God and God vs. the universe

Let's consider the following two scenarios, ordering the states in terms of causal priority.

Scenario 1:

First state of the world:

Timeless state S.

The only object is God, which exists timelessly at S and without a cause.

Second state of the world:

First temporal state T(0).

God exists temporally, and the universe exists. The change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because God intends to bring it about.

Third state of the world:

Second temporal state T(1). The objects are God, the universe, and perhaps some other objects.

Scenario 2:

First state of the world:

First temporal state T(0).

The only object is God, who exists temporally at T(0) and without a cause.

Second state of the world:

Second temporal state T(1).

Third state of the world:

Third temporal state T(2). The objects are God, the universe, and the same other objects as in the previous scenario (if any), with the same causes.

The key point here is that the so-called 'timeless' state in scenario 1 is exactly like the first temporal state T(0) in scenario 2. In other words, there is no ontological difference whatsoever, even if different words are used:

In both cases, what we have is a first state of the world changing into the next, and so on.

In both cases, God exists without a cause of his existence at the first state of the world.

In both cases, the universe exists at the second state of the world, and exists because God intends to bring it about, and so on.

Also, saying that the difference between the two scenarios is that one state – namely, S in scenario 1 – is timeless and the other – namely, T(0) in scenario 2 – is temporal, or that in one of them there at least one tensed fact, whereas in the other one there are no tensed facts, would fail to address the point, since that would simply amount to denying that there is no ontological difference, without explaining how or why that is so, which is a burden on the theist defender of the KCA, since we can conclude that the states are ontologically identical, just by looking at the description of those states, and regardless of the use of the word 'timeless' in the first one.

Someone might say that God in scenario 1 is changeless, but not in scenario 2. However, that is not the case: just as God changes from his first to his second state in scenario 2, he does so in scenario 1.

So, it remains the case that there is an entity – i.e., God – that exists at a first state of the world and without a cause of his existence, changes to a second state, then to a third one, etc., regardless of whether the first state of that entity is called 'timeless'.

Alternatively, someone might raise the following objection:

An ontological difference is that temporal states of God must change as time goes by, whereas the timeless state S in scenario 1 could have remained unchanged. In other words, if God exists at temporal state T(0) – as in scenario 2 –, then necessarily, there will be a second temporal state T(1), and necessarily, God will change from T(0) to T(1), since his knowledge of tensed truths will change. On the other hand, if God exists in a timeless state S (as in scenario 1), then it is possible, given that first timeless state of God, that God never changes.

The problem with that objection is that it follows from any creation hypotheses posited by theist defenders of the KCA – i.e., given what God's first state actually would be, based on the implications of their claims –, that it is impossible that God never changes given that first state, which means both scenario 1 and scenario 2 are indistinguishable in that regard as well, as the following reasoning shows:

Scenario 3:

First state of the world:

Timeless state S. The only object is God, which exists timelessly at S and without a cause.

Second state of the world:

Temporal state T(0). God exists temporally, and the universe exists. The change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because of God intends to bring it about.

Scenario 4:

First state of the world:

Timeless state S. The only object is God, which exists timelessly at S and without a cause.

There are no temporal states of the world.

In scenario 3, if God does not intend at S to change from timeless to temporal, then at T(0) God just found himself altered. In other words, if God's intent to change does not exist at at S, then the change is not something brought because God intends to bring it about, but something that happened to God, beyond his intent. That is so because the change under consideration is a change in God's state, and from his first state at S. In other words, it's a change from S to T(0). So, said change cannot have been caused by God's intent only at T(0), given that S is causally prior to T(0).

So, if God does not intend at S to change from timeless to temporal, then God found himself changed at T(0); the change is something that happened to God, not something that God brought about. But that contradicts the hypothesis that the change in scenario 3 happens because God intends to bring it about. Thus, at S, God intends to bring about his change from timeless to temporal.

Hence, given God's state at S in scenario 3, it is impossible that God does not change, since God can't fail to bring about what he intends to bring about. Moreover, just as in scenario 3 it is impossible that God does not change, the same is true and for the same reasons in scenario 1. Also, the states denoted by 'S' in scenario 3 and scenario 4 respectively, are not the same.

Someone might suggest that, in scenario 3, God exercised his libertarian free will at T(0) to bring about the change, but at S, he does not intend to change. However, leaving aside issues about the coherence of libertarian free will, that is impossible for the reasons I explained above: since the change under consideration is God's change from S to T(0), it cannot have been decided only at T(0). At T(0), the change already obtains. Also, the state S is causally prior to T(0), so a change in God's condition at S cannot have been decided only at T(0). Thus, as concluded above, at S God intends to change from timeless to temporal.

So, the reasoning above shows that, once again, the theist fails to make an ontological difference between scenario 1 and scenario 2.

Since God's first state in scenario 2 is a temporal state, it follows that the same is true of God's first state in scenario 1 – and, for that matter, in scenario 3 -, and that both scenario 1 and scenario 3 should be corrected, and the first state should not be called 'timeless'.

Someone might concede that there is no ontological difference between scenario 1 and scenario 2, but raise an objection and claim that in that scenario God exists timelessly at his first state. So, according to this objection, the right conclusion is not that both scenario 1 and scenario 3 should be corrected, and the first state should not be called 'timeless', but rather, that scenario 2 should be corrected, and the first state of God should be called 'timeless'.

The objection fails, though, since the first state of God in scenario 1 and scenario 2 changes to the second one, just as the second state changes to the third one, and so on, so there is no quiescent or changeless state of God.

The fact that the first state is not preceded by other states is not relevant when it comes to the fact that it changes to the second, just as the second changes to the third, without any period of quiescence or lack of change. So, there is no changelessness or quiescence. But no changelessness or no quiescence entails no timelessness, by the way in which Craig uses the word 'timeless' - assuming, as usual, that he means something by it – and so the first state of God in scenario 1, scenario 2 and scenario 3 should not be called 'timeless' at all.

In any event, we do not even need the previous result, in order to show that positing a creator that is in some mysterious sense – or it seems an incoherent 'sense', but that aside -, 'timeless' sans the universe, but temporal with the universe, will not help theism. So, if a theist insists, against very good reasons, that the first state in scenario 1 is timeless, then we may simply posit, as an alternative, that the universe might as well exist without a cause if its existence at a first state of the world, then change to its second state, and so on. If the first state of God is somehow is properly called 'timeless' in scenario 1, then due to a lack of a relevant difference, the same is true of the first state of the universe in the following scenario:

Scenario 5:

First state of the world:

The universe exists without a cause of its existence. Nothing else exists – there may or may not be some things in the universe, but nothing beyond the universe.

Second state of the world:

The universe has changed and exists in its second state. Nothing else exists.

Just as God exists without a cause in scenario1, scenario 2, and scenario 3, the universe exists without a cause in scenario 5.

Just as God changes from the first to the second state of the world in scenario1, scenario 2, and scenario 3, the universe so changes in scenario 5. Then, God in those scenarios continues to change from one state of the world to the next, and the same is true of the universe in scenario 5.

Thus, there is no ontological difference between scenario1 and scenario 2, and no ontological difference that would justify denying that the first state of God is temporal in either scenario, but wouldn't justify denying that the first state of the universe is temporal in scenario 5.

Someone might bring up 'quiescence', as an attempt to show that there is a difference between scenario1 and scenario 2, and/or that there is a difference that would justify denying that God is temporal at his first state in scenario 1, but would not justify denying that the universe is temporal at its first state in scenario 5. On that note, and in an attempt to distinguish between the universe and God, Craig makes the following claim:

William Lane Craig: [4]

If not, then since the universe cannot ever have existed in an absolutely quiescent state, the universe must have had a beginning.

However, a 'quiescent' objection fails as well, for the following reasons:

First, as I explained earlier, there is no sense in which the first so-called 'timeless' state S in scenario 1 is quiescent, but the first temporal state T(0) in scenario 2 is not. Indeed, in both cases, what we have is one first state of affairs that changes into another, second state of affairs. In both cases, God exists at the first state of the world, and without a cause of his existence. In both cases, also, God changes from his first state at the first state of the world, to the second, and so on. God never remains unchanged for a while in the first scenario but not the second- that would require time -, or differs in any way between the scenarios, by the description of them.

Second – and now addressing Craig's contention about the universe -, the same can be said about the universe in scenario 5: in that scenario, the universe exists at the first state of the world, and without a cause of its existence. Also, the universe changes from its first state at the first state of the world to its second state at the second state of the world, there is no previous change, and no period during which the universe remains unchanged. But that is exactly what happens in the case of God in scenario 1.

Moreover, if, say, a particle exists in the universe at the first state in scenario 5, then any change in such particle from the first to the second state of the world is still a change from the first to the second state of the universe. There is no previous change, or period during which the particle or the universe remains unchanged, but that is exactly what happens in the case of God in scenario 1.

Thus, there is no sense in which God could properly be described as 'quiescent' at his first state in scenario 1, but the universe couldn't properly be described as 'quiescent' at its first state in scenario 5.

As another objection, someone might say that in scenario1 and scenario 2, the change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because God intends to bring it about, whereas in scenario 5, the cause of the change is not specified. That is completely unrelated to the issue of whether God or the universe are 'timeless', changeless, quiescent, etc., but in any case, we may as well further specify the scenario and add that, in scenario 5, the change from the first to the second state of the universe is brought about by the universe's conditions at its first state (including, of course, any particle interactions if there are any, etc.), regardless of whether we put that in terms of substances and causal powers, or in terms of substances and laws, etc. Thus, the universe, which has certain conditions in its first state, brings about the change to its second state, just as God and his intent at the first state brings about the change in scenario1 and scenario 2 (and, for that matter, scenario 3).

This further specification of scenario 5 is not required, though: we might as well leave it unspecified, or alternatively even make the change indeterministic in scenario 5, so that given the first state of the universe, there is more than one possible second state, and only one actually obtains, introducing a certain degree of randomness. That would not make any difference whatsoever in terms of changelessness, quiescence, or anything that might be called 'timelessness'.

