Angra Mainyu's blog: The Kalam Cosmological Argument, once again

This article is for the most part similar to that one, but with some modifications, especially to address Craig's reply to one of my previous objections.

I posted a brief reply to Craig's reply earlier, but I decided to post a new full argument, addressing the matter in more detail.

Also, I've added some new points, remove a few I think were superfluous, and introduced some modifications in the structure of the post and in some of the arguments.

b) The premises of the KCA are: [0]

P1: Everything that begins to exist has a cause.

P2: The universe began to exist.

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 prove a more general result about the incompatibility of a tensed theory of time and the timeless existence of God.

In those two sections, for the sake of the argument I will not challenge the concept of timelessness as used in the Kalam Cosmological Argument.

Later, I will address Craig's reply to the objection to the KCA that I raise in the first two sections - more precisely, his reply to the objection I raised in the first two sections of a previous version of this argument, but the objection is essentially the same.

Leaving aside the objection I mentioned above, I will later challenge on different grounds the claim that God is timeless sans the universe but temporal with it.

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.

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

However, I will also address several potential alternatives, showing that they provide no support for theism, either.

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.

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

William Lane Craig and J. P. Sinclair[2]:

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[3]

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[4]

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”.[5].

Now, if t=0 is the beginning of time, then E(0) is an event that ends 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. [6]

I will address Craig's reply to this objection in more detail later, but in light of that reply, let's clarify a few points:

First, Craig did not define "change" at all.

Instead, he defined "event" as "any change", using "change" in the usual sense of the word, and claimed that any change takes time.

So, I'm in no way confusing different senses of "change".

Rather, I'm using the examples of God's changing from timeless to temporal, God changing from not knowing any tensed truths to knowing some tensed truths, etc., and showing that a contradiction follows from Craig's position.

Second, the quotes in which Craig claims that God changed from timeless to temporal are useful to illustrate the contradiction, but not at all required to make my point.

In fact, it follows from Craig's claims that - for instance - there is some state of the world S at which God does not know any tensed truths - because there are no tensed facts at S -, followed by a state of the world at which God does know at least one tensed truth.
So, God actually changed from not knowing any tensed truths, to knowing some tensed truths or - if one prefers - the state of the world changed, from a state at which there is no entity that knows any tensed truths, to a state at which there is at least one entity that knows at least one tensed truth.

Third, even if one puts aside the claim that the changes in question have a non-zero, finite duration, one can consider - as I did above - both cases:

If the changes are instantaneous - i.e., their duration is zero -, then a contradiction follows.

If the changes, on the other hand, take time - i.e., their duration is greater than zero -, then a contradiction follows.

One way or another, a contradiction follows.

Fourth, as it should be clear, none of the above requires that one define "event" as Craig does.

Again, it suffices to point out that if the changes in question are instantaneous, a contradiction follows, and if it's not instantaneous, a contradiction follows, anyway.

Fifth, in case someone claims that the changes are somehow timeless, or partly timeless, I will point out that uttering the word "timeless" does not constitute a "get out of logic free" card.

What would "timeless change" even mean?

I will address those issues in greater detail when I address Craig's reply to my objection.

2) A tensed theory of time entails that it's not the case that the actual world contains a state of affairs S at which God exists timelessly

Let's assume, under a tensed theory of time, that the actual world contains a state of affairs S at which God exists timelessly.

At S, God does not have any knowledge of tensed truths - if he did, he would know that some events are past (or present), and then God's state would not be timeless; if some events are past at S, then S is past or present.

Yet, today, God knows tensed truths: he knows, for instance, that World War Two has already ended.

So, we can consider the event E(2): “God changes from not having any knowledge of tensed facts, to knowing some tensed truths”.

Since E(2) is an event, it has a duration e>0, and ends at some time t1.

If there is a time t2 < t1, then God does not yet have knowledge of tensed facts. However, there are tensed facts. But that's impossible.

Therefore, there is no time earlier that t1.

But then, given that E(2) is an event of duration e > 0 that ends at t1, there is an interval of duration e that comes before t1, contradicting the conclusion that there is no time earlier than t1.

Someone might object that, perhaps, there are events that have a zero duration, after all, and that E(2) is one such event.

Let's suppose that the event E(2), which ends at t1, and has duration 0.

Then, since E(2) ends at t1, then its beginning is also at t1. Hence, at t1, it is not the case that God has knowledge of any tensed facts – since the event starts at t1 -, but also, at t1, God has knowledge of some tensed facts – since the event ends at t1. But that is impossible.

So, this objection fails.

Another objection might be that E(2) does not start at t1, but at timeless state S.

However, using the word "timeless" does not allow one to get around logic: if the event E(2) ends at a time t=t1, and its duration is actually zero, it follows its beginning is also present at t=t1.

Finally, as a desperate move, I suppose that someone might try something like "The concept of duration doesn't apply to E(2), because E(2) is a partially timeless event".

As I pointed out earlier, the word "timeless" does not constitute a "get out of logic free" card.

What does "timeless change" even mean?

I will address that problem in greater detail when I address Craig's reply to my previous objection, but the conclusion is that if a tensed theory of time is true, the actual world contains no state of affairs at which God exists timelessly.

