More Reflections on Bill Craig and Wes Morriston on the Kalam Cosmological Argument

Josh,

It is great to have you as a contributor here! This is a nice discussion of the issues for the Kalaam argument. I look forward to your future posts.

Best,
Tim

Of course, this definition makes use of states of affairs--the abstract kind that can change from being un-actual [non-obtaining] to actual [obtaining]), and Bill doesn't have those sorts of things in his ontology.

Is there a text where Bill Craig says such a thing--that there's aren't any (abstract) states of affairs?

He does talk, in that book with JP Moreland, about states of affairs quite a bit. See here:

http://is.gd/vDJh

But perhaps you've got a narrower notion in mind.

Thanks. I did find a chapter on "Creatio ex Nihilo and Abstract Objects" in his book with Paul Copan, Creation out of Nothing that considers conceptualist and fictionalist accounts.

I wonder, then, whether Craig could consistently use the following argument any longer in his debates:

"The Argument from Abstract Objects

1. God provides the best explanation for the existence of abstract entities.{2} In addition to tangible, concrete objects like people and trees and chairs, philosophers have noticed that there also appear to be abstract objects, things like numbers, propositions, sets, and properties. These things have a sort of conceptual reality, rather like ideas in your mind. And yet it's obvious that they're not just ideas in any human mind. So what is the metaphysical foundation of such abstract entities? The theist has a plausible answer to that question. They are grounded in the mind of God. Alvin Plantinga, one of America's foremost philosophers, explains:

It seems plausible to think of numbers as dependent upon or even constituted by intellectual activity. But there are too many of them to arise as a result of human intellectual activity. We should therefore think of them as... the concepts of an unlimited mind: a divine mind.{3}

At the most abstract level, then, theism provides a plausible, metaphysical foundation for the existence of abstract objects. And that's the first reason why I think it's plausible to believe in God." (from a 1995 debate)

http://www.leaderu.com/offices/billcraig/docs/washdeba-craig1.html

If there aren't, strictly speaking, any abstract objects, then they hardly provide any good evidence for God's existence.

Joshua,

Great post. I was curious about this passage:

"I think one's intuition about Premise 1 will depend in part on what one means by 'begins to exist'. Here is what I mean: 'x begins to exist' =def 'the state of affairs of x's existing becomes actual', or 'there is a change in a state of affairs in which x exists from being non-actual to being actual'. These accounts make no reference to time, and I personally do find it intuitive that if a state of affairs of x's existing becomes actual, then there was probably a cause of its doing so."

You say that these accounts make no reference to time, and I guess it's true that they don't make any such explicit reference to time. Still, I can't make sense of "existing becomes actual" without some previous time before which the existing was not actual. The same goes for "a change in a state of affairs in which x exists from being non-actual to being actual." What sense of "change" are we working with here that doesn't assume, say, that there was a time at which x is not actual that precedes the time at which x is actual. You could say, I suppose, that there's a kind of beginning to exist according to which x has a finite temporal extension and speak of its edge as being its beginning, but then I (like you?) just don't have the firm intuition that things that have beginnings in this sense (but not in the sense that there were times prior to their existence) must have causes. In fact, I have a hard time seeing how they could have causes that stand in no temporal relation to them (Craig's view, right?).

Also, you note, "There is the scientific argument for a finite past for our universe". Craig often says that this is so, and I'm sure there is such an argument. I'd be interested to know if anyone thought it was good. I think I've read that Earman claims that in standard Big Bang models for every time, t, there is an earlier time, t' and that on such models there is no absolute beginning to the universe. Maybe Earman's wrong about this and perhaps Craig or someone else has explained why, but I don't know where I'd find information on this. Myself, I've always been more interested in questions about what conclusions can be drawn once we assume that the universe has a beginning or lacks one so that and my complete lack of knowledge of the relevant science has made me disinclined to do much research on these 'scientific arguments' for beginnings.

Joshua,

Thanks, a lot of that was useful. I agree completely that the entailment from P to Q does not depend upon there being something about the semantic content of P in virtue of which this entailment holds, but I thought that your point in the post was that there was no entailment from 'X's existing becomes actual' to 'There was a time prior to the event described as 'X's existing becoming actual'. So, my worry is that your account of beginning in terms of 'X's existing becoming actual' still seems to suppose that there is a time prior to X's existence if X has a beginning. I could be mistaken about that, however.

Anyway, is the problem really one of simultaneous causation? I'm all for heads resting on pillows being the cause of the indentation in the pillow, but if God is atemporal, I thought that temporal predicates couldn't be applied to God so there's got to be some fancy footwork done having to do with God being outside of time but God's actions or the results of God's actions being in time.

I believe this article by WLC is very useful:

http://www.reasonablefaith.org/site/News2?page=NewsArticle&id=5321

Contrary to Craig's position, I believe Victor Stenger published an article in Philo in 2006 in which he argued that empty space-time would probably generate universes. It's online somewhere.

