This post is out of date. An improved reply to the KCA can be found here.
Against The Kalam Cosmological Argument – a brief reply
William Lane Craig defends Kalam Cosmological Argument, and further argues that the cause of the universe is a personal being who is timeless sans the universe, but temporal with it. [1]
I will show that Craig's God would actually be an uncaused entity with a temporal beginning at the first temporal state of the world.
Moreover, this applies to any version of the Kalam Cosmological Argument that is defended based on claims of a tensed theory of time, the impossibility of an actual infinity, and the claim that infinitely many actual past changes in the world would constitute an actual infinity.
By 'KCA' I mean the Kalam Cosmological Argument.
By 'Craig's position' I mean Craig's claims and arguments in the context of his case for theism based on the KCA. That includes his reasoning in support of the premises of the KCA, and also in support of the claim that the cause of the universe is God.
By 'event' I mean any actual change, and I use 'change' in the ordinary sense of the word. By saying that the change is actual, I mean that my concern is ontological. Different points in a mathematical model do not count as events. Only real changes in the world do.
I will use bold italic uppercase letters (e.g., J, K, etc.) to denote finite temporal intervals, and bold italic lowercase letters (e.g., t, u, etc.) to denote temporal instants. I will also number them (e.g., t(1), t(2), etc.)
My concern here is ontology, so when I talk of temporal intervals or instants, I'm talking about actual features of the world, not about mathematical models.
Also, when I speak of temporal intervals, I'm assuming those intervals are of finite duration, though not necessarily of equal duration.
By '◄' I mean 'earlier than', in the usual, temporal sense of the word. For instance, J◄K means that J and K do not overlap, and J is earlier than K.
When I prove lemmas, unless otherwise stated, I'm assuming any parts of Craig's position, as required. In other words, those lemmas are statements that follow from Craig's position.
Lemma 1: Infinitely many events in the world are impossible, regardless of whether their duration is equal.
Proof:
This can easily be seen in Craig's defense of the KCA. For example:
William Lane Craig: [2]
The second premise states that an infinite temporal regress of events is an actual infinite.
The point seems obvious enough, for if there has been a sequence composed of an infinite number of events stretching back into the past, then the set of all events in the series would be an actually infinite set.
Craig was talking about events of equal lengths, but clearly, that they constitute an actual infinite does not depend on their length. As long as they are actual changes, infinitely many events meet Craig's requirement for an actual infinity.
William Lane Craig:[2]
So when we say that the number of past events is infinite, we mean that prior to today, ℵ0 events have elapsed.
Once again, that does not depend on the length of the events. And Craig goes on to claim that ℵ0 events are impossible:
William Lane Craig:[2]
Because the series of past events is an actual infinite, all the absurdities attending the
existence of an actual infinite apply to it. For example, if the series of past events is actually
infinite, then the number of events that have occurred up to the present is no greater than
the number that have occurred at any point in the past.
And that would be the case regardless of whether the events are of equal duration.
So, while there might be infinitely many potential changes, and so the future need not be closed, Craig's position entails that there are only finitely many past, actual changes in the world – in other words, only finitely many past events. Moreover, at any time in the future, only finitely changes will have occurred.
Similarly, this entails that any closed temporal interval contains only finitely many events.
In this section, I will establish some results on the nature of time that follow from Craig's position.
Definition: A temporal interval J has property Q if and only if there is some non-negative integer N(J), such that J cannot be divided into more than N(J) smaller temporal subintervals.
Lemma 2: If there are temporal intervals, then every temporal interval J has property Q.
Proof:
Let's assume a temporal interval J does not have property Q.
By lemma 1, there are only finitely many events in J.
So, let m be the number of events in J.
Since J does not have property Q, there is some natural number r > m+4 (for instance), such that J can be divided into r smaller temporal subintervals, J(1)◄J(2)◄ J(3)...◄J(r)
Let us consider the following events, for k in {2,...,r-1}
E(k): God changes from not knowing that J(k) is present to knowing that J(k) is present.
Note that those are actual changes in the world, in particular, in the mind of God.
So, those are r-2 > m+2 distinct events, contradicting the assumption. That proves lemma 2.
Lemma 3: If there are temporal intervals, every such interval J can be divided into finitely many non-dividable temporal intervals.
Given J, J can't be divided into more than N(J) subintervals, by lemma 2.
So, let's divide J into the maximum number of subintervals into which it can be divided. Then, every such subinterval is non-dividable, and lemma 3 is proved.