Also, the previous reasoning does not depend on other assumptions about time that Craig makes, such as relationalism or an intrinsic metric, or whether presentism or a "growing-block" theory is true.

In the cases of relationalism vs. substantivalism, as well as "growing-block" vs. presentism, it's clear that they're orthogonal to the previous points, which don't mention any of the contentious issues.

As for a metric, if there is no intrinsic metric, the duration of E(2) would depend on the metric, and that would be conventional.

However, the fact that E(2) has a non-zero duration would not: on metric relativism about time, events still have a positive, nonzero duration; the previous reasoning against E(2) having a zero duration holds - and assuming a zero duration would still yield a contradiction, using the same argument as before.

An alternative way of seeing this is that, even on metric conventionalism, there still is a relation of before and after; moreover, on conventionalism, it's changes that determine before and after.

So, the beginning of the event E(2) would still happen before the end of it, and so there would be a time prior to t1 contradicting the conclusion that there is no time prior to t=t1.

So, in brief, if a tensed theory of time is true, then it's not the case that the actual world contains a state of affairs at which God exists timelessly.

3) A tensed theory of time and the first premise of the KCA together entail that either there is a beginningless infinite regress of events, or God does not exist

The first premise of the KCA states that everything that begins to exist, has a cause.

While I don't think that Craig's understanding of the terms [8] matches the usual meaning of “comes into being”, or the meaning of "begins to exist", I will assume Craig's understanding of the meanings in this section.[9]

So, let's assume a tensed theory of time, and suppose that the first premise is true and God exists.

Since God does not have a cause, he does not have a beginning.

Since the actual world contains no state of affairs at which God exists timelessly, then there is no first time t at which God exists.

So, it follows that for every time t, there is a time u < t, such that God exists at u. [10]

Now, at t, God has knowledge of at least one tensed truth that he does not know at u: namely, that u is past, and t is present. In other words, God's knowledge of tensed truths is upgraded as time goes by, regardless of whether there is any other change in any other entity.

So, if u < t, then we can consider the event E(u,t): “God comes to know that u is past, and t is present”.[11]

Therefore, considering a sequence of times t(k), for every natural number k, in which t(k+1) < t(k), and considering that God exists at t(k) for every natural number k, we can conclude that there are infinitely many events E((k+1),k)), for every natural number k.

From the way the sequence is constructed, it's clear that it has no beginning point; moreover, since God does not begin to exist and doesn't exist timelessly, there is no t=0.

Also, in the previous arguments in this section, no assumption other than a tensed theory of time and the first premise of the KCA were made.

In particular, the result is independent of the issues time relationalism vs. substantivalism, intrinsic metric vs. metric conventionalism, and presentism vs. "growing-block" theory.

On the other hand, if there is an intrinsic metric of time and any entity with a metric-finite past begins to exist, then under these assumptions (i.e., the first premise of the KCA, plus a tensed theory of time), either there is a metric-infinite past, or God does not exist - since God did not begin to exist and doesn't exist timelessly.

4) Assuming a tensed theory of time, arguments against an infinite regress of events do not provide any support for theism in the context of the KCA[12]

William Lane Craig provides two philosophical arguments intended to show that an infinite regress of events is metaphysically impossible, and in that way support the second premise of the KCA.

However, neither the first nor the second argument, nor any other argument against such possibility, provide any support for theism in the context of the KCA[12], and under a tensed theory of time.

In fact, given the result of section 3, on a tensed theory of time, if such an infinite regress of events is impossible - or just not actual -, then either the first premise of the KCA is false, or God does not exist.

Thus, no argument intended to establish that an infinite regress of events is logically or metaphysically impossible, or even that there is no such regress in the actual world, can help a theistic case based on the KCA.

This result is general in the sense that it's not limited to Craig's particular philosophical arguments, and also in that it does not depend on assumptions such as time relationalism, an intrinsic metric of time, or presentism - since the result of section 3 does not depend on any such assumptions, either.

It still uses Craig's understanding of "begins to exist", but later I will show that alternative readings of "begis to exist" do not help a case for theism, either.

5) Assuming a tensed theory of time, modern cosmology does not support theism in the context of the KCA[12]

In addition to the two philosophical arguments, Craig maintains that modern (scientific) cosmology supports the second premise of the KCA. However, that's not our concern in this section.

The issue is whether, if that were true, that would provide support for theism in this context.

If a cosmological model entails an infinite regress of events[13] in the universe, and a beginning point, that's incompatible with a tensed theory of time, since an infinity can't be reached by finite successive addition from a beginning point.

Note that that does not depend on whether the events are of equal duration. Even if they are increasingly short, and even if the infinite series converges, it seems one couldn't engage in an infinite addition - any number of finite steps would remain finite.

If a cosmological model entails that there is only a finite regress of past events and a beginning at some time t=0, then in light of section three, a theist who supports a tensed theory of time and the first premise of the KCA ought to accept, on pain of inconsistency, that there are infinitely many events prior to the beginning of the universe.

But if so, someone might posit a multiverse, megaverse, older universe - or whatever one calls it - as a possible candidate to be the cause of the universe - i.e., as an alternative to God.

Cosmological models of the universe do not contain a claim that a beginning of what they call “the universe” is also a beginning without any previous universes, multiverses, etc., and the second premise of the KCA does not provide any support for theism if "universe" is understood in a restrictive sense, excluding older universes, multiverses, etc.