Hi Josh:

It's nice that you've posted your reflections on Bill's work. Yes, your experience with Bill Craig and Wes Morritson gave you an opportunity to discuss these issues from various, conflicting angles. The same with me here but in another similar context. Besides having studied Bill's work and having had a chance to study with him, I've also studied with Quentin Smith. Just wanted to share the following key ideas from Smith's recent work that is relevant to the discussion here and it'd be cool if some of you would also respond to Smith's "Kalam Cosmological Argument for Atheism" in Cambridge Companion to Atheism (2007).

Here are some of my summaries of the relevant section from Smith:

"Smith argues that the universe has begun to exist, and the universe has a cause
for its existence; that is, the universe is self-caused. Smith claims that the universe’s
causing its own existence, self-causing its own existence, is not equivalent to or analogous to saying that “B causes B” where “B” refers to the beginning of the universe.
By “B is self-caused” he means, “each part of B is caused by earlier parts of B, B’s
existence is logically entailed by its’ parts existence, and the basic laws instantiated by
these parts are caused to be instantiated by earlier parts that also instantiated these laws”.
Smith goes on to argue that each later state of the universe is causally explained by prior
states of the universe such that the explanation for the existence of each successive states
of the universe logically entails the existence of the series that consists of the whole
universe; or, the existence of the whole universe is logically required by the existence of
each states of the universe.
Smith also claims that the basic laws of nature such as “the law of conservation of
mass-energy and the law of increasing entropy or disorder” etc., exist because they have
instantiated themselves. Accordingly, each state of the universe is instantiated in such a
way that the basic laws of nature with their dispositional properties occurrently realized
causally explain that each successive state of the universe exist and it follows from this
that the universe is internally-caused for there is no need, Smith claims, to appeal to an
external cause such as God.
Smith works with an open-interval model of
the universe such that the universe’s existence is half-open in the earlier direction. This
implies that “…there is no instant corresponding to the number zero in the real line
interval that contains an infinitely many (continuum-many) numbers grater than zero and
either less than one or one. 0>x x that immediately follows the hypothetical “first instant” t=0. This is because between
any two instants, there are an infinite number of other instants”.
The preceding reasoning commits Smith to the existence of a set of an actually
infinite number of instants and instantaneous states of the universe, for example, as the
universe’s first second-long state, which is an interval of continuum-many instants. Again,
the universe’s second-long state, which is an interval of continuum-many instants in
half-open interval model of the universe, implies that there is literally no first instant for
the universe’s existence. If there is literally no first instant for the universe's existence, then there is no need to appeal to God for God to bring about the beginning of the universe.

Joshua,

Do you happen to know where it is that Rowe and Craig discuss the problem you mention? Thanks.

http://www.colorado.edu/philosophy/vstenger/Godless/Origin.pdf

This is the paper I mentioned above.

I find it interesting that the responses to the KCA (infinite past in quantum-gravity and probablistic spawning from empty space time) don't mix.

Great post, Josh! (And thanks for the kind words.)

I totally agree with your suggestion that the kalam argument "is more likely to appeal to the common man or woman than to your average philosopher." I think that's why it's so rhetorically effective in public debates. I received a post the other day from an agnostic who'd been listening to a lot of Bill Craig's debates. He said that the kalam argument was the one that nobody seemed to have an effective reply to. He thought he was about to become a theist on account of it. (Question: Is it good or bad for a Christian to tell a non-believer what's wrong with an argument for God's existence if that person is moved by it? I say it is the right thing to do. Wahrheit uber alles!)

I want to ask some questions about the "modal kalam argument" you propose at the end of your discussion of "premise 2."

Here's the first premise of the modal argument.

1. Beginnings always can have a cause (or at least some possible intrinsic duplicate of any beginning can have a cause).

That sounds innocent. But consider the following proposition:

(*) There could have been a beginning of everything.

At first blush, (*) looks pretty innocent too. But an immediate implication is that there could have been a beginning that could not have had a cause.

You might object that (*) implicitly rules out the possibility of necessary beings. But that is no more and nor less fair than implicitly assuming them to be possible (as you plainly do).

So how can we be sure that (*) isn't true?

Here's your second premise.

2. There can be a beginning to the existence of all contingent things (being contingent can begin to be exemplified): e.g., a Big Bang of contingent things is possible

I wonder if you should call this a "Big Bang of contingent things." The Big Bang (if there really was such an event) was the beginning of an expansion. It is an expansion of "something." Perhaps of an "initial singularity?" Who knows? Whatever we say, the Big Bang probably won't be a beginning of the first contingent thing.

But this is a minor point about usage. Here's a more serious worry.

Some people think that

(**) Contingent things can only be produced by other contingent things that (at least partially) precede them in time.

I don't have an argument for (**). On the other hand, I don't see any reason to think it's not metaphysically possible. If (**) were metaphysically possible, then the same S5 considerations invoked by your argument are going to take you were you don't want to go.

Isn't that the main problem with modal versions of these arguments?

I worry that we're just moving the "modal pieces" around the board. If they are arranged one way, we get one result. if arranged another way we get a quite different result. It seems like cheating just to arrange them in a way that gives you the result you want. So we appeal to "intuitions" that favor our preferred way of arranging them. Unfortunately, different people have different intuitions. And the more philosophy you study, the less clear your intuitions are. (At least that's been my experience!)