All that aside, a theist defender of the KCA might suggest that, perhaps, the universe did not exist at the second state of the world, but only at some later state. However, that clearly wouldn't make a difference, either. We may simply posit scenarios like, say, scenario 1, 2, and 3, but without introducing the universe at the second state of the world, and keep scenario 4 and scenario 5 unchanged. The same reasoning as above yields the same results, defeating the attempt to make a distinction.

So, to summarize, if God does not begin to exist in scenario 1 because somehow he's 'timeless', 'changeless' and/or 'quiescent', then the universe does not begin to exist in scenario 5 for the same reasons, and the KCA fails, since the proponent of the KCA does not have any argument to rule out something like scenario 5.

If, on the other hand, God begins to exist in scenario 1, then the KCA fails for that reason.

The previous considerations are sufficient to show that no current version of the KCA provides any support for theism. For the sake of thoroughness, though, in the next sections, I will raise other objections, which on their own suffice to show that no version of the KCA provides any support for theism, independently of the previous arguments.

However, and before moving on to those other objections, I will add another subsection to this section, dedicated to an even more detailed analysis of the comparison between God and the universe, when it comes to beginning of existence.

While the previous considerations in this subsection are enough to establish the failure of the KCA – as explained above -, I've found a very misguided but very persistent theistic objection involving causation, freedom and indeterminism, which shows a serious misunderstanding of the arguments given earlier in this subsection, in addition to a mistaken conception of freedom.

There is no need for a refutation of the conception of libertarian freedom, so I will leave such a refutation for later, and dedicate the next subsection to a detailed comparison of God and the universe, in terms of beginnings, trying to clarify any points that remained unclear in this section, and addressing the issue of freedom only in the context of the scenarios under consideration, but in considerable detail as well.

7.3) No ontological difference – God vs. the universe, in even greater detail

Let's consider the following scenarios, ordering the states of the world in terms of causal priority:

Scenario 5:

First state of the world:

The universe exists without a cause of its existence. Nothing else exists – there may or may not be some things in the universe, but nothing beyond the universe.

Second state of the world:

Temporal state of the world. The universe has changed and exists in its second state. Nothing else exists.

Scenario 6:

First state of the world:

Timeless state of the world. God exists without a cause of his existence.

Second state of the world:

Temporal state of the world. God exists and the universe exists. God is the creator of the universe.

In this subsection, I will show that Craig's arguments, or similar theistic arguments, fail to support the contention that even though the first state of God in scenario 6 is a timeless state – assuming here that 'timeless' is meaningful -, the first state of the universe in scenario 5 would be a temporal state, and the universe would be something that has a beginning – i.e., something that begins to exist – but not a cause of its existence.

More precisely, Craig and other theist defenders of the KCA claim that the universe began to exist, and that everything that begins to exist has a cause of its existence, concluding that the universe has a cause of its existence. Also, they posit God as the cause of the existence of the universe, but deny that God began to exist, claiming that he is timeless sans the universe. I will show that Craig and others do not have any good reasons at all to make that distinction and claim or imply that God is timeless sans the universe, but the first state of the universe would be temporal in scenario 5.

Given that they do not explain what they mean by 'timeless', I will assess their claims based on their assertions about the properties of timeless objects, more precisely changelessness and quiescence.

7.3.1) Quiescence and changelessness

In scenario 6, God changes from his first state – at the first state of the world -, to his second state – at the second state of the world. God does not remain unchanged for a while – which would require time.

He changes from the first state to the next. That is precisely what happens in the case of the universe in scenario 5.

There is no need to posit that there are particles in the first state of the universe in scenario 5. However, that would make no relevant difference, either: If we assume for the sake of the argument that there are particles at the first state of the universe in scenario 5, then any change in any particle is still a change in the universe from its first to its second state. That's precisely what happens in the case of God, who changes from his first to his second state.

It is true that, in scenario 6, there is no change in God prior to the change from his first to his second state – obviously -, but the same is true of the universe in scenario 5 – also, clearly.

So, it is not the case that God can properly be called 'changeless' at his first state in scenario 6, but the universe can't properly be called 'changeless' at its first state in scenario 5, and it is not the case that God can properly be called 'quiescent' at his first state in scenario 6, but the universe can't properly be called 'quiescent' at its first state in scenario 5.

Moreover, while the previous reasoning in this subsection is sufficient to show that theist defenders of the KCA fail to make a relevant distinction between scenario 5 and scenario 6, an even stronger case can be made: namely, we can see from the previous reasoning that the proper characterization of the first state of the universe in scenario 5 and the first state of God in scenario 6 is that such states are not changeless or quiescent.

This is clear from the fact that, say, the first state of God in scenario 6 changes to the second one, just as the second state will change to the third one, and so on.

The fact that the first state is not preceded by other states is not relevant when it comes to the fact that it changes to the second, just as the second changes to the third, without any period of quiescence or lack of change. So, there is no changelessness or quiescence. But no changelessness or no quiescence entails no timelessness, by the way in which Craig uses the word 'timeless' - assuming, as usual, that he means something by it, which by now appears extremely doubtful – and so the first state of God in scenario 6 should not be called 'timeless' at all.

Still, leaving the stronger results aside for now, given that the first state of the world in scenario 6 is by assumption timeless, let us posit that the first state of the world in scenario 5 is timeless as well.

Then, objections based on an alleged lack of quiescence or changelessness of the universe fail, since there is no difference between scenario 5 and scenario 6 in terms of quiescence or changelessness. Since there appear to be no other objections to the timelessness of the universe at its first state, the theistic case fails.

7.3.2) Causation

Given the results of subsection 7.3.1), we may as well stop at that.

Also, it seems clear that what caused the change from the first state to the second state in God has nothing to do with whether the first state of God is a beginning of existence of God, and the same goes for the universe. That seems clear by the meaning of the expression 'begins to exist'.

Still, and just for the sake of the argument, I will address the matter of causation in the rest of this subsection.

7.3.2.1) God's change, causation, and the change in the universe

In scenario 6, God changes from timeless to temporal

If God's intent to change from timeless to temporal does not exist at the first state of the world, then at the second state of the world, God found himself changed.

Since nothing else was there to cause the change, then God's change was random.

Someone might say that God only exercised his freedom and chose to change only at his second state, so the change wasn't random even if God's intent to change did not exist at the first state of the world.

However, the first state of the world is causally prior to the second one, so a change in that first state of the world cannot have been caused merely by something that only existed at the second state of the world.

Since the first, timeless state of God obtains at the first state of the world, the cause of the change in God from timeless to temporal must have existed at that first state of the world, unless the change was random and God found himself changed and temporal.

So, the possibilities are that either God changed randomly and found himself changed and temporal, or that God's intent to change existed at the first state of the world in scenario 6.

But clearly, the non-theist can match that:

For instance, if God's intent to change from timeless to temporal existed at the first state of the world in scenario 6, we may posit as an alternative scenario that sufficient conditions to bring about a change in the universe from a first state to a second state also existed at the first state of the world in scenario 5.

To be clear, we don't need to take a stance on whether, in scenario 5, the change would be deterministic.

We may suggest, as a possibility, that the conditions at the first state of the world in scenario 5 were sufficient to bring about a specific second state of the universe (i.e., deterministic change).

We may also suggest, as an alternative possibility, that the conditions at the first state of the world in scenario 5 were only sufficient conditions to guarantee that one of, say, n different potential second states of the universe would come to obtain, but which one of those states actually obtains is not determined by the conditions at the first state of the world.

That is all compatible with scenario 5, so we have options.

So, if a theist claims that non-determinism in the change from the first to the second state is required for the first state to be timeless, he would have the burden to explain why that is so.

However, even if we assume that indeterminism in the change from the first to the second state is required for the first state to be timeless, we may still posit a timeless first state of the universe, which would be indeterministic. In fact, there already are indeterministic interpretations of Quantum Mechanics (QM), so why not an indeterministic first state of the universe?

So, even showing that indeterminism is required for timelessness would be a dead end for the theist.

That said, and before I move on to the next subsection, I would like to reiterate that I'm merely assuming for the sake of the argument that defenders of the KCA mean something by 'timeless', and applying the conditions for timelessness they suggest or might suggest. However, there seems to be no good reason to think that they're using the word 'timeless' meaningfully.

Furthermore, and regardless of whether they're using 'timeless' meaningfully, it seems apparent – just by the meaning of the words – that whether the universe in scenario 5 or God in scenario 6 begins to exist at the first state of the world has nothing to do with whether any change from the first to the second state of the world is determined by the conditions at the first state. In other words, the issues of beginning of existence and non-determinism are orthogonal. Still, even if they weren't, that would not help the theist's case, as I explained above in this subsection, and as I will further address in the next subsection.

7.3.2.2) Free will, determinism and indeterminism

As we saw in the previous subsection, an indeterministic first state is not a difficulty for non-theists, though there is no good reason to assume that if there were such a first state, it would be non-deterministic.

After all, it is clear by the meaning of the words that whether the universe in scenario 5 or God in scenario 6 begins to exist at the first state of the world has nothing to do with whether any change from the first to the second state of the world is determined by the conditions at the first state. Any ambiguity in the concept 'begins to exist' is clearly not connected to whether the change from the first to the second state is deterministic.

That aside, let's assume – at this point, clearly against good reasons – that somehow in order for the universe not to begin to exist in scenario 5, it is required that the second state of the universe not be determined by the conditions of the first state.

As I mentioned, there are non-deterministic interpretations of Quantum Mechanics, so a non-theist may simply suggest, as a possibility that defenders of the KCA have failed to refute, a non-deterministic first state of the universe in scenario 5.

So, according to this, given the conditions at the first state, there are a number of potential second states, even though in the end, only one of them came to obtain.

An objection that a theist might raise here would be something like the following:

Why, then, the universe changed to the state that it did, rather than one of the other states? Is that random? Theists do not have that problem, since God has free will, and can choose indeterministically without randomness.