So, this attempt to support theism using scientific cosmology fails.

A possibility that we still need to consider is a scientific model with a metric-finite past but with an infinite regress of past events in the universe, and no beginning point.

Under such model, and under the main alternative understandings of "begins to exist", the universe did not begin to exist, so that would be of no help for the KCA.

However, under Craig's understanding of "begins to exist", the universe did begin to exist in that case.

There are, however, insurmountable problems for the theist defender of the KCA under this hypothesis.

For instance, under these conditions, a metric-finite past entails a beginning of existence.

Hence, if God exists, then he does not have a finite past, since he did not begin to exist.

That entails that if God exists, he existed at some time t before the infinitely regress of past events in the metric-finite past of the universe occurred. That means that, from t to, say, the year 2000, an infinite progress of events has happened, by finite successive addition and from a beginning point, which is impossible under a tensed theory. Hence, God does not exist. So, this road is closed to the theist as well.

6) Alternative readings of "begins to exist" do not support a case for theism in the context of the KCA[12]

I will analyze two alternatives, and conclude that they provide no such support.

While I can't rule out that someone might come up with a different alternative, it seems to me they would probably include highly counterintuitive scenarios like two-coordinate time, or undifferentiated time, etc. - the usual ones seem to be covered.

If so, it's not clear that we would have any reliable intuitions about causation in such scenarios - apart from the fact that that would probably not match any common usage, either -, so it's not clear how they would derive support for the first premise.

So, it seems to me that the following two variants cover most ground (and, in any case, the burden would be on someone who proposes an alternative reading).

6.1) First alternative reading

On this reading, "B begins to exist" is understood as meaning the same as "B comes into being" - as Craig claims -, but "B comes into being" (and so, "B begins to exist") is not understood in the sense posited by Craig, but in the sense that there is an event "B comes into existence" - i.e., a change from a state of affairs at which B does not exist, to one at which B does exist.

On this understanding of "B begins to exist", a first moment of the universe would not entail the universe began to exist.

In order for the universe to begin to exist, there would have to be a change from a state at which the universe does not exist, to one at which it does.

Moreover, that state of affairs at which the universe does not exist would have to be something other than a multiverse, etc. - "universe" in the second premise has to be understood broadly, including such multiverses; else, someone might always posit an older universe, multiverse, etc., blocking the argument to theism,

Modern cosmology makes no claims about that kind of state and/or event, and even if an argument established that an infinite regress of events is logically or metaphysically impossible, or that at least there is no such infinite regress in the actual world, that alone would not entail that the actual world contains a state at which no universe, multiverse, etc., exists, and then an event "the universe comes into existence".

Someone could try to establish such state and event by means of other kinds of arguments - say, a contingency argument, or an argument to design -, and then draw support for theism from that.

I don't believe any such argument succeeds; however, if one such argument were successful, it would be inaccurate to say that the KCA provides any support for theism. Rather, the fact would be that the other argument provides support both for theism, and for the second premise of the KCA as well.

So, the conclusion is that this alternative reading of "begins to exist" does not help a case for theism in the context of the KCA[12], either.

The results of this subsection make no special assumptions about a theory of time; so, they hold regardless of whether relationalism is true, whether time has an intrinsic metric, or even whether a tensed theory of time is true.

6.2) Second alternative reading

Another alternative reading - which I think is the closest match of the meaning of the words; see section 10 for more details - would be:[14]

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.

I will address the matter of whether belief in the first premise is justified in section eleven, but for the moment let us assume, for the sake of the argument, that it is justified under this understanding of "begins to exist".

Could the KCA be used to support theism, then?

The answer is still no: under this understanding of "begins to exist", all the relevant results of sections three, four and five can be derived as well, by means of essentially the same reasoning, and just the obvious, minor adaptations. For the sake of brevity, I will not repeat those points here.

7) No version of the KCA provides any support for theism, assuming a tensed theory of time

The previous sections show that, under Craig's reading of "begins to exist":

a) Craig's version of the KCA provides no support for theism.

b) Assuming a tensed theory of time, dropping assumptions like an intrinsic metric of time, time relationalism or presentism does not help a case for theism, either.

c) In general, assuming a tensed theory of time, arguments against the logical and/or the metaphysical possibility of an infinite regress of events - or even against the existence of such regress in the actual world - would not help the theist's case, either.

d) Arguments allegedly based on science do not provide support for theism in this context, either.

That seems to leave no possibilities left, at least assuming a tensed theory of time, and Craig's reading of "begins to exist".

Moreover, assuming a tensed theory of time, section 6 shows that two alternative readings of the first premise would not help a case for theism, either: Those readings seem to cover most possible non-unusual readings.

So, the previous sections show that, on a tensed theory of time, the KCA provides no support for theism.

At this point, there appears to be no options left to consider, if one accepts Craig's assertion that a tensed theory of time is a requisite for the KCA [15].

Still, one need not agree with Craig on that, so let's assess whether someone could assume a tenseless theory of time, and then use the KCA to support theism.

8) No version of the KCA provides any support for theism, assuming a tenseless theory of time

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.

On the other hand, under the first alternative reading of the first premise considered above, things can begin to exist on a tenseless theory of time.