Lemma 4: If there are temporal instants, then for every two instants t and u such that t ◄ u, there is some non-negative integer N(t,u), such that there are not more than N(t,u) instants between t and u.
Proof:
Essentially the same as lemma 2, with only the obvious changes.
Lemma 5: Either there are non-dividable temporal intervals, or there are instants.
Proof:
That seems clear on a tensed theory of time. Temporal becoming is a real feature of the world, so if there are no intervals, it seems that there are instants. If there are intervals, there are non-dividable intervals, by lemma 3.
5. An absolute temporal beginning
In this section, will prove that Craig's arguments entail that there is a first actual temporal state of the world, a second one, etc.
Lemma 6: If there are non-dividable temporal intervals, there is an absolutely first non-dividable interval K(0). There is no temporal interval that begins before K(0) begins. Moreover, there is a second such interval K(1), a third one, and generally the past is composed of finitely many such intervals.
Proof: Let's assume there is a sequence of non-dividable intervals K(n+1) ◄ K(n), for all natural numbers n.
Let's consider the events
F(n): God changes from not knowing that K(n) is present to knowing that K(n) is present.
Then, there are infinitely many past events, contradicting lemma 1.
That proves that if there are non-dividable temporal intervals, there is a first one K(0).
If there is some other interval J such that begins earlier than J than K(0), then by lemma 3 we can divide J in non-dividable intervals, and one of them would be earlier than K(0), a contradiction.
By a similar procedure, we can construct a second one, and so on, and the total number up to the present time must be finite by lemma 1, since otherwise we could construct an infinite sequence of events.
That proves lemma 6.
Lemma 7: If there are temporal instants, there is a first temporal instant t(0). Similarly, there is a second instant t(1), a third one t(2), and generally the past is composed of a finite number of such instants.
Proof:
Like the proof of lemma 6, removing superfluous parts and making some obvious changes.
Lemma 8: Either there is a first temporal instant t(0), or a first non-dividable interval K(0).
Proof:
It follows from lemmas 5, 6, and 7.
Lemma 9: There is an absolute first, non-dividable temporal state of the world T(0). Moreover, there is a second such state T(1), a third T(2), and generally the past if composed of finitely many such states.
If there are instants, then let T(n) be the state of the world at t(n), for all past instants.
Then, for k>n, at T(k) God knows that t(n) is past and that there are more than n past instants, whereas at T(n), it is not the case that God knows that t(n) is past and it is not the case that God knows that there are more than n past instants. So, if k>n, then the states T(k) and T(n) are different from each other.
Also, since each T(n) corresponds to a single instant, it cannot be divided.
If there are non-dividable intervals, then let T(n) be the state of the world at K(n), for all past non-dividable intervals.
Then, for k>n, at T(k) God knows that K(n) is past and that there are more than n past non-dividable intervals, whereas at T(n), it is not the case that God knows that K(n) is past and it is not the case that God knows that there are more than n past non-dividable intervals. So, if k>n, then the states T(k) and T(n) are different from each other.
Also, since each T(n) corresponds to a single non-dividable interval, it cannot be divided. [4]
Let's consider the following two scenarios, ordering the states in terms of causal priority.
First state of the world:
Timeless state S.
The only object is God, which exists timelessly at S and without a cause.
Second state of the world:
First temporal state T(0).
God exists temporally, and the universe exists. The change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because God intends to bring it about.
Third state of the world:
Second temporal state T(1). The objects are God, the universe, and perhaps some other objects.
First state of the world:
First temporal state T(0).
The only object is God, who exists temporally at T(0) and without a cause.
Second state of the world:
Second temporal state T(1).
God exists temporally, and the universe exists. The change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because God intends to bring it about.
Third state of the world:
Third temporal state T(2). The objects are God, the universe, and the same other objects as in the previous scenario (if any), with the same causes.
The key point here is that the so-called 'timeless' state in scenario 1 is exactly like the first temporal state T(0) in scenario 2. In other words, there is no ontological difference whatsoever, even if different words are used:
In both cases, what we have is a first state of the world changing into the next, and so on.
In both cases, God exists without a cause of his existence at the first state of the world.
In both cases, the universe exists at the second state of the world, and exists because God intends to bring it about, and so on.