Actually, free will does not entail non-determinism, and libertarianism is not the correct understanding of free will, as I will show later. So, this objection is based on a misunderstanding of what freedom is.

But that aside, this objection would be an objection to any non-deterministic interpretations of QM, not just to a non-deterministic first state of the world.

The matter of determinism vs. non-determinism does not appear to be settled, and it would be up to the theist to show that non-deterministic interpretations of QM are not true. To be clear, suggesting that they might not be true is not enough. The theist would need to provide enough reasons to conclude at least that non-deterministic interpretations of QM are probably false, if he wants to make a case against an initial non-deterministic state of the universe.

Another potential theistic objection might go as follows:

Why is it that the first state only allows for a certain number of second states? Why not anything? Theists have an answer: God can freely choose to bring about a certain universe, but he will choose something good, because of who he is.

Even leaving aside problems such as the Evidential Problem of Evil, Problem of Suffering, Problem of Divine Hiddenness, etc., as direct objections to God as a creator of our universe, a problem with the theistic objection above is that the theist is assuming that there is a creator with a certain psychological makeup. Surely, the non-theist may as well suggest as a possibility – without even having to commit herself to that – a first state of the universe with certain properties that constrain the possible second states.

7.3.2.3) Agents acting 'in and of themselves'?

Another objection I've encountered holds that scenario 5 should be rejected because only free agents, as far as we know, can act 'in and of themselves', start new causal chains, act 'without being caused to do so', etc., and the universe is not a free agent, but God is.

This is not an objection to a claim that, in scenario 5, the universe is timeless at its first state, but rather, it's an objection to the possibility, or at least the plausibility of something like scenario 5.

This objection confuses causation with lack of freedom, and holds that an agent whose decisions are caused by previous states of herself would somehow not be free because it would be 'caused to act'.

A way to refute this objection is to show that libertarian freedom is a mistaken conception of freedom, which I will do later.

In this subsection, however, I will deal with this objection on different grounds:

First, as explained in subsection 7.3.1), the proper conclusion is not that both the first state in scenario 6 and in scenario 5 are timeless, but rather, that neither of them is, and that the assumption that the first state in scenario 6 is timeless is false – assuming that 'timeless' is meaningful at all.

Indeed, all the attempts of showing changelessness or quiescence failed. That is enough to block all present-day versions of the KCA, regardless of any other matters.

Second, leaving that aside, theist defenders of the KCA have not refuted non-deterministic interpretations of QM, which would include states of affairs not determined by previous ones, without involvement of any agent.

It is true that, in all the cases we've encountered, those states of affairs require at least some non-deterministic previous conditions, but surely the same can be said about any decisions made by any agents we're familiar with, even if we assume that such agents are non-deterministic.

Third, even if we had evidence that humans are non-deterministic, we certainly do not have any evidence of humans or any other agents existing without any causes of their existence.

It's true that we don't have evidence of any beings or states existing without any previous states, either, but the point is that even in scenario 6, the theist is positing something that has nothing to do with our experiences of causation, or beginnings of existence.

Moreover, if we can nevertheless use the evidence that we do have as a means of trying to ascertain whether a first cause would plausibly be a personal being, we can point out the following:

The non-theist observes that, as far as she can tell, all of the causes of us which existed two billion years ago are non-agents, and that as far as she can tell, everything that exists can be traced back, deterministically or not, to only non-intelligent causes. There is no good reason for her to come to believe that if there is a first cause at all, it's more plausible that a first cause would be intelligent.

All that aside, as I mentioned, I will refute the 'in and of themselves' objection on different grounds later, when I refute the libertarian account of freedom.

Now, let's move on to other, very different objections to the KCA.

8) The meaning of 'begins to exist'

First, let's compare Craig's hypothesis about the meanings of 'begins to exist' and 'comes into being'[11], with an alternative hypothesis AH1, and test the two hypothesis to see which one is closer to matching the meaning of the words:

AH1

A. x begins to exist at [t1,t2] iff there is a finite closed interval [t1,t2] such that x does not exist at any time prior to t1, and x exists at t2.

B. x comes into being iff there is an event – that is, change – from a state of affairs at which x does not exist, to a state of affairs at which it does.

Here, "x"is just as in Craig's hypothesis – i.e., it can be any being -, and 0 ≤ t1 ≤ t2.

As for the interval [t1,t2], an interval seems to be required because otherwise, there might be a problem in cases of vagueness: e.g., there may not be a specific instant t such that the Moon existed at t, but at no u < t: the word "Moon" may be too vague for that.

That also seems to be in line with common speech: when we say that something began on a day, or a year, etc., we're considering intervals, not instants. Even when we speak in terms of seconds, or millisecond, we're speaking in terms of intervals, even if very short ones.

Under a tensed theory of time, everyday examples will not help us test one vs. the other, since both hypotheses yield the same results. However, under a tenseless theory of time, the difference is striking:

Let's assume a tenseless theory of time, and let's consider, for instance, Napoleon.

It seems clear that, even if the past, present and future exist tenselessly, there is a time at which Napoleon did not exist, and a later time at which he did.

So, it seems that he came into being, and began to exist. That's in line with hypothesis AH1.

On the other hand, under Craig's hypothesis, assuming a tenseless theory of time, nothing begins to exist, and nothing comes into being. In particular, Napoleon neither came into being, nor began to exist. But that seems clearly conceptually wrong. In fact, the questions of whether a tensed theory is true and whether Napoleon came into being, or began to exist, appear to be orthogonal.

It seems rather odd that Craig would include tense in the definition of "begins to exist", but he argues that, under a tenseless theory of time, a universe with a first event did not begin to exist just as a meter stick does not begin to exist just because it has a first centimeter.[12]

That argument is odd as well, though:

While a meter stick does not begin to exist in virtue of having a first centimeter, that's not relevant, since having a first centimeter is a spatial, not a temporal claim, while "begins to exist" - at least, in this context – is clearly about time, not space.

In fact, the stick in question does have a beginning in space because it has a first centimeter, and similarly, even if a tenseless theory of time is true, the stick does have a beginning in time as long as there is, say, a first year at which it exists.

It is true that, in order for us to say a year is first, we need to pick an order in time – from past to future, not the other way around, but that direction is actually implicitly built-in hypothesis 2, and in our language about time.

Also, to say that the stick has a spatial beginning require that one picks a direction in space to say which centimeter is first – in this case, explicitly or by context.

A difference is that, in the case of space, one needs to pick the direction explicitly or by context, whereas in the case of time, it's built in the meaning of the words, but that does not appear to be relevant to the point that there is a beginning.

Since to say that the stick begins to exist – in the sense that's relevant in the context of the KCA, at least – is the same as to say that the stick has a temporal beginning, or a beginning in time, then it follows that the stick does begin to exist, even on a tenseless theory of time.

Then, it seems to me that hypothesis AH1 gives the right result, whereas Craig's hypothesis does not.

Let's consider a different scenario; scenario S1:

Let us suppose that there is a t=0, and an entity B that exists at t=0. Let us suppose that there is no time earlier than t=0. Let's further suppose that there is no state of the world at which B does not exist, and the actual world does not contain any timeless states of affairs whatsoever, or any kind of two-coordinates time, or undifferentiated time, or any such temporally counterintuitive state of affairs[13].

Does B begin to exist?
Does B come into being?

According to Craig's hypothesis[11], if a tensed theory is time is true, then B begins to exist and comes into being, whereas if a tenseless theory of time is true, then B neither begins to exist nor comes into being.

On the other hand, according to hypothesis AH1, regardless of the tensed vs. tenseless issue, B does begin to exist, but does not come into being.

Readers will use their own intuitive grasp of the words, of course, but mine tells me that hypothesis AH1 gives all the right results again: to come into being seems to entail that there is a state at which the entity in question does not exist, followed by one in which it does, whereas to begin to exist seems to indicate an initial time or moment of existence.

I don't know whether hypothesis AH1 is entirely accurate, but it does seem to be much closer to capturing the meaning of the words than Craig's hypothesis[11].

Another alternative (say, hypothesis AH2) would be just like hypothesis AH1 but allowing open and semi-open finite intervals.

Hypotheses AH1 and AH2 given the same verdict in daily cases, under either a tensed or a tenseless theory of time, but there would be a difference in, say, open models of the universe with a metric-finite past, assuming an intrinsic metric.

In any case, both alternatives seem to fare much better than Craig's hypothesis, at least in all the cases tested above – in which both hypotheses AH1 and AH2 seem to give the right results, but Craig's does not.

In addition to that, it seems clear that, when people ordinarily says 'begin to exist', they're not making obscure claims about timelessness – which, if coherent at all, does not seem to be a concept that most people even grasp.

So, it seems clear that Craig's hypothesis about the meaning of 'begins to exist'[11] is false.

It's true that Craig might simply stipulate what he means by 'begins to exist', rather than making a claim of meaning, and someone might suggest that Craig is doing merely that.

That doesn't look like that to me – though I would grant that Craig is rather obscure -, but there is no need to get into that: Even if Craig merely stipulated what he means by 'begins to exist', or even if he presented a hypothesis and we assume – against good reasons, as explained earlier in this section – that such hypothesis [11] is true, his arguments fail to provide support for either the first or the second premise of the KCA, as the following sections will show.

9) The first premise of the KCA

Let's turn now to the question of whether there are good grounds for believing that everything that begins to exist has a cause.

William Lane Craig maintains that the first premise, namely the claim that everything that begins to exist has a cause, is intuitively clear. Moreover, he claims that there is empirical confirmation of that.

He tries to back up that claim by appealing to our intuitions about causation – what he calls "metaphysical" intuitions -, and by bringing up scenarios that purportedly show the absurdity of denying it, such as, say, horses popping into existence uncaused. [14]

However, all of those scenarios would also be a case of denying other candidates to being intuitive principles, such as the principle that every event/change of the form "B comes into existence" - or, more generally, every event/change – has a cause.