However, under that reading, the KCA provides no support for theism, even under a tenseless theory of time.

So, let's consider an argument based on the second alternative reading of "begins to exist", assuming a tenseless theory of time.

Would a variant of the KCA based on that reading provide any support for theism?

I will argue in the section eleven that belief in the first premise is not justified, anyway, but that's another matter.

Here, the question is whether - granting both a tenseless theory and the first premise under the second alternative reading -, the KCA provides support for theism.

It seems not:

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.

Hence, a theist attempting this line of argumentation ought to accept that, necessarily, if God exists, he will eventually become still and never act again.

Of course, if a theist also holds that God exists necessarily, she ought to accept that, necessarily, God will eventually become still and never act again.

That necessity could be metaphysical or logical depending on the case, but given usual descriptions of God, it's hard to see a way around that in either case, even if the precise moment at which the end of time will happen is still a contingent matter.

But let's say that that is not a problem after all. Even then, it seems intuitively clear that there is no contradiction involved in the claim of an infinite future progress of events.

Also, there appears to be no intuitive support for the idea that the future is closed in that way - in fact, that's highly counterintuitive -, so attempts to use intuitions to show metaphysical impossibility would fail just for that reason, independently of other considerations about such arguments.

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.

9) Craig's reply, events, and timelessness

After someone raised the issue on his website, Craig replied[16] 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". [16]

However, 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.

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

William Lane Craig[16]

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.

But let's see a little more of the reply:

William Lane Craig[16]

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

But that is obviously false. Since it's 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 is obvious from my previous quotation on his book.

Yet, in his reply to the objection I raised, Craig claims [16] 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 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[16].

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[16] 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 subsection shows.

9.1) A contradiction, no matter what

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.

If E(2) has a duration e>0, then since E(2) finished at t=0, there is a temporal interval of duration e>0, prior to t=0. But that is a contradiction.

If E(2) has a zero duration, then since the final state of E(2) - namely, the state of God's having property P(2) for the first time - obtains at t=0, and the duration of E(2) is actually zero, then the initial state of E(2) - a state at which it is not the case that God has property P(2) - also obtains at t=0.

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 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, my point here is that if the end of the event of zero duration is at t=0, and the duration is, well, zero, then the conclusion is that the beginning of the event is at t=0 as well, entailing a contradiction.

In brief:

1) If E(2) has a non-zero duration - which follows from Craig's original claim, in this book -, then a contradiction follows.

2) If E(2) is instantaneous - which is what Craig says in his reply to my objection -, then a contradiction follows.

The contradiction is inescapable.

Note that even if Craig chooses to use the word 'change' in a non-standard way, and no longer calls that change in God (and it's a change in the ordinary sense of the word 'change') a change, that is irrelevant to my point. I'm using 'change' in the ordinary sense, and showing that a contradiction follows anyway.

9.2) Timeless change?

I guess Craig or someone else might then claim that those changes - and they are changes, in the usual sense of the word 'change' in English - do not have either a zero duration, or a non-zero duration, but somehow they're timeless or partially timeless, and somehow for that so-called 'reason' one shouldn't speak of duration.

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.[17]

In addition, I would take issue with the meaningfulness of his claims:

Craig claims that the changes are 'instantaneous', but somehow they don't have a zero duration?

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

Moreover, how are those changes are somehow 'timeless' or 'partially timeless' changes?

What would that even mean?

If by "X is timeless", Craig means that X does not stand in any temporal relations, then the problem remains: how can an object exist in the first state of the world, and then change, and still be timeless in that first state, given that it seems it does not differ from a temporal state at t=0?

And if "timelessness" is something like "absence of all events" (i.e., an absence of all changes), then there cannot be a timeless change, so the changes I take into consideration either have a non-zero duration (and so, a contradiction follows) or a zero duration (and still, a contradiction follows).

In fact, as I pointed out above, Craig himself contends that God, in his timeless state, is changeless. [17], so 'timeless change' (if meaningful at all) would also contradict Craig's claims.

What if Craig means something else by 'timeless'?

In any case, 'timeless change' is not an option, by Craig's own words.

Regardless, let's leave the previous contradictions aside in this subsection for a moment, and show that, in any case, a 'timeless' God who becomes temporal is an untenable claim: more precisely, the reason the contradictions can derived is that what he proposes is actually ontologically indistinguishable from God at t=0, even though he calls the state 'timeless' and denies that it's t=0, so he's describing a first temporal state, and yet denying that it's temporal.

Let's consider two scenarios, ordering the states of the world in terms of the direction given by supporters of the KCA - i.e., the world changes from one state to the next.

Scenario 1:

First state of the world:

Timeless state S. The only object is O, which exists uncaused.

Second state of the world:

Temporal state. t=0. The objects are O and U, and O is the cause of the existence of U; they all exist temporally at t=0.

Third state of the world:

Temporal state; t=r > 0. The objects are O, U and, perhaps some other objects.

Scenario 2:

First state of the world:

t=0. The only object is O, which exists uncaused.

Second state of the world:

Temporal state. t=a>0. The objects are O and U, and O is the cause of the existence of U.

Third state of the world:

Temporal state; t=r > a. The objects are O, U and, perhaps some other objects.

A key question here is: What is the ontological difference between the two?