Josh,
Glad to see you posting and that you're a contributor!

As a side point, in case anybody's interested, Plantinga makes that distinction (failing to see something is impossible vs. seeing that something is possible) in print in his response to Ernest Sosa in Nous, "Why We Need Proper Function", on pp. 77-78. The preceding article by Sosa is also very good. Both go into it a bit on the value of our modal intuitions w/r/t that distinction.

Josh,

Thanks for all that.

I have to confess that I don't clearly "see" what is and isn't metaphysically possible at this level of abstraction. So I find it hard to say whether the "modal kalam argument" is an improvement on the original. It's certainly given me something new to think about!

A lot of what your wrote about the original (non-modal) version seemed spot on to me. Perhaps I should mention a couple of disagreements, though.

1. At the level of raw intuition, it seems to me that time (and the series of events within time) could have no beginning. In fact, I have trouble seeing how the opposite could be true! A time before which there is no time? Seems really weird to me. (And it doesn't seem any less weird when I'm informed that a timeless person created time out of nothing and, in doing so, put itself into time.)

So... Why do you think that infinitely many discrete chunks of time could not have "elapsed?" Why does that seem so strange to you?

We need to be wary of falling into the fallacy of composition here. To see what I mean, consider what it is for a period of time (a minute, say) to "elapse." The minute begins, sixty seconds pass, and the minute comes to an end.

Given this understanding, it's obviously one thing to say that each member of an infinite series of minutes has elapsed, and quite another to say that the whole infinite series of minutes has elapsed. The second claim is impossible, since (ex hypothesi) there is no first minute. But the second claim does not follow from the first.

I suspect that a lot of people who think the first claim is impossible have confused it with the second.

2. I don't share your intuition that the "becoming actual" of any and every state of affairs must have a cause. It seems to me to make all the difference what state of affairs we're talking about. (Here we are again... I just don't have very many clear intuitions at this level of abstraction.)

In any case, there is a standard counterexample to this claim. I'm thinking of the spontaneous emergence of particle pairs in a quantum vacuum. Now there is a state of affairs whose "becoming actual" doesn't have a proper cause!

Bill Craig's response at this point is to say that this is not a true case of "coming from nothing," since a quantum vacuum isn't just nothing. But that isn't to the point. The quantum vacuum provides at most a physically necessary condition for the emergence of particle pairs. There is no cause that makes them come into existence.

If the standard interpretation of this phenomenon is correct, we have an actual case (and not just a possible one) in which something begins without anything causing it to exist.

Surely well confirmed scientific theories ought to trump weak a priori intuitions!

(Sometime you'll have to tell me about that scavenger hunt. Sounds like quite a way to ask somebody to marry you! Perhaps not on Prosblogion, though. :-))

Hi Wes,

You say that, "At the level of raw intuition, it seems to me that time (and the series of events within time) could have no beginning. In fact, I have trouble seeing how the opposite could be true! A time before which there is no time? Seems really weird to me. (And it doesn't seem any less weird when I'm informed that a timeless person created time out of nothing and, in doing so, put itself into time.)"

I think we might be equivocating between something "beginning to exist" (or as you say elsewhere, extratemporal beginnings or something of that nature) and something "coming into existence" (or intratemporal beginnings). While the latter requires that the thing has not always existed and (plausibly, and perhaps can be supported by argument) there be a time at which the thing did not exist, mere "beginning to exist" simply requires that there is no prior time at which the thing existed.

This distinction has interesting applications on Craig's causal premise, for under standard relativistic cosmology (or anything assuming a first interval of time), the universe may be said to begin to exist, but not perhaps "come to exist." If the causal principle is phrased such that "whatever comes to exist has a cause", it does not require timeless causation. However, if the causal principle is phrased such that "whatever begins to exist has a cause", then it does require timeless causation. This ties in nicely with the nature of intuitions that motivate the causal principle. All of the intuitions Craig has provided are intuitions about things "coming to exist" (or, as you might say, intratemporal beginnings or beginnings within the natural order), but that itself does not reflect on things that begin to exist yet do not come to exist.

What say you on something like that? Because, if so, it seems that one can hold that the universe began to exist (i.e. it has existed for a finite amount of time), yet it did not come to exist.

What do you think?

Wes, you write

The quantum vacuum provides at most a physically necessary condition for the emergence of particle pairs. There is no cause that makes them come into existence.

But isn't the quantum vacuum the cause of virtual particles?
IIRC, a quantum vacuum is a state where the energy is at a minimum. So virtual particles never begin to exist without being produced by a state of minimal-energy. Why shouldn't that be the cause? What's often overlooked is that probablistic causation is possible.

My favorite agnostic recently wrote an excellent critique of Bill's argument here:

http://skepticalstudies.blogspot.com/2009/01/on-kalam.html

Wes,
how do you define "everything" in your (*)? It doesn't make sense to me.

Puemblo,

I was sloppy with the word "everything." As Joshua correctly saw, I was entertaining the proposition that there could have been a beginning of "everything concrete." If that were so, it would follow that there could have been a beginning that couldn't have a cause.