So, let's consider the following alternative principle:

AP1: Every event (i.e., every change) has a cause of why it happens.

In other words, someone may not accept that everything that begins to exist has a cause, while accepting that, for instance, every event/change has a cause. They don't need to actually deny that everything that begins has a cause, but simply not affirm it.
Actually, AP1 is also debatable, and I'm not suggesting that we ought to accept it, but the point here is that it's an alternative that avoids any of the issues raised by Craig, and – at least to me – it seems more intuitive, so if we are to accept a principle, AP1 seems good enough.

That would not commit us to assuming that only events/changes have causes, of course – just as Craig does not assume that only that which begins to exist has causes -, but that's beside the point.

The point is that this is an intuitive alternative (though still debatable), and that none of the scenarios that Craig brings up – like a horse coming into existence uncaused – would present any problem for that position, since that position holds that events/changes would not happen without a cause.

On the other hand, using Craig's definition of 'begins to exist'[11], the issue of 'timelessness' alone is a serious problem: without a good understanding of what that even means, plus good reasons to adopt it, there appears to be no justification for believing that kind of principle that Craig proposes, even if we assume that the claim is coherent – which we don't have sufficient reasons to believe.

Still, there is no need to settle the matter of what 'begins to exist' mean. Let's consider the following definition of 'temporal beginning'.

TB: X has a temporal beginning if and only if:

a) X exists at some time t, and has existed for a finite amount of time before t (zero counts as finite).

b) If 'timeless' is coherent, then there is no state of the world at which X exists timelessly.

Let's consider the following questions:

Q1) Do we have sufficient reasons for believing not only that every event has a cause, but that everything that has a temporal beginning even when no change is involved, has a cause?

In other words, do we have sufficient reasons for believing that every X that has a temporal beginning has a cause, even when there is no change from a state of affairs at which the X in question does not exist, to a state at which it does?

Q2) Do we have an epistemic obligation to believe that everything that has a temporal beginning even when no change is involved, has a cause?

Q3) Should we believe that everything that has a temporal beginning comes from a change/event 'X comes into existence'?

In order to assess our intuitions on the matters [15] of Q1 and Q2, we would need to consider unusual scenarios, such as S1.

I have to say that I don't have any general intuition that, in such scenario, B would have a cause.

In fact, in some scenarios, my intuitions tell me otherwise:

For instance, in S1, let us stipulate that B is the universe, or a multiverse, and there is nothing else that exists. Or let's stipulate that B is an omnipotent being, and let's stipulate that, at t=0, there are no other beings – no timelessness involved.

In those cases, intuitively, I'd say that B begins to exist but may well not have a cause. At least, I have no intuition that B would have a cause.

Someone might protest that I'm constructing scenarios that would be exceptions to the principle, but the scenarios in question are counterintuitive and we shouldn't use them as a guide.

However, in order to construct scenarios in which one could test whether one has an intuition that every X that begins to exist has a cause, independently of whether there is a change/event 'X comes into existence', it seems to me one needs precisely to separate temporal beginnings of existence from changes/events, and that does not happen in ordinary cases.

Otherwise, it might be that what's intuitive to one is just the principle that every event – that is, any change – has a cause, and the correlation with a temporal beginning arises because it just happens to be the case than, in daily life, things that have a temporal beginning are just those things X for which there is a change/event 'X comes into existence' - i.e., a change from a state of affairs at which X does not exist, to one at which it does.

So, in order to accept something like 'everything that begins to exist, has a cause' as intuitive, one would not only have to lack an intuition that, in some scenarios, some beings that begin to exist would probably not have causes: one would have to have an intuition that those beings would plausibly have causes.

As for Q3, there appears to be no intuitive reason to think that that's always the case.

In fact, if time had a beginning point (which can't be ruled out on intuitions alone), it seems more than intuitively clear that there is no event 'time comes into existence': a change from a state of affairs at which there is no time, to one at which there is time, seems to be impossible, for reasons similar to those used to derived a contradiction earlier.

So, it seems intuitions do not support an affirmative answer to Q1, Q2 or Q3. [16]

As for empirical reasons, someone might try to use objects in daily life as examples, and claim that everything that begins to exist, also comes into existence, and that would allegedly support Q3.

However, that's really empirical evidence, but simply the consequence of the definitions, for any object not as old as the universe. [17]

So, it seems that we're at the very least justified in not affirming that every X that has a temporal beginning, comes from an event 'X begins to exist', or that everything that has a temporal beginning, has a cause.

Finally, someone might raise the issue that cosmologists who worked on the Big Bang model did not come to the conclusion that they had resolved all the mysteries and moved on, instead of looking for causes.

However, it's clear that the model does not provide an understanding of the universe beyond a certain point, where effects from forces other than gravity should be taken into consideration.

In other words, it makes perfect sense that scientists would try to figure out the causes of a very hot, dense, and small universe that existed about 13.7 billion years: indeed, we don't know the causes; a theory that only considers gravity but no other forces is inadequate to provide a good understanding of it.

But those scientists seem to be asking the question: 'Where did that hot, dense, really small universe come from?' (or similar ones), on the understanding that before the first state of the universe that can be analyzed with present-day models, there were other states of the universe that are beyond the descriptive capabilities of current scientific understanding – states that later changed into a state that is within said capabilities.

In other words, they apparently were/are looking for the causes of an event/change, as well as for a model of how the universe works under conditions not covered by present-day models.

So, it seems that Craig's arguments fail to provide support for the premise; at the very least, there is no epistemic obligation to accept it – and that's not even counting issues related to indeterministic interpretations of Quantum Mechanics.

Still, even if we grant the first premise for the sake of the argument, Craig's arguments do not support the second one.

Someone else might come up with new arguments, but it's a heavy burden, especially given that all arguments in support of either premise have failed so far, and the KCA is a very old argument, which as been debated at length. In any case, the burden would be on them, of course.

10) The 'Hilbert Hotel' argument

One of the arguments that Craig gives in support of the second premise of the Kalam Cosmological Argument intends to establish that an actual infinity is metaphysically impossible – though there is no claim of logical impossibility.

Let's assess Craig's argument:

William Lane Craig and J.P Sinclair[18]:

But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are occupied. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. “But of course!” says the proprietor, and he immediately shifts the person in room #1 into room #2, the person in room #2 into room #3, the person in room #3 into room #4, and so on out to infinity. As a result of these room changes, room #1 now becomes vacant, and the new guest gratefully checks in. But remember, before he arrived, all the rooms were occupied! Equally curious, there are now no more persons in the hotel than there were before: the number is just infinite. But how can this be? The proprietor just added the new guest’s name to the register and gave him his keys – how can there not be one more person in the hotel than before?

Such questions are the result of an ambiguity about what it means for there to be “more persons” in the hotel.

For instance, if by “more persons” one means “all the persons who were there remain, and there is at least one who wasn't there, but now is there”, or if one means that the set of guests after the new arrival (let's call it “GF1”) minus the set of guests before the new arrival (let's call it “GI”), has a greater cardinality than GI minus GF1 [19], then are are more persons (more precisely, one more) after the new guest checks in.

On the other hand, the set of guests in the beginning GI has the same cardinality as the set of guests after a new guest arrives, GF1, so if by "GF1 has more persons than GI" one means that the cardinality of GF1 is greater than that of G1, then there are no more persons after the arrival.

That the sets have the same cardinality only means that there is a bijection between the two sets, which is not only not counterintuitive, but is actually obvious: it's the same as comparing the set of natural numbers N (i.e., {1, 2, 3, …}), with the set of non-negative integers N₀(i.e., {0, 1, 2, 3,...}).

So, in the usual mathematical sense of cardinality, N and N₀ have the same number of elements, but that only means there is a bijection between the two (which is, again, obvious, since we can define F: N₀→ N, F(k) = (k+1)).

On the other hand, there is one number in N₀that is not in N (namely, 0), so in that sense, there is one more element – also, the cardinality of N₀minus N is 1, which is greater than the cardinality of N minus N₀, which is zero. So, understanding “more elements” in either of those senses, it is the case that N₀has more elements than N (one more, to be precise).

The case of the hotel is no different in that regard; making the example concrete does not change the fact that any puzzlement arises from the ambiguity about what's meant by “same number”:

In the same sense of “same number” in which N₀has the same number of elements as N – namely, in the sense that there is a bijection between the two-, the sets of guests after and before the arrival have the same number of guests.

And in the two senses I mentioned above in which N₀has one more element than N, there is one more guest after the new guest arrived.

If the example shows something counterintuitive, that's not the actual infinity, but the infinite hotel – which of course we could never build – the practical impossibility of communicating with infinitely many people at once, etc.

But that does not appear to be a problem for, say, infinitely many galaxies, or infinitely many universes (in some sense of “universe” used in modern cosmology), infinitely many particles, etc.

So, if one explains what one means by "more", then there is no problem whatsoever, regardless of whether there is a unique usual meaning of "more", according to which there are (or there aren't) more persons after the arrival.

I actually doubt that only one common meaning of "more" exists, but that is beside the point.

The point is that there simply appears to be nothing remotely puzzling here, but merely a confusion that arises from some ambiguity in what is meant by "more".

The rest of the arguments against an actual infinity are based on that ambiguity as well.

For instance, Craig expresses some sort of amazement at the alleged strangeness that even if (denumerably) infinitely many more guests arrive, the number of guests is the same as before.[18]

As in the previous case, there is no puzzlement at all if what's meant be "same number" is explained:

The set of guests after the infinitely many (more precisely, ℵ₀) new guests arrive (let's call it GFℵ₀₎ has all the members of the initial set of guests GI, and it also has infinitely many guests that GI does not have.

Also, GFℵ₀minus GI has infinitely many guests or members, whereas GI minus GFℵ₀has zero.

On the other hand, there is a bijection between GI and GFℵ₀.

All that is clear, and there is no puzzlement.

The question "Are there any more guests?" is not be problematic once one explains what's meant by "more guests".