Saying that one has a timeless state and the other does not, so that is the ontological difference, would miss the point:

The point is that this so-called "timeless" state seems to behave exactly like a temporal state at t=0, even if the word "timeless" is deployed.

In other words, there is no ontological difference, even if different words - of very dubious meaningfulness to say the least - are used.

Furthermore, on the issue of timelessness, Craig makes the following claim:

William Lane Craig: [2]

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

In which sense can object O be in an “absolutely quiescent” state in scenario 1, but not in scenario 2?

In both cases, what we have is one first state of affairs that changes into another state of affairs.

How would any of them be any more "quiescent" than the other?

It seems clear that that cannot be so: in both cases, O just changes from the first state to the second.

O never remains unchanged for a while - which would require time.

The mere uttering of words like "quiescent" or "timeless" is not a "get out of logic free" card, and should not be accepted as making a distinction that is not there.

Given the previous considerations, it seems clear that the "timeless" claim amounts to trying to make an exception to the premise that everything that begins to exist, has a cause of its existence, just by using the word "timeless", but failing to actually denote any ontological differences...

10) The meaning of "begins to exist"

While the results of the previous sections show that the KCA provides no support for theism, there are further, independent and conclusive reasons to reject it.

In the this and the following sections, I will provide sufficient reasons to conclude that the KCA provides no support for theism, even if all of the arguments I gave so far were to be rejected.

In this section, I will assess the meaning of "begins to exist"; first, let's compare Craig's hypothesis about the meanings of "begins to exist" and "comes into being", with the second alternative reading considered in section six (let's call this alternative hypothesis "hypothesis 2") [14], and test the two hypothesis to see which one is closer to matching the meaning of the words.

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. .

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, 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 to me that he came into being, and began to exist. That's in line with hypothesis 2.

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.[18]

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 7time 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 2 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[19].

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

According to Craig's hypothesis, 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 2, 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 2 gives 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 2 is entirely accurate, but it does seem to be much closer to capturing the meaning of the words than Craig's hypothesis is.

Another alternative (say, hypothesis 3) would be just like hypothesis 2 but allowing open and semi-open finite intervals.

Hypotheses 2 and 3 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 alternatives 2 and 3 seem to give the right results.

11) The first premise

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. [20]

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

In other words, someone may not accept that everything that begins to exist has a cause (they don't need to actually deny that everything that begins has a cause, but simply not affirm it), while accepting that, for instance, every event/change has a cause; that's also debatable, but the point is that it's an alternative that avoids any of the issues raised by Craig, and - at least to me - it seems more intuitive. That does not mean that one ought to assume that only events/changes have causes, of course, 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 those events/changes would not happen without a cause.

In any case, a question is: would belief that everything that begins to exist has a cause be warranted?

Another one is: is lack of belief in that claim, unreasonable?

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

In other words, one ought not to believe it,even if the assumption that "timeless" (in Craig's usage) is coherent, were justified.

Moreover, even if we leave the issue of timelessness aside, there appears to be no good reason, either intuitive or empirical, to believe that everything that begins to exist has a cause, either in the sense of hypothesis 2 , or hypothesis 3, or Craig's hypothesis about the meaning - minus the "timeless" condition.

Still, there is no need to settle the matter of what "begins to exist" mean.

We can just leave that undefined.

Still, the question is whether there is support for the claim that anything has a temporal beginning has a cause - which is what the KCA claims, after all.

While it's true that, in daily life, anything that has a temporal beginning seems to have causes, in daily life it's also the case that every event/change seems to have causes, and what is intuitive is may well be that every event - i.e., every change - has a cause.

So, two questions are:

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 begins to exist 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?

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

In order to assess our intuitions on the matter, 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.

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 an change/event "X comes into existence", it seems to me one needs precisely to separate beginning of existence from changes/events - which does not happen in ordinary cases.

Otherwise, it could be that what's intuitive to us is just the principle that every event - that is, any change - has a cause, and the correlation with a beginning arises because it just happens to be the case than, in daily life, things that begin to exist are just those X for which there is an 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.

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 principle ought to be accepted, or even merely that it's rational to do 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 have causes.

A possible alternative line of arguing, in support of claim that everything that begins to exist has a cause, would be to say that if X begins to exist, then it's clear - either intuitively or empirically - that there is an change/event "X comes into being" - i.e., a change from a state of affairs at which X does not exist, to one at which it does.

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

In fact, if time had a beginning (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.

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.

But using objects in daily life as examples might as well be used to claim that no object is timeless, or that all persons came into existence, etc., so this avenue does not seem promising for the theist, either - in any case, they'd have to make their case.

So, it seems that we're not justified in believing that every X that begins to exist comes from an event "X begins to exist" - let alone not justified in not believing it -, or that everything that has a temporal beginning, has a cause.

It's true that someone might have different intuitions on the subject, so that might depend on the person - assuming that we consider those particular intuitions reliable.

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 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, as well as for a model of how the universe works under conditions not covered by present-day models.[21]

12) 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[22]:

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 [23], 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.[22]

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[22], 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.

13) 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!

Counterintuitiveness aside, the question is whether there are any good reasons to believe 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, I agree that it's impossible, on a tensed theory of time, to have an infinite past if there is a first event/change.

Indeed, if a tensed theory of time is true and there is a first event/change, then there is no infinite chain of events, one after the other, 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.