Also, saying that the difference between the two scenarios is that one state – namely, S in scenario 1 – is timeless and the other – namely, T(0) in scenario 2 – is temporal, or that in one of them there at least one tensed fact, whereas in the other one there are no tensed facts, would fail to address the point, since that would simply amount to denying that there is no ontological difference, without explaining how or why that is so, which is a burden on the theist defender of the KCA, since we can conclude that the states are ontologically identical, just by looking at the description of those states, and regardless of the use of the word 'timeless' in the first one. Still, let's go further and show that Craig's implication that a timeless state would be changeless also fails to make a difference. In fact, 'both' states are not changeless. :just as God changes from his first to his second state in scenario 2, he does so in scenario 1. So, it remains the case that there is an entity – i.e., God – that exists at a first state of the world and without a cause of his existence, changes to a second state, then to a third one, etc., regardless of whether the first state of that entity is called 'timeless'.
Alternatively, someone might raise the following objection:
An ontological difference is that temporal states of God must change as time goes by, whereas the timeless state S in scenario 1 could have remained unchanged. In other words, if God exists at temporal state T(0) – as in scenario 2 –, then necessarily, there will be a second temporal state T(1), and necessarily, God will change from T(0) to T(1), since his knowledge of tensed truths will change. On the other hand, if God exists in a timeless state S (as in scenario 1), then it is possible, given that first timeless state of God, that God never changes.
The problem with that objection is that it follows from any creation hypotheses posited by theist defenders of the KCA – i.e., given what God's first state actually would be, based on the implications of their claims –, that it is impossible that God never changes given that first state, which means both scenario 1 and scenario 2 are indistinguishable in that regard as well, as the following reasoning shows:
First state of the world:
Timeless state S. The only object is God, which exists timelessly at S and without a cause.
Second state of the world:
Temporal state T(0). God exists temporally, and the universe exists. The change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because of God intends to bring it about.
First state of the world:
Timeless state S. The only object is God, which exists timelessly at S and without a cause.
There are no temporal states of the world.
In scenario 3, if God does not intend at S to change, then at T(0) God just found himself altered. In other words, if God's intent to change does not exist at at S, then the change is not something brought because God intends to bring it about, but something that happened to God, beyond his intent. That is so because the change under consideration is a change in God's state, and from his first state at S. In other words, it's a change from S to T(0). So, said change cannot have been caused by God's intent only at T(0), given that S is causally prior to T(0).
So, if God does not intend at S to change from his first state to his second state, then God found himself changed at T(0); the change is something that happened to God, not something that God brought about. But that contradicts the hypothesis that the change in scenario 3 happens because God intends to bring it about. Thus, at S, God intends to bring about the change.
Hence, given God's state at S in scenario 3, it is impossible that God does not change, since God can't fail to bring about what he intends to bring about. Moreover, just as in scenario 3 it is impossible that God does not change, the same is true and for the same reasons in scenario 1. Also, the states denoted by 'S' in scenario 3 and scenario 4 respectively, are not the same.
Someone might suggest that, in scenario 3, God exercised his libertarian free will at T(0) to bring about the change, but at S, he does not intend to change. However, leaving aside issues about the coherence of libertarian free will, that is impossible for the reasons I explained above: since the change under consideration is God's change from S to T(0), it cannot have been decided only at T(0). At T(0), the change already obtains. Also, the state S is causally prior to T(0), so a change in God's condition at S cannot have been decided only at T(0). Thus, as concluded above, at S God intends to change.
That aside, someone might concede that there is no ontological difference between scenario 1 and scenario 2, but claim that in that scenario God exists timelessly at his first state.
At this point, there appears to be no good reason to think that 'timeless' would denote anything at all in this context, but in any event, in that case we might simply posit, as an alternative, that the universe[5] might as well exist without a cause if its existence at a first state of the world, then change to its second state, and so on. If the first state of God is somehow is properly called 'timeless' in scenario 1, then the same is true of the first state of the universe in the following scenario:
First state of the world:
The universe exists without a cause of its existence. Nothing else exists – there may or may not be some things in the universe, but nothing beyond the universe.
Second state of the world:
The universe has changed and exists in its second state. Nothing else exists.
Just as God exists without a cause in scenario1, scenario 2, and scenario 3, the universe exists without a cause in scenario 5.
Just as God changes from the first to the second state of the world in scenario1, scenario 2, and scenario 3, the universe so changes in scenario 5. Then, God in those scenarios continues to change from one state of the world to the next, and the same is true of the universe in scenario 5.
Thus, there is no ontological difference between scenario1 and scenario 2, and no ontological difference that would justify denying that the first state of God is temporal in either scenario, but wouldn't justify denying that the first state of the universe is temporal in scenario 5.