It would be somewhat ambiguous to say that there would never be a single person more in the hotel than before, as Craig does[18], but as before, once one clarifies what one is saying, the puzzlement should disappear: in the usual mathematical sense of cardinality, there are no more persons, which is to say nothing but that there is a bijection between the set of guests before the new infinite ones arrive, and the set of guests after they do arrive.

In the two other senses I mentioned above, there are more people after the arrival.

All of this is straightforward, so there should be no need to delve any further into it: Craig's "Hilbert Hotel" argument provides no good reason to reach any conclusion about whether actual infinities exist, or whether or not they're "metaphysically possible", since it is just the result of terminological ambiguity and the resulting confusion.

11) Philosophical arguments against an infinite past

In addition to the Hilbert Hotel argument against an actual infinity, Craig presents other philosophical arguments against an infinite past on a tensed theory of time – not against all actual infinities.

Before I go on, I have to admit that an infinite past on a tensed theory of time appears counterintuitive to me. However, on the other hand, so does a beginning of time!

That aside, the question is whether there are enough reasons that would settle the matter in the sense that, on a tensed theory of time, an infinite past is indeed impossible.

I used to think that there were – though not for the same reasons as Craig -, but after further consideration, reading counterarguments, and so on, I have to admit I can't find such reasons.

To be clear, on a tensed theory of time, there is no infinite ordered chain of events, one after the other, with a beginning point, since it's impossible to reach an infinity by a finite number of instances of finite addition. Moreover, that is true regardless of whether the events are of equal duration – assuming an intrinsic metric of time; else, how close they are is a conventional matter -, or even whether the past is metric-finite. Indeed, even if the lengths of the events added up to a finite number, the fact is that it's not possible to reach an actual infinity by finitely many times adding something finite.

However, the real question is whether a beginningless series of ordered past events, one after the other, is possible, under a tensed theory of time.

Craig maintains that that is impossible, pointing to the objectivity of temporal becoming under a tensed theory of time, and presenting some arguments that allegedly would result in contradiction.

I will consider the arguments that purportedly show some absurdities in a moment, but before that, I'd like to point out that if the objectivity of temporal becoming on a tensed theory of time precluded an infinite past, it would also preclude a metric-finite past but with infinitely many past events/changes.

On that note, when Craig replies to the objection that some of his arguments resembles Zeno's paradoxes.[20], he maintains that there are two crucial differences: the events are of equal duration and actual in his argument whereas the intervals are potential and unequal in Zeno's paradoxes.
However, at least the equal or unequal duration of the intervals is not a relevant difference, as long as each of them involves actual events/changes, since in any case, there would be infinitely many instances of temporal becoming in the past, regardless of whether they're all temporally equidistant from each other.

So, the question remains: does the objectivity of temporal becoming precludes the existence of infinitely many instances of temporal becoming in the past, one after the other?

Actually, it seems that what would be ruled out is the existence of such instances with a beginning point. In other words, what would be ruled out is a first temporal state T(0) without any changes within it, followed by the next such state T(1), and so on, until reaching a time T(ℵ₀).

However, if there is no beginning point, between any two events there would be only finitely many ones, so there would be no infinity to be reached from any point. So, there is no contradiction, only counterintuitiveness. However, a past with a beginning point is also counterintuitive.

Moreover, modern physics has taught us that while our intuitions about time are good enough in daily life, we should be wary about extrapolating them to the whole universe (or even some parts of it, like, say, a galaxy).

So, it seems that on intuitions alone, the matter can't be settled.

Let us now consider Craig's arguments that purportedly show some absurdities in the case of an infinite past without a beginning.

11.1) The contradictory case of Tristram Shandy

One of Craig's arguments against an infinite past is based on the story of Tristram Shandy. [21]

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

However, Craig does not provide any good reason to believe that it's obviously coherent – or, indeed, coherent – to write an autobiography at that rate counting from infinity.

What is obviously coherent is to write such an autobiography starting at a specific day.

Moreover, there is a good reason why Craig does not provide any good reasons to believe that it's coherent to write an autobiography at that rate while having kept that pace 'from infinity': namely, such a deed is logically impossible.

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: [22]

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(-k*365) = F(0) - k ≤ -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.

Someone might suggest that precisely the fact that we reach a contradiction is what should lead us to the rejection of such an infinite past. However, that would be a confusion, as it should be clear from the previous proof: what's logically impossible is the scenario itself, and it's not surprising that absurdities follow from a contradiction, since everything follows from a contradiction.

Surprisingly, Craig actually acknowledges that the scenario is contradictory, yet claims that because it's "obviously" coherent to write one's autobiography at a rate of one day per year, the problem is with the infinity of the 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. I honestly do not understand what else is needed to reject the argument.

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

Alice Shandy writes a novel, 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 potentially infinite future, 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, that's only a curiosity. I would say that should in any case reject the 'Tristram Shandy' scenario because it's contradictory, and so the fact that it results in absurdities does not tell us anything about whether an infinite past with the order type of the negative integers is metaphysically possible.

Still, while the proof above should be enough to debunk the Tristram Shandy scenario, in case someone is not persuaded by it, let me point out that the proof in question does not depend on whether a tensed or a tenseless theory of time is true. But an infinite past seems clearly logically possible if we assume a tenseless theory of time, just as an infinite future is.

Also, somebody might suggest that there might be even more past years, changing order types, etc.

However, that would be beside the point:

The point here is that the previous proof shows that if the set of past years is of the same order type as the set of non-negative integers, the Tristram Shandy case is logically impossible.

Therefore, the Tristram Shandy scenario fails to present any challenge to the possibility of an infinite past in which the set of past years has the same order type as the set of non-negative integers, and so it fails to show that infinitely many past years are impossible.

11.2) Orbits and parity

Another one of Craig's arguments against an infinite past on a tensed theory of time is based on a scenario involving planets completing infinitely many orbits.

First, he claims that somehow it's absurd that if Jupiter completes 2.5 orbits for each one Saturn completes, they would both have completed the same number, if they have been orbiting the Sun 'from eternity past'. That would be somehow a "magical" result[23].

Now, apart from the fact that any planet, star, etc., has a finite expiration date, the fact is that there is no absurdity at all.

As in the case of the Hilbert Hotel argument, this is merely a confusion with words.

That the number of orbits is the same if they've been orbiting forever and there is an infinite past merely means that there is a bijection between the set of orbits completed by one of the planets, and the same set for the other planet.

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

Indeed, no one is suggesting that planets might do that: we know enough about physics to tell otherwise.

Incidentally, in any case, the number of orbits completed from any given time would be finite, and there would be nothing like Jupiter falling "infinitely far behind Saturn", or that the "disparity" has become increasingly greater from infinite, etc.: again, there is no beginning from which to count to infinity.

William Lane Craig:[23]

For a cardinal number n is even if there is a unique cardinal number m such that n = 2m, and n is odd if there is a unique cardinal number m such that n = 2m + 1. In the envisioned scenario, the number of completed orbits is (in both cases!) ℵ0, and ℵ0 = 2ℵ0 = 2ℵ0 + 1.

Actually, using usual mathematical definitions of “even” and “odd” – and those definitions match common usage of the words -, integers are even or odd, but not transfinite cardinals.

So, using the words in their usual sense, ℵ₀is neither odd nor even.

Also, that ℵ₀= 2ℵ₀+ 1 only means that there is a bijection between ℵ₀and (ℵ₀x {0, 1} U {1}), and that ℵ₀= 2ℵ₀only means that if there is a bijection between ℵ₀and (ℵ₀x {0, 1}). But that's all true [24].

Surely, going by the definition Craig provides, ℵ₀would be both odd and even, and so would be any other transfinite cardinal, but that is not at all a problem, as long as one keeps in mind what Craig means by the words.

12) The "Standard Hot Big Bang Model", a tensed theory of time, and the KCA:

Back to Craig's argument, he claims that what he calls the "Standard Hot Big Bang Model" (SHBBM), supports the second premise of the KCA. He also claims that a tensed theory of time is true.

W. L. Craig and J. P. Sinclair[25]

The standard Hot Big Bang model, as the Friedmann–Lemaître model came to be called, thus describes a universe which is not eternal in the past, but which came into being a finite time ago. Moreover – and this deserves underscoring – the origin it posits is an absolute origin ex nihilo. For not only all matter and energy but also space and time themselves come into being at the initial cosmological singularity. As Barrow and Tipler emphasize, “At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo” (Barrow and Tipler 1986, p. 442). On such a model the universe originates ex nihilo in the sense that it is false that something existed prior to the singularity.

There is no good reason to think that we can assume the model to be an accurate description of the universe beyond a point at which there was a hot, dense and very small universe – but not – a singularity of infinite density (what would that even mean?).

Moreover, there is no need to add a singular point, even if one keeps extrapolating backwards in time, nor a way of getting out of the singularity, so to speak.

However, let's let all that pass, and let's assume, for the sake of the argument, that the model Craig offers in support of his arguments is indeed an accurate portrayal of the early universe.

Then, under such assumption:

1) There is a time t(1) in the past, such that the average density d(1) of the universe at t(1) was greater than the density at a time in the year 2000 (any time) d(0), so there is a change from a universe with a density d(1) to a universe with a density d(0).

Thus, the model entails that there is at least one event/change, E(1), which happens in semiopen interval [t(1), t(0))

2) Let's suppose the model entails there are at least k events, E(1), E(2), E(k), where E(j) happens in the semi-open interval [t(j+1), t(j)), and 0 < t(j+1) < t(j), for all j between 1 and k.

The average density of the universe from E(k+1) began to the present day, is bounded, and so is less than some number d(M).

Since the model predicts that the density tends to infinity as we move back in time, there is some time t(k+2), such that 0 < t(k+2) < t(k+1), and such that d((k+2)) > d(M).

So, there is a change from a state of the universe with density d((k+2) to a state of density d, such that d(M) > d > d(k+1), and that's the event E((k+1)), which happens in the interval [t(k+2), t(k+1))

Thus, on this model, there is an infinite temporal regress of events, which Craig claims is impossible.