One objection raised against that argument is that it resembles Zeno's paradoxes.[24]

Craig's reply to that objection is based on a claim 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.

As I explained above, the length of the intervals is actually not relevant. However, that does not seem to work against Craig's argument in this case: Whatever the solution to Zeno's paradoxes is, the fact remains that one cannot possibly form an infinity by finitely adding the number one, or any finite numbers.

Still, whether or not the arguments resemble Zeno's paradoxes in some way is not the point here.

Rather, the point here is whether we have good reasons to believe that an infinite past is impossible on a tensed theory of time.

I will argue that at least Craig provides no such good reason. If there is any, it should be found elsewhere.[25]

13.1) The contradictory case of Tristram Shandy

One of Craig's arguments against an infinite past is based on the story of Tristram Shandy. [26]

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 - a fact that, to my knowledge, was first pointed out by an anonymous poster who goes by the name "Dante Alighieri".

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: [27]

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.

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.

13.2) 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[28].

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:[28]

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 [29].

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.

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

Craig 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[30]

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 get an actual infinity of events by finitely many times adding a finite number of them (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".

15) 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 let 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. [31]

15.1) 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. [17]

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.

15.2) Changelessness and immateriality

Craig maintains that the first cause must be "changeless", since an infinite regress of changes cannot exist. [17]

But if so, then the only thing one can infer from that is that there has to be a first change.

So, that is not a problem for even particles: as long as there is a state and no previous state (hence, no previous change), or for some kind of field before particles form, etc.; all of that would be "changeless" in the sense that, well, there is no previous change.

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 [17], which is allegedly impossible for particles and the like.

But then, in that case, changelessness does not follow from a lack of infinitely many past changes, and he incurs a non-sequitur.

In any event, the point is that no infinite regress of changes only entails a first change, not a "changeless" state in whatever sense Craig of "changeless" Craig intends to use the word.

Moreover, if the first cause were God, he would change from not knowing any tensed truths (for instance), to knowing some tensed truths. That's a change.
Furthermore, as particles, fields, etc., change, God's knowledge of them would, so he would be changing constantly as well.

And if there is a first state in which there are no particles, fields, etc., God would still change from that state to the next state, just as any field, etc., in a first state would change from that state to the next.

On that note, let's consider the two scenarios I introduced earlier: once again, the first cause changes, just as an object at t=0 would change.

So, the claim appears to be either contradictory, or meaningless.

Now, Craig claims is that the first cause is changeless "sans the universe". [17]

But once again: what does that even mean?

In the usual sense of the words, one would understand that an object is changeless if it does not change as times goes by. But if there is no time, what does that mean?

In any event, the object of course would change, as the previous scenarios illustrate.

So, in addition to the claim that God is timeless sans creation, and temporal with creation - which is contradictory, if meaningful at all - Craig adds another mysterious claim - to say the least -, namely that God is changeless sans the universe.

In addition, as I pointed out, Craig claims that, since it's changeless, the first cause is also immaterial.

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.

15.3) Timelessness, once again

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

In this subsection, I will briefly recap some of the reasons I've already given, and then stress the point that even leaving aside any considerations of durations of the events/changes like 'God changes from not knowing any tensed facts, to knowing at least one tensed fact' - or similar ones -, the claim that God is timeless sans creation but temporal with it is untenable; in this subsection, I will also consider other potential objections, such as simultaneous causation and 'timeless will'.

According to Craig, time cannot exist in the absolute absence of all events - in other words, in the absolute absence of all changes -, and so the first cause must be timeless. [17]

However, as I explained earlier, this purported first cause would change exactly as an object at t=0 would.

Also, Craig claims that time has a beginning, so the cause of time must be timeless.

But that only highlights the problems I just mentioned: for any change/event 'time comes into existence' would take time, and so there would be time before the beginning of time, which is impossible. And if the event/change were instantaneous, still a contradiction would follow, for similar reasons as I argued before.

Using the word 'timeless' does not avoid that problem: rather, it's just a misuse of the word "timeless" to describe what is not ontologically different, making in practice an exception to the claim that everything that begins to exist, has a cause.

Someone might raise the issues of simultaneous causation, or a 'timeless will' (whatever that is), but that would not block my objections:

First, in the case of the duration of the events/changes, the issues of simultaneous causation and a 'timeless will' are orthogonal to the matter at hand, since a contradiction can be derived on other grounds, without making any assumptions about them.

Second, leaving the duration of the events/changes aside, let's consider again the following scenarios, ordering the states of the world in terms of the direction given by supporters of the KCA - i.e., the world changes from one state to the next:

Scenario 3:

First state of the world.

Timeless state S. The only object is God, who timelessly wills to create the universe.

God exists uncaused.

Second state of the world.

Temporal state at t=0.

The only objects are God and the universe - including, of course, all the objects in the universe.

God is the cause of the existence of the universe.

Scenario 4:

First state of the world.

Temporal state t=0. The only object is God, wills to create the universe.

God exists uncaused.

Second state of the world.

Temporal state t=r>0.

The only objects are God and the universe - including, of course, all the objects in the universe.

God is the cause of the existence of the universe.

It is clear that scenario 4 would contradict a claim that everything that begins to exist has a cause, at least under common readings of "begins to exist", and under Craig's.