What you say about the quantum vacuum doesn't sound right to me. In the context of the kalam argument, a cause is active in the sense that it makes something happen. (God doesn't cause the universe "probabilistically," whatever that might mean.)

I thought it was obvious that a given energy level doesn't make a pair of particles pop into existence. (But see my reply to Joshua below.)

I'm familiar with the idea that some of the laws of physics are statistical in character, but I have no idea what you mean by "probabilistic causation."

Joshua,

You seem to be suggesting that there might be an analogue to agent causation here - that a quantum vacuum might "spontaneously cause" particle pairs from time to time.

I don't know how to make real progress on this. It doesn't seem terribly plausible to say that a quantum vacuum has "causal powers" that it occasionally and inexplicably "exercises." But what else could you mean by "spontaneously cause?"

But who knows? Just about everything in quantum mechanics is a mystery to me. I'll chew on this some more.

(I'll try to have something to say about a couple of the other points in your last point later.)

Wes,
let's say you are correct and the quantum vacuum doesn't make virtual particles.
What does this scenario look like?
You have this quantum vacuum and then there are virtual particle.
Remove the quantum vacuum and there won't be virtual particles.
So, even on quantum mechanics, some conditions are necessary for something to come into existence. This seems to be what Craig is arguing.

If he is correct in his latest podcast (have you listened to it already? It's here:
http://www.rfmedia.org/RF_audio_video/RF_podcast/Debate-on-the-Kalam-Argument.mp3), you said that "Being does not come from non-being" is really the same as "Whatever begins to exist has a cause".

This could inspire a new Kalam:

(1) Being does not come from non-being
(2) The universe came to be
(3) Therefore, the universe comes from being
(4) An unembodied mind is the only possible explanation for why the universe came to be.
(5) Therefore, God exists.

Premise (1) is not violated by quantum vacuums, is it?
The problem is (2). In the article from Stenger, he assumes that there is spacetime. Let's say, physicists gave us a proven theorem that the universe can't be past-eternal (Vilenkin did it if you ask me).
Does this support (2)? Some say no:

http://www.eequalsmcsquared.auckland.ac.nz/sites/emc2/tl/philosophy/articles/does-the-creator-have-a-creator.cfm

Joshua,

Several small things... I'm not intending to give real arguments here, but just to share thoughts.

• Yes, I really did mean that - at the level of what I called "raw" intuition - a time before which there is no time seems impossible to me. I don't put much weight on such intuitions. But I think this one of mine deserves just as much respect as the intuitions of others that, for example, every beginning must have a cause, or that a pair of particles can't have occupied infinitely many different positions in space.
• The type/token distinction doesn't help me all that much. I don't have too many intuitions about states-of-affairs in general. It's only when you start thinking in terms of something more specific that I start to have intuitions.
• Yes, it would be much better to think in terms of looking for explanations rather than in terms of some top-down deductive argument that relies of "intuited" first principles. If you can think of a good causal explanation for something, that's a point in favor of thinking that the something in question has a cause. In the present context, we need to think about whether "God did it" is a particularly good explanation.
• We can define "elapsed" any way we like, but when we think of units of time elapsing, we're always thinking in terms of something beginning, enduring, and ending. At least I am. But if you just mean "has become past," then I suppose a beginningless series has "elapsed" when its last member has become past. I fail to see any problem here, though.
• You say:

When I imagine that two particles collide into each other after having traveled across an infinite extent of space (at a finite rate), I have a feeling of oddness, and the feeling isn’t ameliorated by the thought that these particles never started moving. This situation doesn’t strike you as odd?

Well, we experience only finite things and processes. So everything about the infinite is bound to seem "odd." But hey, you get used to it. And for me the feeling is "ameliorated" when I remember that there is no starting point for those particles in either space or in time. It has to be ameliorated somewhat, because if you suppose a starting point the scenario becomes logically contradictory.

I have long thought that all this talk about the impossibility of "traversing the infinite" begs the question against those who think the past has no beginning.


• Just think about what Craig needs to mean by "cause" in the context of the kalam argument. He explicitly acknowledges only two kinds of cause: mechanical causes that are sufficient for their effects, and personal causes. In both cases, the cause makes the effect happen. We're not supposed to be talking about he presence of some necessary condition.
• I'm still inclined to think your proposal about the quantum vacuum "spontaneously causing" the particle pair assimilates it to an agent causation model that makes sense only for persons. But I need to think more about that.
• You make a really good point about not begging the question by just assuming that God couldn't be the cause of the emergence of those particle pairs. It's hard to believe that God is that busy with the behavior of subatomic particles. But given omnipotence, I suppose it's possible. :-)

Pumbelo,

You say:

You have this quantum vacuum and then there are virtual particle.
Remove the quantum vacuum and there won't be virtual particles.
So, even on quantum mechanics, some conditions are necessary for something to come into existence. This seems to be what Craig is arguing.

Yes, that is exactly what Craig says, and it's not to the point for the reason I gave earlier.

But might it provide the basis for your "new" kalam argument? Look at your first three steps:

(1) Being does not come from non-being.

(2) The universe came to be.

(3) Therefore, the universe comes from being.