Note that even if the events are increasingly shorter, that would be an actual infinity under a tenseless theory of time, or under a growing-block tensed theory.
Craig claims that even on presentism, an infinite regress of events/changes is an actual infinity.

If so, then Craig's "Hilbert Hotel" argument has a false conclusion.

Furthermore, according to Craig, this model entails that time has a beginning at the singularity.

If so, we could then conclude, on the assumption of this model, that the universe contains an infinite regress of events with a beginning point, and so no tensed theory of time is true: even though the duration of the events is not equal, and even though the sum of all of the durations is convergent, the fact remains that it's not possible to reach an actual infinity of events by finitely many times adding a finite number of them, starting with only a finite number (in reality, the model offers no way out of this "singularity", and adding it is at best superfluous; without that addition, what we get is a beginningless series of past events/changes, but that's no better for Craig's position).

But what if we drop the assumption that we can extrapolate arbitrarily back in time, and actually take into consideration the fact that we're not justified in applying General Relativity to a very small universe, where forces other than gravity should be taken into consideration?

In that case, all we could say is that the universe was in a hot, small, dense state S1 at some time t over 13 billion years ago, which seems to have came after a state S2 whose description is beyond present-day understanding of physics.

So, the state S2, and the event E(S2,S1): = "The universe changes from its condition at S2 to its condition at S1" are both beyond the present-day understanding of physics. And that is it: There is no suggestion of a beginning of time, or of the universe, or anything of the sort.

There is a beginning of the states of the universe whose description is within the present-day understanding of physics. Of course, that fact provides no support whatsoever for the second premise of the Kalam Cosmological Argument, and thus neither does the "Standard Hot Big Bang Model".

The same is true of modern cosmology in general: there is no claim that there is a beginning of time; models with a metric-finite past only call for new physics to describe things that are beyond present-day understanding, but that is all.

So, science does not provide support for the KCA.

13) The KCA and a tenseless theory of time

Craig's KCA is entirely based on a tensed theory of time, but to be thorough, I will consider in this section whether it could work on a tenseless theory.
On a tenseless theory, and going by Craig's understanding of "begins to exist", then the second premise of the KCA is not true.

As a matter of fact, on a tenseless theory of time, nothing begins to exist in the sense of "begins to exist" proposed by Craig, since there are no tensed facts.

However, his understanding of 'begins to exist' does not seem to match common usage, so someone might reject it and still try to make the KCA work.

Yet, there are insurmountable problems for that task:

First, as earlier sections show, Craig's philosophical arguments against an infinite past fail even under a tensed theory. That does not change on a tenseless theory.
Second, while a theist might try alternative arguments, that might also be said of a KCA run on a tensed theory; in any case, the burden would be on the claimant, but the KCA has been discussed for many years, and it's hard to see what kind of new argument might work, after every argument so far failed.

Third, arguing against an infinite past on a tenseless theory has very counterintuitive results, and even though our intuitions might not be reliable, usually KCA defenders try to appeal to intuitions, so counterintuitiveness is at least a problem.

For instance, on a tenseless theory of time, it appears that the past, the present and the future are ontologically equivalent. So, it seems then that any successful argument for the metaphysical (or logical) necessity of a beginning of time could be adapted to be an argument for the metaphysical (or logical) necessity of an end of time. At least, that is very counterintuitive,

Perhaps, an alternative would be for a theist to argue for the claim that even if a beginning of time may not be logically or metaphysically necessary, it is at least factual.

However, that kind of argument would have to be empirical, and there is no support in present-day cosmology for such a claim: even if a scientific model posited no infinite regress of events the universe in a very narrow sense of the word "universe", they would probably make no claim about an entire series of past events, which might comprise an older universe, multiverse, etc.

In any event, there seems to be no good reason to assume such impossibility.

So, for all of the reasons given earlier in this section, it seems that a KCA run on a tenseless theory of time would fail as well.

14) The (purported) a cause of the universe: further analysis

Given that there seems to be no sufficient reason to accept the first premise of the KCA, then it seems the argument failed.

Still, assuming that the universe had a beginning and a cause, earlier in this article, I've analyzed some of the consequences of the properties assigned by William Lane Craig to the cause of the universe, showing that a contradiction is entailed.

I also assessed Craig's reply to that contention, showing that it's inadequate.

In this section, though, I will assess mostly other arguments in which Craig uses conceptual analysis in order to support of some of the claims about the properties of the cause of the universe, whose existence is allegedly established by Kalam Cosmological Argument. [26]

14.1) A single first cause?

Before addressing the conceptual claims, I will assess a different one:

According to Craig, the philosophical arguments in in the KCA show that there is a first cause, not only a cause of the universe.

In addition, he claims we ought to posit a single cause, not many, allegedly due to Occam's razor. [9]

Even assuming that the KCA succeeded in establishing both a cause of the universe and a first cause, that would not be a proper use of the razor:

First, if we do not know what caused a hot, dense state of the universe that existed about 13.7 billion years ago, there is no warrant for believing that it had a single cause, or that that particular cause was in turn uncaused.

Cosmologists understand that, and keep trying to find better models – models that can describe the early universe as well -, rather than assuming that the hot, dense, early universe was just brought up by a single uncaused cause, so science can go on.

Second, even if we knew that something caused the universe, multiverse, etc. - i.e., that there is a previous cause that does not match, for some reason, any description used by physics, today or in the future -, and even if we knew that there is some uncaused cause, there would appear to be no reason to make any assumptions about the number of causes of the universe/multiverse, etc., or that said cause or causes are uncaused. Who knows?

Still, let's leave that aside for the sake of the argument, and assess the rest of Craig's arguments for the properties of the cause of the universe, assuming that said cause would also be the first cause.

14.2) Changelessness and immateriality

Craig maintains that the first cause must be "changeless", since an infinite regress of changes cannot exist. [9]

But from no infinite regress of changes one can only infer from that is that there has to be a first change, not a 'changeless' state, unless 'changeless' only means a first state with no previous changes.

However – assuming for now that Craig's claim of changelessness is meaningful -, Craig seems to mean a lot more than the lack of previous changes by "changeless", since he claims that the first cause exists in a state of "absolute changelessness", which [9], which is allegedly impossible for particles and the like. So, it seems that he's not only claiming that there was a first change/event. But if he's claiming something else, then it seems changelessness does not follow from a lack of infinitely many past changes.

In any case, I've already showed that a first state of God wouldn't be changeless, and if we assumed it is, the same would be true of a similar first state of the universe.

In addition, Craig claims that, since the first cause is changeless, the first cause is also immaterial.

However, that's another mistake, since the first cause proposed by Craig changes just as the universe does, in a similar scenario.

Leaving aside potential problems with the concept of "immaterial", clearly the conclusion is not warranted, as the claim that the cause is changeless is not warranted, either.

14.3) Timelessness and the open interval variant

In earlier sections, I already made a detailed case against the claim of timelessness of God as the first cause.

In this subsection, I will consider an alternative: someone might accept infinitely many past events/changes without a beginning point, and then still claim that God is temporal with creation – on a tensed theory of time -, and timeless without it.

That's incompatible with Craig's position, but someone else might raise that issue.

However, that would be of no help for the defender of the KCA: not only do the arguments in support of the premises fail just as before, but if the proponent of the KCA accepts infinitely many past events/changes, then they ought to accept the possibility of infinitely many past years, since the difference in duration of the events/changes, and whether they are equally long, are not relevant matters from the perspective of whether a tensed theory of time allows such infinite regress.

However, the possibility of infinitely many past years defeats the KCA, as one might simply posit that, perhaps, there is an infinitely old universe or multiverse, before the states of the universe describable by present-day physics

14.4) Spacelessness

The property of spacelessness allegedly follows from timelessness and immateriality.

Since I already showed that the claim of timelessness fails, that is sufficient to show that the claim of spacelessness fails as well, since it's unwarranted.

But let's leave that aside for the moment and for the sake of the argument, and let's also assume that the timelessness claim makes sense. Then, why can't, say, a multidimensional manifold be timeless? Why not some sort of field?

There is no need for particles, for instance.
Note that it wouldn't help to say that any field would "immediately" change, make particles, etc., since with the same criterion, any "timeless" object also "immediately" changes, as the previous arguments show.

And if a field or something like that can be "timeless", but can't be immaterial, then timelessness does not entail immateriality, anyway.

So, the claim of spacelessness only adds more problems to the insurmountable problems an argument for theism based on the KCA already has.

14.5) Power

According to Craig, the first cause must be very powerful, since it caused all of "physical reality" to exist, without any material cause. [9]

Leaving aside issues about the concepts of "material", and "physical", and of course the decisive objections I explained earlier, the claim that the object in question is very powerful does not follow from that.

In other words, given the assumption that some entity is the cause of the universe, it might be – purely for example – that the object in question is only capable of causing things like our universe or similar ones, and is incapable of acting within them, or making much of anything else, etc. There are plenty of options.

Moreover, it might as well be incapable of changing at all, so it wouldn't be able to learn anything at all.

14.6) Personhood

Craig gives three arguments in support of the claim that the first cause is personal:

14.6.1) Personal explanations and scientific explanations

Craig claims that, as Swinburne "points out", there are two kinds of explanations: personal and scientific. [9]

Of course, Swinburne argues for that, but the matter is surely contentious.

Craig does not defend the distinction, and it would be beyond the scope of this article to show all that's wrong with Swinburne's claim, but I will point out that a personal agent acting on some volition can also be put in terms of a law and some conditions.

For instance: "If agent A decides X, then X happens", and "Agent A decides X" would be a way of putting it in such terms.

If an agent with a "timeless" volition is posited as a cause of the universe that is temporal with the universe, and one assumes – against very strong reasons – that the claim is coherent, then one might as well posit some non-personal timeless stuff, with the property that it causes – deterministically or not – the universe.