Someone might bring up 'quiescence', as an attempt to show that there is a difference between scenario1 and scenario 2, and/or that there is a difference that would justify denying that God is temporal at his first state in scenario 1, but would not justify denying that the universe is temporal at its first state in scenario 5. On that note, and in an attempt to distinguish between the universe and God, Craig makes the following claim:
William Lane Craig: [3]
If not, then since the universe cannot ever have existed in an absolutely quiescent state, the universe must have had a beginning.
However, a 'quiescent' objection fails as well, for the following reasons:
First, there is no sense in which the first so-called 'timeless' state S in scenario 1 is quiescent, but the first temporal state T(0) in scenario 2 is not. Indeed, in both cases, what we have is one first state of affairs that changes into another, second state of affairs. In both cases, God exists at the first state of the world, and without a cause of his existence. In both cases, also, God changes from his first state at the first state of the world, to the second, and so on. God never remains unchanged for a while in the first scenario but not the second- that would require time -, or differs in any way between the scenarios, by the description of them.
Second – and now addressing Craig's contention -, the same can be said about the universe in scenario 5: in that scenario, the universe exists at the first state of the world, and without a cause of its existence. Also, the universe changes from its first state at the first state of the world to its second state at the second state of the world, there is no previous change, and no period during which the universe remains unchanged. But that is exactly what happens in the case of God in scenario 1.
Moreover, if, say, a particle exists in the universe at the first state in scenario 5, then any change in such particle from the first to the second state of the world is still a change from the first to the second state of the universe. There is no previous change, or period during which the particle or the universe remains unchanged, but that is exactly what happens in the case of God in scenario 1.
Thus, there is no sense in which God could properly be described as 'quiescent' at his first state in scenario 1, but the universe couldn't properly be described as 'quiescent' at its first state in scenario 5.
Someone might say that in scenario1 and scenario 2, the change from the first to the second state of the world, including the creation of the universe and God's own change from timeless to temporal, takes place because God intends to bring it about, whereas in scenario 5, the cause of the change is not specified.
That seems completely unrelated to the issue of whether God or the universe are 'timeless', changeless, quiescent, etc., but in any case, we may as well further specify the scenario and add that, in scenario 5, the change from the first to the second state of the universe is brought about by the universe's conditions at its first state (including, of course, any particle interactions if there are any, etc.), regardless of whether we put that in terms of substances and causal powers, or in terms of substances and laws, etc. Thus, the universe, which has certain conditions in its first state, brings about the change to its second state, just as God and his intent at the first state brings about the change in scenario1 and scenario 2 (and, for that matter, scenario 3).
This further specification of scenario 5 is not required, though: we might as well leave it unspecified, or alternatively even make the change indeterministic in scenario 5, so that given the first state of the universe, there is more than one possible second state, and only one actually obtains, introducing a certain degree of randomness. That would not appear to make any difference whatsoever in terms of changelessness, quiescence, or anything that might be called 'timelessness'.
All that aside, a theist defender of the KCA might suggest that, perhaps, the universe did not exist at the second state of the world, but only at some later state. However, that clearly wouldn't make a difference, either. We may simply posit scenarios like, say, scenario 1, 2, and 3, but without introducing the universe at the second state of the world, and keep scenario 4 and scenario 5 unchanged. The same reasoning as above yields the same results, defeating the attempt to make a distinction.
So, to summarize, if God does not begin to exist in scenario 1 because somehow he's 'timeless', 'changeless' and/or 'quiescent', then the universe does not begin to exist in scenario 5 for the same reasons, and the KCA fails, since the proponent of the KCA does not have any argument to rule out something like scenario 5.
If, on the other hand, God begins to exist in scenario 1, then the KCA fails for that reason.
Conclusion
Craig claims that God is timeless sans creation but temporal with it.
However, the 'timeless' claim is a confusion; Craig's claim about God's timelessness at his first state is false if meaningful at all, and even assuming meaningfulness, he fails to give any way to distinguish between God's first state and the universe's first state, when it comes to whether the state in question is timeless. In particular, in terms of alleged 'quiescence' or 'changelessness', no difference exists.
The same applies to other present-day versions of the KCA, which share the same relevant features.
[1]
Source: William Lane Craig and J.P. Sinclair, "The Kalam Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6
[2]
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; pages 115, 116.
[3]
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 106.
At this point, one might wonder whether there is an ontological distinction between instants and non-dividable intervals, or it's just a matter of notation. But there is no need to address the matter here.
[5]
I wrote a more detailed comparison of scenario 5 and a scenario in which God allegedly exists timelessly sans creation but temporally with it, in subsection 7.3 of this essay (some other sections of that post are outdated, though).
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