Observe that (3) does not logically follow from (1) and (2). What does follow is only that the universe didn't come "from" anything.

Pumbelo,

I noticed I small mistake in my last reply to you. I was right in saying that 3 does not follow from 1 and 2 in your "new" kalam argument. But what does follow? I wrote:

What does follow is only that the universe didn't come "from" anything.

What follows is that EITHER the universe came from being OR the universe didn't come from anything.

Wes,
I was about to point out that mistake, but I wasn't able to sign in.
Let's look at your conclusion:

(C) The universe came from being OR the universe didn't come from anything.

There are two things I would like to point out here:
1) I don't think there's a big step from (C) to "It's possible that the universe came from being". This supports the modal kalam.
2) How do you interpret "the universe didn't come from anything"?

How do you make sense of the following:

(1) Being does not come from non-being.
(2) The universe came to be.
(3) The universe didn't come from anything.

Craig would argue that (3) contradicts (1).

Pumbelo,

I'll try to explain why there is no contradiction between (1) and (3).

(1) is about whether being can enter into a relation (the 'comes from' relation) with non-being. But (2) is about whether being (in particular, the universe) can fail to enter into that relation. So even if it is impossible for being to come from non-being, that doesn't mean it's impossible for being to not come from anything.

As Hume put it, "when we exclude all causes we really do exclude them".

Hi Wes,

You say that, "At the level of raw intuition, it seems to me that time
(and the series of events within time) could have no beginning. In
fact, I have trouble seeing how the opposite could be true! A time
before which there is no time? Seems really weird to me. (And it
doesn't seem any less weird when I'm informed that a timeless person
created time out of nothing and, in doing so, put itself into time.)"

I think we might be equivocating between something "beginning to exist"
(or as you say elsewhere, extratemporal beginnings or something of that
nature) and something "coming into existence" (or intratemporal
beginnings). While the latter requires that the thing has not always
existed and (plausibly, and perhaps can be supported by argument) there
be a time at which the thing did not exist, mere "beginning to exist"
simply requires that there is no prior time at which the thing existed.

This distinction has interesting applications on Craig's causal
premise, for under standard relativistic cosmology (or anything
assuming a first interval of time), the universe may be said to begin
to exist, but not perhaps "come to exist." If the causal principle is
phrased such that "whatever comes to exist has a cause", it does not
require timeless causation. However, if the causal principle is phrased
such that "whatever begins to exist has a cause", then it does require
timeless causation. This ties in nicely with the nature of intuitions
that motivate the causal principle. All of the intuitions Craig has
provided are intuitions about things "coming to exist" (or, as you
might say, intratemporal beginnings or beginnings within the natural
order), but that itself does not reflect on things that begin to exist
yet do not come to exist.

What say you on something like that? Because, if so, it seems that one
can hold that the universe began to exist (i.e. it has existed for a
finite amount of time), yet it did not come to exist.

What do you think?

Joshua,
I agree with the second point.

Well, the first premise of the "new kalam" is actually
(1) Being does not come from non-being.
and NOT "Nothing comes to be from nothing".

By that I mean that concrete objects don't "come to be" (oh no, now that needs a definition too ...) without having concrete objects (such as particles in quantum fluctuations) as a necessary condition.

Is it modest enough or has it the same problems?

Josh,
you are quite right that I have to argue for your two points. But that wasn't my intention. My intention was to formulate a version of the Kalam that does not rest on a premise that is defeated by quantum mechanics.

Of course, I'm just someone who has an interest in philosophy in his free time and you guys are the professional philosophers

Wes made the point in his dialogue with WLC that "We need to show that the whole of physical reality, including whatever universes exist or have ever existed, has a cause."

First, let's focus on point 2. If there is a concrete necessary condition for the whole of physical reality to come to be, must it be divine?
Well, it must be non-physical. Quentin Smith argued that the universe is self-caused, but I can't make much sense of this. Let's say for the sake of the argument that Smith is wrong.

What's non-physical, concrete and may be required for physical reality to come to be?
Craig says it's a mind.
What alternative non-phyical substance do you have as an example? Someone wrote "Some timeless substance". Well, mind-body dualism faces an interaction problem. How does the non-physical mind interact with the physical realm? But an unembodied mind atleast makes sense of this scenario. How does a non-physical substance that's even less than a mind do a better job? It actually sounds worse.
To borrow from Craig in his dialogue with Lewis Wolpert: "What you call a non-physical substance capable of producing the wholy of physical reality is probably God."
A more modest proposal would be: There's almost no leap of faith here so even if one accepts evidentialism and Plantinga's reformed epistemology fails, it may justify belief in God and can be considered as persuasive by non-theists.

But now on the first point:

"We need to show that the whole of physical reality, including whatever universes exist or have ever existed, came to be"

As I said before, "to come to be" is undefined, unfortunately.
Let's say Vilenkin is correct (and many professional mathematicians say he is) and the universe can't be past-eternal. There are still 2 problems:

1) An interpretation of general relativity theory says that time isn't absolute but, take a wild guess, relative. Craig simply uses a different interpretation (and I think so does Wes because he's an A-theoriest too) but if Hawking is correct, the kalam could be considered dead.