There would be initial conditions too, but – one could say, mirroring the theist's claims – not initial in a temporal sense, but in the (mysterious) "timeless" sense in which Craig's deity would be timeless, and whose coherence I'm assuming in this subsection and merely for the sake of the argument.

14.6.2) Other properties of the alleged first cause

Craig maintains that, is based on his previous conclusions, the first cause is timeless, immaterial, beginningless, uncaused, and spaceless. [27]

However, as I've shown in the previous sections of this article, those previous 'conclusions' are at best unwarranted, when not clearly untrue, so this claim fails as well.

14.6.3) 'Free agency'

The third avenue Craig takes, in order to support the claim that the first cause is personal, is based on what he calls "free agency", and "agent causation". [27]

While I have no objections to the claim that, say, humans sometimes act on their own free will, that does not have anything to do with non-determinism; further, the kind of "freedom" posited by Craig should not be characterized as "freedom", but more properly randomness, and randomness surely does not require agency, or even minds.

But let's take a look at the matter in more detail:

First, Craig claims that because the agent is free, he can bring about things in absence of previously conditions determining it. [27]

That clearly is not a good characterization of human freedom, and while Craig is talking about God, he's using an understanding of freedom allegedly based on human freedom.

Yet, indeterminism in humans has nothing to do with freedom in humans – or rather, it might get in the way.

To see that, let's consider the following scenario:

Alice has been a good police officer for ten years.

She's kind, committed her job, good to her children, and so on.

Now, one morning, Alice goes to work as usual.

The police get a call about a domestic disturbance, and Alice and another officer are sent to the address they're given.

When they arrive there, they encounter Harry, a thirteen-year old kid high on drugs, acting completely irrationally.

He tells Alice: 'You're a police officer, so you're evil. Why don't you shoot me?'

Alice has no reason at all to shoot Harry.

He poses no threat to her, and can be easily arrested if needed.

However, it's clear that she has the power to shoot him, and is free to choose whether to shoot him.

All she'd have to do is pull her gun, point it at Harry, and shoot.

No one would see that coming, so no one could stop her if she did that – no human, anyway; the point is that she wouldn't be stopped.

But Alice – of course – feels no inclination whatsoever to shoot Harry, does not shoot him, and follows procedure.

The point is that saying that Alice can shoot Harry, that she has the power to shoot him, that she is free to choose whether to shoot him, etc., means that she would shoot him if she chose to do so, that she's not being coerced, etc.

It does not at all mean that, even given Alice's mental state at the time she chose to follow procedure, and even given all the conditions of the world at that time and previous times – including Alice's goals, beliefs, character, etc. -, it was still possible that Alice would shoot Harry.

On the contrary, if, given all those previous states, it was possible that Alice shot Harry, then it seems that there is a possible world W with the exact same past as ours prior to Alice's decision to follow procedure, at which Alice shot Harry instead.

But that is not an exercise of freedom, in the usual sense of the words. Rather, it's an unfortunate event that happens to Alice.

To see this, let's consider Alice's mental processes leading to her 'decision' to shoot Alice – say, decision D. Alice never considered shooting her, and had no desire, intention, etc., before decision D happened.

However, at some time, earlier states of the world, including her earlier mental processes did not determine her later mental processes. There is an event "Alice decides to shoot Harry" that happens irrespective of any previous states of Alice's mind, and no matter how much Alice would loath being a murderer.

All of Alice's previous reasoning, desires, behavior, intentions, etc., are incapable to stop 'decision' D from happening. But how's that Alice's decision?

It seems D is not a decision Alice made, but rather, it's something that happened to Alice.

It's not something Alice could have anticipated, or prevented: at some point her mental processes changed from normal to 'shoot Harry', without forewarning, and without any cause in previous mental processes.

Someone might claim that necessarily, there is always some hidden reason to shoot people, or to do anything one can do, but that would have to be argued for, and even then, that would not change the fact that, in that case, Alice could not have prevented his mental processes from changing at some point from normal to 'shoot Harry', no matter what she did before – and that change could not be reasonably said to be her decision, since she had never considered that before, and the change took her by surprise.

Those considerations show that that kind of thing should not be called 'freedom', but more like 'an unfortunate kind of randomness'.

That does not mean that human non-determinism isn't true. But that is surely not required for freedom, and in fact, it might undermine it, as the previous scenario shows.

Perhaps, there are situations after which, after assessing the pros and cons, a human is undecided between A or ¬A; if so, maybe there is a truly random outcome generator for such cases (which might involve also several mutually exclusive options: A1, A2, A3,...)

However, if that is the case, that is not required for free will: a random generator that delivers 'decisions' in cases in which the mind remains undecided clearly does not result in more freedom than a mind that actually makes decisions.

So, if there is such indeterminism, as long as the indeterministic events happen when a person is undecided (based on her previous feelings, desires, reasoning, etc., she is undecided and does not cause any outcome), maybe that randomness is compatible with free will, but that's all.

On the other hand, if there is an indeterministic feature of human behavior that happens to be like Bob's example above – i.e., if it happens against everything that the person stood for, his previous considerations, etc. -, then, and as the previous example shows, that kind of indeterminism – at least, when it happens – would actually preclude free will; rather, the 'decision' would be an unfortunately random will.

There is another way to see this, taking into account that even under the exact same preexisting conditions – including, of course, the previous mental states of the libertarian-free agent.

So, let's consider the following scenario (relativizing time as required):

Alice is a libertarian-free human, and at t(s), the state of worlds W and W' is exactly the same – that includes, of course, Alice's mental processes.

Later, Alice libertarian-freely chooses A at W, and B at W', even though the states of the worlds prior to Alice's decision were the same (A is different from B).

In other words, W and W' are exactly the same until Alice's mental processes diverge.

Now, let p be a Planck time, and n a non-negative integer, starting with 0.

Let's consider times t(s)+n*p, and the states of W and W', W(n) and W'(n) respectively.

Let n(l) be the last n such that W(n) = W'(n).

Since the 'decision' was made even given the exact same prior conditions, it seems that the 'decision' happened between t(s)+n(l)*p, and t(s)+(n(l)+1)*p = t(s)+n(l)*p+p, in other words, the 'decision' was made in not more than a Planck time.

That's way too fast for any human conscious decision, though. So, it becomes clearer that the first indeterministic event E that distinguishes between W and W' is same random alteration of Alice's mental processes.

Someone might suggest that, previous processes in her mind made E in probable, but weren't enough to bring it about, something still altered her mind randomly; let's assume that that would be a coherent interpretation of probability (else, this objection fails already).

Even then, the fact would remain that her mind was altered without a cause, and with nothing she could do earlier to stop it; moreover, in some cases, the improbable 'decision' might happen. And in those cases in which the improbable 'decision' happens – i.e., the decision that her previous mental processes made improbable – we're back with something like the unfortunate case of the libertarian-free police officer.

Someone might still object that, if such a random change in her mind happened, she still could have changed her mind, and refrained from carrying out the decision – in the case of the first example, the shooting.

The problem is, though, that if you can have such a random event between t(s)+n(l)*p, and t(s)+(n(l)+1)*p, it seems you can have another one at every single Planck time that follows, until the "decision" that was completely against everything the person previously stood for, actually happens.

But let's suppose someone introduces some fuzziness in some way – which they would have to explain, of course; else, the previous reasoning stands. Even then, the fact would remain that the agent would have a random component – a change in her mind she can't bring about, because it happens no matter what she tried previously; it's just that we wouldn't be able to see that by means of analyzing the process step-by-step, but all of the other reasons I've given above remain.

A theist might say that that's 'actually the agent acting', or something like that but – whatever that means -, the fact would remain that that would a partially random agent acting, not one in which mental processes are sufficient to bring about behavior; it would be an agent with a randomly altered mind – i.e., a mind that suffers some alterations that have no sufficient causes; it's akin to dice-throwing, and in some cases, it might go against everything the agent had stood for up till then.

So, for all of the previous reasons, the claim that non-determinism is required for freedom ought to be rejected.

That does not mean we can't act of our own accord, of course. We can and sometimes do have freedom; it's just that indeterminism is not required for that.

Now, there is an objection available to the theist, which seems to be Craig's position: namely, that is lack of causal determination that is required for freedom to exist, not lack of determinism.

However, if an event is determined by previous conditions, then it seems it's causally determined too, since some the previous conditions would be causes. How would it be otherwise?

It seems puzzling.

But regardless, we can make a case against the requirement of causal indeterminism independently. If causal indeterminism is true, then no matter what Alice does up to some time t, all of her thought processes, intentions, desires, memories, reasoning, are all insufficient to bring about her decision. So, it seems that the "decision" might just happen to her, and she might still shoot Harry.

Again, the theist might say that that's the agent acting. But how can she act so quickly - indeed, instantaneously?

Humans aside, someone might posit that the first cause is God and is not deterministic, even though as we saw by analyzing the case of humans, indeterminism surely isn't a requirement for freedom, and can at best hamper it.

However, that fails as well, as explained earlier, since – at least – one may as well posit a non-deterministic universe as an alternative that the theist defender of the KCA has failed to refute.

Of course, the non-theist need not be committed to indeterminism, or an indeterministic universe, or a first cause, etc.; she may simply posit that there are alternatives that the theist defender of the KCA hasn't refuted.

14.7) The meaning of "God"

As previous arguments show, Craig's arguments fail to support the conclusion that there is a first cause, or a cause of the universe, or that – assuming that there is such a first cause -, the cause has the properties he claims it has.

But there is one more point I'd like to address here, and it's about the meaning of "God":

William Lane Craig:[28]

5.0. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

This, as Thomas Aquinas was wont to remark, is what everybody means by “God.”

Actually, that is not what everybody means by 'God'.

Plausibly, it is not even be what most people mean by 'God', or what most philosophers mean by 'God'.

For instance, by 'God', Richard Swinburne[29] means "a person without a body (i.e., a spirit) who necessarily is eternal, perfectly free, omnipotent, omniscient, perfectly good, and the creator of all things".