So, under those readings, scenario 4 would contradict the first premise of the Kalam Cosmological Argument. In addition, if there is a claim that all causation is simultaneous, then scenario 4 would contradict that as well.

However, leaving all of that aside, a more direct and obvious problem is that scenario 3 is ontologically the same as scenario 4.

In fact, it's not the case that state S in scenario 3 is a state of absolute changelessness, whereas the temporal state at t=0 in scenario 4 somehow changes immediately, for in both cases, the state changes to the next, and in both cases, there is no lapse of time during which a state remains unchanged.

So, in both cases, there is an entity - namely, God - who exists at the first state of the world, and has a will at that state. God creates the universe, and changes - coming to know that the universe exists, for instance -, and that is the case under both descriptions.

In other words, in scenario 3, the word "timeless" is used, and it's not used in scenario 4.

However, this so-called 'timeless' state of God also changes, and in fact plays exactly the same role that the temporal state at t=0 plays in scenario 4:

So, the word "timeless" is actually misused, since there is a false claim that time only starts at the second state of the world; scenario 4 is the same as scenario 3, but without making false claims of timelessness.

Of course, the same problem arises if one changes the description of the timeless state in some way - e.g., altering the description of the "timeless will", etc., since for the same reasons, there is no ontological difference between the two modified scenarios - just a misuse of the word "timeless" in one case.

15.4) Spacelessness

The property of spacelessness allegedly follows from timelessness and immateriality.

Since the claim of timelessness is untenable, this conclusion fails.

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

And if a field or something like that can be timeless, but can't be immaterial, then timelessness does not entail immateriality, anyway (of course, if the so-called "timeless" object were to change and exist temporally at t=0, that would also entail a contradiction, but only as it does in the case of God).

15.5) Power

According to Craig, the first cause must be very powerful, since it caused all of "physical reality" to exist, without any material cause. [17]

Leaving aside issues about the concepts of "material", and "physical", and of course the decisive coherence 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 first cause of the universe, it might be - purely for example - that the object in question is only capable of causing things like our universe, and is incapable of acting within them, or making much of anything else.

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

15.6) Personhood

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

15.6.1) Personal explanations and scientific explanations

Craig claims that, as Swinburne "points out", there are two kinds of explanations: personal and scientific. [17]

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 good 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 part of the article for the sake of the argument.

15.6.2) Other properties of the first cause

Another argument Craig gives is based on the previous "conclusions" that the first cause is timeless, immaterial, beginningless, uncaused, and spaceless. [32]

As I've shown earlier, most of those claims have insurmountable problems, so this argument fails as well.

15.6.3) "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". [32]

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 present conditions. [32]

That clearly is not a good characterization of human freedom.

In fact, indeterminism in humans has nothing to do with freedom - or rather, it might get in the way.

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

Bob has been a good police officer for ten years now.

He's kind, committed to protect and to serve the public, good to his children, and so on.

Now, one morning, Bob goes to work as usual. The police get a call about a domestic disturbance, and Bob and another officer are sent to the address they're given.

When they arrive there, they encounter Mary, a fourteen-year old girl high on drugs, acting completely irrationally. She tells Bob: "You're a police officer, so you're evil. Why don't you shoot me?".

Bob has no reason at all to shoot Mary. She poses no threat to him, and can be easily arrested if needed. Also, Bob is a good person.

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

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

No one would see that coming, so no one could stop him if he did that.

But Bob - of course - feels no inclination whatsoever to shoot her, does not shoot her, and follows procedure.

The point is that saying that Bob can shoot Mary, that he has the power to shoot her, that he is free to choose whether to shoot her, etc., means that he would shoot her if he chose to do so, that he's not being coerced, etc.

It does not mean that, even given Bob's mental state at the time he chose to follow procedure, and even given all the conditions of the world at that time, it was still possible that Bob would shoot her.

That can be ascertained by introspection and analysis of the meaning of the terms.

But if that is unpersuasive, let's suppose otherwise, and let's assume that Bob has the kind of "freedom" proposed by libertarians.

Then, since Bob could have shot her, but libertarian-freely decided not to shoot her, it seems that there is a world W with the exact same past as ours prior to Bob's decision to follow procedure, at which Bob shot Mary instead.

But that is not an exercise of freedom, in the usual sense of the words.

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

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

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

It seems D it's not so much a decision Bob made, but rather, it's something that happened to Bob. It's not something Bob could have anticipated, or prevented: at some point his mental processes changed from normal to "shoot Mary", 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, Bob could not have prevented his mental processes from changing at some point from normal to "shoot Mary", no matter what he did before - and that change could not be reasonably said to be his decision, since he had never considered that before, and the change took him 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 agent 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 kind of 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.

And if previous processes in her mind made E in some sense probable - assuming that objective probability makes sense -, but weren't enough to bring it about, something still altered her mind randomly.

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 Bob, 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, libertarian free will ought to be rejected.

That does not mean we can't act of our own accord, of course. We can have freedom; it's just that the libertarian account of freedom is the wrong account.

Second, humans aside, someone might posit that the first cause is not deterministic, even though as we saw, indeterminism doesn't have anything to do with freedom.