But not everyone agrees Hawking is correct. In Craig's chapter in the Blackwell Companion in which he has a cosmologist as a contributor (I can't really remember his name, something like Frank Sinclair perhaps?), who discusses the many models of contemporary cosmology (and I believe I saw an article on this at Craig's site, but I can't find it right now). Take Vilenkin as an example. His model interprets interprets the creation of the universe to be a "tunneling from nothing" (just check out the Stenger-article I linked above).
In this case, we would have good reason to conclude that the universe "came to be".

By the way, I wonder if Vilenkin thinks his model is compatible/incompatible with theism, because I remember Quentin Smith arguing against theism based on Hawking-cosmology (old Hawking-cosmology I believe).

2) If the Hawking-Hartle-model fails and we have good reasons to conclude that the past can't be infinite (let's say we have a great philosophical argument against it and everyone agrees that this is an irrefutable proof), there is still what Wes likes to point out, that "begins to exist" can't just be applied to the beginning of time without resolving some problems.

Josh:

Here is a way to criticize premise 2 of your very nice modal argument (maybe this comes up somewhere in the above discussion): If all necessary beings are essentially atemporal, then in any world w in which the sum of contingent things has a beginning, there is an empty time preceding that sum. But an empty time preceding a later time is absurd, whether because an empty time is absurd simpliciter or because there is no way to tie an empty time into the temporal order (e.g., through potential or actual causal relation) and make it come before anything else. Therefore, if all necessary beings are essentially atemporal, then premise 2 is false.

But at least apart from considerations of divine revelation which the atheist will not grant (i.e., the Incarnation), it is epistemically possible that all necessary beings are essentially atemporal. (Moreover, if the components of Christ's human nature count as contingent entities, then the Incarnation is not a counterexample to the thesis that all necessary beings are essentially atemporal.) Moreover, it is not just epistemically possible, but fairly plausible. After all, plausibly, no necessary being is essentially in time. (Time is tied to space, and the geometry of spacetime seems so capable of variation between worlds that it would be really weird if necessary beings were tied to it.) And the idea of necessary beings entering into time in such a way as to place no contingent being in time is not very plausible.

I think both you and Bill Craig would be better off simply defining "x came into existence" as "there was a time t at which (a) x existed and (b) there is a finite number u such that every time t' that is at least u units before t has the property that x does not exist at t'." Then it's extremely plausible that possibly the sum of contingent beings came into existence.

Wes:

Is it your intuition that there cannot be a first moment of time, or that the past cannot be finite? (The two claims seem to me to be logically independent, though I think a lot of people will say that the second entails the first.)

I just cannot get myself to have the intuition that there was a first moment of time. Are you sure your faculty of intuition isn't just subconsciously committing the fallacy "If there is a time t such that not: (there is time before t), then there is a time t such that before t: (there is no time)"? (The latter claim is plainly absurd. The reason I mention this is that Aristotle's argument for the eternality of motion seems to commit this fallacy.)

Alex,

I confess that I was not making a sharp distinction between the two claims mentioned in your first paragraph. I know that some people think the first moment of time might have had no beginning. I'm not sure what to say about that possibility. I guess it depends on what you're willing to count as a "moment."

For what little it's worth my "intuition" is as follows. Mark any "point" in past time. It's hard for me to seriously entertain the possibility that there was no time earlier than that point. So, then, I guess my "intuition" really is that the past cannot be finite.

You wrote:

I just cannot get myself to have the intuition that there was a first moment of time.

I'm a little confused. Did you mean that you can't get yourself to have the intuition that there could NOT have been a first moment of time?

About the crucial distinction in your last paragraph... I've long been well aware that there is a difference between the incoherent claim that there was a time before the first moment of time and the claim that there was a first moment of time. I may be confused, but not, I think, about that.

I'm not inclined to put much, if any, weight on my intuition that the past can't be finite. Two considerations tell against it. (1) Other people smarter than I don't seem to share this intuition. (2) I suspect that my intuition is driven by the fact that every chunk of time that I (or any other human being) ever experiences occurs in a robust temporal and causal context.

Something like "force of habit" may sometimes produce "intuitions" that are phenomenologically indistinguishable from genuine a priori insights.

A.Y.,

I agree that if we distinguish between "coming into existence" and "beginning to exist" in precisely the way you suggest, then it's logically possible that the universe "began" to exist but did not "come" into existence. (I fear that most people won't find this terminology to be especially felicitous, however.)

I didn't really mean to be putting a lot of weight on my "intuition" that the past must be finite. (See my reply to Alexander Pruss above.)

So... Let's suppose that the past really is finite, and suppose (just for the sake of argument) that the beginning of time coincides with the beginning of the universe. In that case, I'd say the implications for Craig's causal principle are just the ones you point out. His defense of this principle often seems to move from intuitions about what can happen within time (and, I would add, within an established natural order) to a conclusion about the beginning of the whole of nature (and time).

I myself do not think that all comings into existence within time necessarily have causes (in the relevant sense of cause). But even if I am wrong about that, it doesn't follow that the beginning of "the whole shebang" had a cause.