There is nothing in Craig's description quoted above that entails omnipotence, omniscience, moral goodness – let alone moral perfection -, etc.

Moreover, Swinburne explicitly denies that timelessness is part of the meaning of 'God'. [29]

But let's take a look at the matter from another perspective:

If an omnipotent, omniscient, morally perfect creator of all other beings existed, and moreover he intervened in human history, but he were not timeless, it would be hard to find many people saying that God does not exist, on account of a lack of timelessness (assuming that "timeless" is meaningful, that is).

The same goes for changelessness.

On the other hand, if an entity like the one Craig describes existed (assuming again that the description is coherent), but – for example – he were not omniscient, not omnipotent, not morally perfect (or even morally good), and never intervened in human history – no afterlife, either -, it seems to me that plenty of people would be inclined to say that God does not exist, without committing an error.

In fact, even if the Kalam Cosmological Argument – or, more generally, any argument – succeeded in showing that the universe has a cause, and even if further argumentation succeeded in showing that said cause is an intelligent being with some of the properties Craig ascribes to him in the previous quotation – or all of them, assuming they all make sense -, that would still not establish that God exists, in the sense the word 'God' is used by many, plausibly most theists, and would be compatible with – for instance – deism.

15) Conclusion:

The KCA provides no support for theism, both on William Lane Craig's version of the Kalam Cosmological Argument, and on many other actual or potential versions.

Furthermore, there appears to be no good reason, based on present-day science or philosophy, to suspect that that's going to change: there are numerous problems, and several of them appear clearly insurmountable.

Notes and references:

[1]

Source: 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
Page 102.

[3]

[4]

Source: http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5673&printer_friendly=1

[5]

Source: http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5971

[6]

The choice of the change in God from timelessness to temporalness as the event is only one possibility.

There are alternatives. For instance, let say the actual world contains a state of affairs S at which God exists timelessly.

Then, at S, time does not exist, so it's not the case that God knows that time exists. On the other hand, at t=0, God knows that time exists.
Let E(1) be the event “God comes to know that time exists”

Another alternative would be:

At S, there are no tensed facts. So, it's not the case that God knows any tensed truths. At t=0, there are tensed facts, so God knows tensed truths. Thus, God's mind changed – he came to know tensed truths -, and one can consider the event E(2) “God changes from not knowing any tensed facts at S, to knowing some tensed facts at t=0”.

[7]

Source: http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=9269

[8]

[9]

[10]

https://en.wikipedia.org/wiki/Big_bang

[11]

W. L. Craig and J. P. Sinclair

In affirming that things which begin to exist need a cause, the mutakallim assumes the following understanding of that notion, where “x” ranges over any entity and “t” ranges over times, whether instants or moments of nonzero finite duration:

A. x begins to exist at t iff x comes into being at t.

B. x comes into being at t iff (i) x exists at t, and the actual world includes no state of affairs in which x exists timelessly, (ii) t is either the first time at which x exists or is separated from any t′ < t at which x existed by an interval during which x does not exist, and (iii) x’s existing at t is a tensed fact.

Source: 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; pages 184, 185.

[12]

[13]

Assuming here, and for the sake of the argument, that "timeless" is coherent.

[14]

[15]

Of course, a potentially serious problem may be the reliability of our intuitions in such cases, but that's no help for someone claiming that the first premise ought to be accepted, or even merely that it's rational to do so.

[16]

Readers, of course, will check the matter by their own intuitions, as always.

[17] Incidentally, if we take objects in daily life as examples for inductive arguments, we might as well conclude that no object is timeless, or that all personal beings came into existence, and so on.

[18]

Source: The Blackwell Companion to Natural Theology

Edited by William lane Craig and J. P. Moreland; page 109.

[19]

By “Set A minus set B” I mean the set C whose elements are all the elements that are in A, but are not in B.

[20]

Page 119.

[21]

Sources:

For Craig's argument: 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

Pages 120-124

The contradiction was first proved by Josh Dever, in "Worlds Apart", Taiwanese Journal for Philosophy and History of Science, 10 (1998).

[22]

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 count leap years. Also, the stipulation that the past has the order type of the negative integers is reasonable, given that Craig considers that we should reject that alternative due to the 'Tristram Shandy' argument.

[23]

Page 120.

Incidentally, the 'orbits' argument also fails to distinguish between a tensed and a tenseless theory of time.

[24]

I'm using the definition of the cardinal of an ordinal n as the least ordinal m that can be put in a one-to-one correspondence with n (ordinals are sets, and so are cardinals), but that's not important here. The relevant point is that there is no absurdity or counterintuitive result, once one takes into consideration what the words actually mean, under any mathematical definition of cardinality.

[25]

[26]

[27]

[28]

[29]

Swinburne, Richard "The Existence of God", Second Edition.

Clarendon Press Oxford.

Page 7.

7 comments:

יאיר רזק said...: Your monographs are far too long for me to read through at the moment, though they appear very interesting. I would like to note on the appendix, though:

Craig's ineptitude notwithstanding, the fact the the future or past do not exist (under Presentism) does not actually imply that they cannot cause anything at the present. Under presentism, and a causal-power understanding of causation that usually goes with it, my Will at time t0 has the "causal power" to alter the following present moments so that it "causes", at time t0+delta, a change that propagates in time similarly until my hand lifts at time t1 (where t1>t0+delta).

The past therefore can affect the future, by determining how existence changes in the next moment, because the past already existed at time t0. The future cannot affect the past, however, because the future (say, time t2) never existed yet at time t1 so could not have made any changes that propagated to t1.

I find the entire discussion metaphysically nonsensical. To go back to Parmenides, what exists exists and what doesn't doesn't. I believe in Eternalism. But still, I think your characterization of causality under Presentism is unfair - well, ungenerous; it's fair to foolish Craig, not to the general position.

Yair (aka Panpsychist); February 17, 2012 at 10:48 AM
Angra Mainyu said...: Hi, Yair

How are you doing?

I was focusing on Craig's version of presentism, so you may be right about the general case, so I would have to correct that. Thanks.
Before I get to that, I have some questions, though.
a) Does the t0+delta involves some infinitesimal, continuous time, etc.?
b) Is the position you're describing presentism, strictly speaking, or a 'growing-block' tensed theory?
If it's the former, how is it that the past can affect the future? I mean, okay, it existed, but it does not do so. Are you saying that it causes the next instant to occur? (if time is discrete).; February 17, 2012 at 2:52 PM
Angra Mainyu said...: Yair,

I've considered the matter and I think that in any case, the post is way too long already, so I'll remove the appendix instead of limiting it to Craig's position.
I'm still curious about the questions I asked you in the previous comment, though. If you have time for a brief reply, I'd appreciate that. :); February 17, 2012 at 4:28 PM
יאיר רזק said...: Hi to you too :) I'm doing fine. A little occupied by other things, but fine.

a) dt is an indication of "the next moment"; it might be the next point in discrete time, or the infinitesimally close "point" in continuous time.

b) I'm describing presentism - at least, as I understand it. Under presentism, the present changes. That's what the march of time is all about. The way it changes is determined by things with "causal power" - like god, and those oh-so-special human, with their image-of-god souls.

It may be that each moment is a separate creation by God alone; this is, I think, the standard Calvinist position. I believe most others maintain that God causes the "standard" changes, while we humans cause the "rest", through our Free Will. Either way, we don't so much cause the next moment to occur as we cause the present to change in a certain way.

Again, I must say this is all bobbly-gock. "Causal power" is just another word for "MAGICC!!!!". Furthermore, the present cannot "change" except in time, and change in time is what we're out to explain to begin with! But anyways, that's the position. As far as I understand it, at least.

Cheers,

Yair; February 17, 2012 at 9:35 PM
Angra Mainyu said...: Thank you for the clarification. :)

With regard to a), a tensed theory plus theism seems to entail discrete time; I had argued for that in section 7.2, but decided to weaken the claim and merely argue that it does so under Craig's claims about infinities, since that's the only result I need, and I prefer to block potential objections that.

As for b), I'm not sure your representation of it is more flattering than mine was;) - though, admittedly, your criticism is different; I was going by Craig's own 'reasoning'.

Cheers,

P.S.: By the way, I've considered the problem of the length of the post and the time it takes to read it, and I've written a brief reply to the KCA which I've not posted yet.
The difficulty with a short reply is that I have to pick just some part of the counterargument, and leave all of the rest aside.
So, if that part fails to persuade, then the brief counterargument fails to persuade, and it's difficult to assess in advance what parts readers will find to be the most persuasive. I'm planning to focus on the meaning of the claim of timeless God that becomes temporal, showing that he's just playing with words, but that only addresses Craig's version of the KCA.; February 18, 2012 at 4:22 AM
יאיר רזק said...: I just wanted to comment that apparently Plantinga appears to accept the standard "God & souls act" view, as seen here

http://wordsideasandthings.blogspot.com/2012/02/on-where-conflict-really-lies-pt-6.html

in some quantum-mechanical mambo-jumbo.

Cheers,

Yair; February 22, 2012 at 6:42 AM
Angra Mainyu said...: I'm not sure what part of the post that view would apply to.

Is it the part about free will, the first premise of the KCA, or something else?

If it's about uncaused events, that's interesting, because Craig actually questions non-deterministic interpretations of QM in his defense of the KCA (p. 183 of the book I cited) - of course, he would have to make reject deterministic interpretations when they involve humans.
Craig also argues that even in the indeterministic interpretations, everything that begins to exist has a cause because particles wouldn't come into being 'out of nothing', and so they allegedly have causes. There would still be events without efficient causes, so that can be used to object to the KCA on different grounds, but for now I've not decided to include that.

If it's about free will, quantum mambo-jumbo wouldn't get him out of the problem (apart from all the other problems with his quantum mambo-jumbo of course). Even souls wouldn't get him out of the problem, since the argument does not assume either souls or no souls, etc.

Cheers,; February 22, 2012 at 7:41 AM

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Wednesday, February 15, 2012

Against the Kalam Cosmological Argument - a new full reply

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