But if the first cause and its "timeless" volition - assuming coherence in this part of the rebuttal for the sake of the argument, but against good reasons - aren't sufficient conditions to bring about the universe, then that only detracts for the first cause's power, as he might have failed to bring about the universe.

15.7) 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:[33]

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".

It may not even be what most people mean by "God".

For instance, Richard Swinburne[34] 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 that entails omnipotence, omniscience, moral goodness, etc.

Moreover, Swinburne explicitly denies that timelessness is part of the meaning. [34]

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 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 make sense -, that would still not establish that God exists, in the sense the word "God" is often - perhaps usually - used by theists, and would be compatible with - for instance - deism.

16) Conclusion:

The arguments made above show that the KCA provides no support for theism, at least if either a tensed or a tenseless theory of time is true.

The results may not cover all interpretations of the premises, or perhaps uncommon theories of time.

However, they are quite general, covering not only William Lane Craig's version of the Kalam Cosmological Argument, but a number of alternatives as well, including, it seems to me, all the main possibilities in present-day philosophy.

Notes and references:

[0]

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.

[1]

With the difference that any statements like “the actual world contains no state of affairs S at which God exists timelessly” should be simply ignored if "timeless" is meaningless. But the main result is the same.

[2]

[3]

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

[4]

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

[5]

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”.

[6]

On his website, Craig[7] says that it's not clear to him that creation itself is an event which determines a before and an after.

However, that E(0) – or, for that matter, E(1), or E(2) [5]– is an event follows straightforwardly from the definition of “event”: an event is any change, and Craig himself says that God changed.

Also, Craig claims that any event takes time, and a contradiction follows.

In fact, the definition of "event" is not even needed.

The claim that any change takes time is sufficient to derive the contradiction.

On that note, let us suppose the the event E(2) “God changes from not knowing any tensed facts at S, to knowing some tensed facts at t=0” has zero duration.

So, at the beginning of the event, it is not the case that God knows any tensed facts - since the event is precisely the change in God from not knowing any tensed facts, to knowing some tensed facts.

On the other hand, at the end of the event, God does know some tensed facts.

Now, since the event ends at t=0 and its duration is zero, its beginning is also at t=0.

Thus, at t=0, God does not know any tensed facts, and at t=0, God knows some tensed facts. But that's impossible.

The previous argument can alternatively be put in the following way: if the change in God from knowing no tensed facts to knowing at least one tensed fact is literally instantaneous and occurs at t=0, then at t=0 both the state from which God changes and the state into which he changes are present. So, at t=0, it's not the case that God does not know any tensed facts, and at t=0, God knows at least one tensed fact. But that is impossible.

Someone might object that E(2) does not begin at t=0, but at the "timeless state" S.

However, using the word "timeless" is not a license to circumvent logic: if the event ends at t=0, and its duration is literally zero, then its beginning is also present at t=0 as well.

[7]

http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=9069&printer_friendly=1

[8]

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.

[9]

Later, I will consider alternative readings of "begins to exist", showing that alternative versions of the KCA based on them provide no support for theism, either.

Also, I will analyze the meaning of "begins to exist" in more detail in the section ten.

[10]

Someone might not accept the claim that, on a tensed theory of time, the fact of temporal becoming alone - i.e., the passage of time - counts as a change.

According to such a view, even if there were infinitely many times t(n+1) < t(n), for all n, without any change in any entity, that would not be enough to establish that there are infinitely many past events/changes.

There is no need to settle that matter here, since in this case, by assumption, God exists at t and at u < t, and that entails an event, as I show in section three.

[11]

A consequence that might be of interest is the following one:

Since, for every two times u < t, one can consider the event E(u,t): “God comes to know that u is past, and t is present”, it follows that for every two points in time, there is a corresponding event.

Since, on a tensed theory of time, there can't be infinitely many events between two given points, then it follows that there can't be infinitely many points in time between two given points in time.

In other words, on a tensed theory of time, there cannot be infinitely many events, one after the other, in a closed temporal interval [t1,t2].

Thus, given the God assumption, such an interval can't contain infinitely many instants, either.

It follows that time is discrete, not continuous.

[12]

By "in the context of the KCA" I mean that I make no claim here as to whether something provides support for theism in other contexts - i.e., whether something would support an argument for theism different from the KCA, in any of its versions.

Such a claim would far exceed the scope of this article.

[13]

As always, an event is any change.

[14]

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.

[15]

[16]

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

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[18]

[19]

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

[20]

[21]

That aside, let me stress that adopting the view that all events have causes does not require one to adopt the view that only events have causes, and not adopting the view that everything that begins to exist has a cause does not require one to adopt the view that some things that begin to exist have no causes.

[22]

Source: The Blackwell Companion to Natural Theology

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

[23]

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.

[24]

Page 119.

[25]

Of course, the KCA would still fail for some the other reasons explained in this article, even if all of Craig's arguments against an infinity were successful. But I'm trying to be thorough.

[26]

Pages 120-124

[27]

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.

[28]

Page 120.

Incidentally, it seems that the 'planets' argument also fails to distinguish between a tensed and a tenseless theory of time.

[29]

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.

[30]

[31]

[32]

[33]

[34]

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

Clarendon Press Oxford.

Page 7.

Angra Mainyu's blog

Pages

Wednesday, January 4, 2012

The Kalam Cosmological Argument, once again

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