I also agree with you that if Craig's causal principle about "beginnings" were accepted, and if time itself had a beginning, then it would be hard to avoid a non-temporal cause.

Josh,

Two comments.

(1) You’re appraisal of the KCA indicates that Craig gives “3 arguments for Premise 2 [i.e. the universe began to exist].” Craig actually gives four arguments for premise 2. You’ve dealt with the first two (the impossibility of an actual infinite; the impossibility of traversing an actual infinite). You touch on the third (big bang cosmology), concluding simply that we should be more cautious in accepting this argument to support premise 2. But you omit any discussion of Craig’s fourth argument: the argument for thermodynamics. I’d be interested to see you interact with that argument.

(2) Much or your dispute with the two philosophical arguments for premise 2 and your trouble with premise 1 seem to arise from your B-Theory of time. For example, you write: “perhaps because of my view that times are abstract states of affairs that stand in B-Relations.” And, referring to premise 4, you write: “It’s just that given my own views about causation and time, they don’t hold weight for me.”

I’m wondering whether you’d see things differently if you accepted Craig’s A-Theory of time. Craig has often said that the KCA (at least as he’s formulated it) depends on an A-Theory. Thoughts?

Wes,

In your earlier post after your debate with Craig, you and Alex presented a argument against the two a priori arguments in support of Craig’s premise 2 (i.e. that the universe began to exist). In that post, and the series of comments that followed, you never addressed the two empirical arguments Craig gives to support premise 2. But in Josh’s post, and in the comments that follow, it appears Craig’s entire argument is on the table, empirical evidence and all.

In the discussion about whether virtual particles are legitimate examples of things that come into being uncaused, you wrote: “Surely well confirmed scientific theories ought to trump weak a prior intuitions!” I realize you were making that comment in response to the causal premise, but that comment seems equally applicable to the empirical arguments (i.e. big bang cosmology and the thermodynamics argument) Craig offers for the second premise. You may have trouble with a priori arguments, but if you’re willing to adhere to “well confirmed scientific theories” to trump a prior intuitions, why do you still doubt the empirical arguments and therefore the truth of premise 2?

Josh,

Thanks for the clarification. I’ve got a few questions about your concern with equating finitude with “beginning to exist.” After noting the empirical arguments Craig gives to support the premise that the universe began to exist, you note that we should be cautious about putting to much stock into them. Nevertheless, you say, you’re willing to “tentatively grant a finite past.” You’re concern then becomes “how does a finite past entail that the universe began to exist?” Your wrote:

But how does a finite past entail that the universe began to exist? Bill thinks God has a finite past but has no beginning. So before we can conclude that something with a finite past has a beginning, we need to see why that thing is relevantly different than God.

I asked Bill about this once. If I remember right, his answer at the time was that the universe appears to be a changing thing--indeed, essentially changing. That means it cannot fail to be in time. God, by contrast, can be timeless sans creation. So the difference between the universe and God is that God can be timeless, whereas the universe cannot be.

I'm not satisfied with that answer. Why can't something that is essentially changing have a first state without having come to be? Imagine a first state in which physical things are moving away from each other. Why think the particles in this state began to exist? Why think that things must come from a state of their non-being in order to be in a (tensed) state of becoming?

You’re willing to grant the finitude of the past on the basis of empirical arguments, but question whether that finitude entails “beginning to exist.” But, whatever the merits of you questions, the question (and ensuing argument you offer) about that entailment is an a priori argument. What about the empirical argument from big bang cosmology that at the big bang *time* and *matter* came into existence. If that’s true, then empirically, the universe’s finitude entails the universe’s coming into being. Because relativity theory requires space (and thus matter) and time to be bound together, the beginning of time is the beginning of space (and thus matter); and vice versa. So, it seems that Wes’s earlier comment about “well confirmed scientific theories” trumping “a priori intuitions” ought to apply here as well.

Ryan,
if you watch Wes' presentation:
http://spot.colorado.edu/~morristo/Reply2BillCraig.ppt

you will notice that Wes actually argued that Craig's scientific argument don't work if quantum gravity predicts a cyclic universe (a scientific objection to a scientific argument).
However, I would still argue that Vilenkin disproved this.

Wes objection is actually inconsistent with his other comment: "The Big Bang (if there really was such an event) ..."
I wonder why Wes remains sceptical of the Big Bang. Almost no cosmologist believes in steady-state theory anymore. The evidence is quite powerful.
And it's actually more powerful than for a cyclic universe. So Wes, you actually have to be fair ;-)

Ryan, Pumbelo,

So what about the "scientific" arguments for saying that the universe has an absolute beginning?

Let me be clear. I have absolutely no idea what a quantum gravity theory (if a satisfactory one is ever discovered) would predict. Here's what I do say.

The so-called "earliest" stages of the history of our universe are really misnamed. We're looking into the past, and we can see only so far. Looking back into the past as far as we can, it appears that about 13.7 billion years ago the particles were very tightly packed and the levels of energy were extremely high.

Now here's the crucial point. Nobody (not Vilenkin, not Bill Craig, nobody) really knows what laws of physics apply when the energy levels are that high. There is therefore simply no telling how long the universe was in a state of high density and energy or how it got to be in that state.

Bill Craig himself (in Theism and Big Bang Cosmology, pp. 67-9) wrote these telling sentences:

“Prior to 10^–12 sec, however, the physics becomes speculative.”

“Prior to 10^–35 sec the physics becomes extremely speculative and even unknown.”

What Craig says here is exactly right. What he fails to do, however, is to draw out the obvious implication - viz., that we have absolutely no idea what was going on prior to those "times."

Note also that when physicists talk about t^-12, they are really talking about an energy level of 100 GeV (100 billion electron volts). And when they talk about t^-35, they are talking about 10^14 GeV. They aren't "locating" t=0 and working forward. Current physics gives us no guarantee whatever that there was a t=0.

So what about Vilenkin's "proof?" I checked that book out of the library and took a look. Please understand that I have no expertise in this area. But I noticed two things right away. First, the title of the book is "Many Universes in One." Vilenkin is not only a strong proponent of the Big Bang, but he is also a strong proponent of the idea that our universe is but one of incredibly many universes. I bet you won't hear Bill Craig quoting Vilenkin when he's defending the fine-tuning argument.

So... Is Vilenkin an authority when he agrees with Bill, and not when he doesn't?

Second, I discovered that Vilenkin, Borde and Guth made one crucial assumption in the "proof" that Bill Craig likes to cite. Here's how Vilenkin puts it.

The only assumption we made was that the expansion rate of the universe never gets below some non-zero value, no matter how small. (p. 175)

But of course, if we don't know what laws of physics apply that deep in the past, then who knows whether Vilenkin's assumption holds in the relevant time period?

Before I met with Bill at Westminster College, I took the trouble to ask a couple of experts at my own university what they thought about all this. One of them was Michael Shull, who is a Professor of Astrophysical and Planetary Science and a College Professor of Distinction. He was actually teaching a course in cosmology here at the University of Colorado when I wrote to him. Here (in part) is what Shull told me:

I find it surprising that someone would claim that the extrapolated Hubble expansion, back to "time zero" (13.7 billion years ago) was the start of everything. We know so little about the laws of physics at these times, small lengths, enormous energies, even the nature of space and the vacuum (physicists use vacuum to mean "lowest energy state” which need not be empty – certainly not "nothingness"). 

Another expert from whom I got a comment was Senareth P. De Alwis, who is a Professor of Physics here and specializes in string theory. Here's what he said:

As you correctly point out, at times before about 10^-35 sec, the energy scale is beyond anything that any current standard theories of physics can address, and hence we cannot yet make scientific statements about that (earliest) period of evolution.

I have no idea what the scientists will eventually decide about all this. So I think Bill Craig is really jumping the gun.

It's not an accident that Scientific American and Astronomy Magazine have recently published reports on cosmological speculations that are inconsistent with the Big Bang theory. I understand that Vilenkin is a respectable cosmologist. But so are Steinhardt and Turok, and their views (while not confirmed) have not been disconfirmed and are being taken very seriously. Unless and until the physicists give us more to go on, we philosophers have no business cherry picking the cosmological speculations that support our preferred theological positions. But that, I suspect, is precisely Bill Craig is doing.

I know that Bill will be happy to tell you why Steinhardt and Turok have it all wrong. But you won't understand his arguments any better than I do because you (like me) are not physicists. Maybe he's right. But then again, maybe not. Don't forget that Bill isn't a physicist either!

If ever there was a place where philosophers ought to learn - and exercise - the virtue of epistemic humility, surely this is it!

For a really good professional treatment of the points I've made here, see a paper by my philosopher of physics colleagues, Brad Monton. you can find it here:

http://philsci-archive.pitt.edu/archive/00004094/

It's a Microsoft Word document. Section 5 ("The Big Bang and the Kalam Cosmological Argument") is the one you want to look at.

I got a lot of help from Monton in deciding what to think about Crag's two "scientific" arguments for an absolutely beginning of the whole of physical reality.

How about changing

3. If x has not existed for an infinite extent of time, then x came into being some time ago, for any x.

to:

3a. If x has not existed for an infinite extent of time, then either x does not exist, or x exists eternally and timelessly, or x came into being some time ago (for any x).

(The first disjunct is just nitpicking. On one reading of "has not", Sherlock Holmes has not existed for an infinite extent of time, because he has not existed at all, and it does not follow that he has come into existence.)

To satisfy Bill Craig, we read "exists eternally and timelessly" in such a way as for that to be compatible with coming to exist in time. In other words, "exists timelessly" means "exists in a mode independent of time" and at least prima facie does not entail "does not exist in time".

Then we just add the plausible thesis:

3b. The universe does not exist eternally and timelessly.

Actually, unless we have an argument that gappy existence is impossible, 3a needs another disjunct: "or x has suffered from gappy existence". (Imagine a being that existed from 1001 BC to 1 BC, from 2501 BC to 2001 BC, from 3251 BC to 3001 BC, from 4126.1 BC to 4001 BC, etc. This being has existed for a finite amount of time, namely 1000 + 500 + 250 + 125 + ... = 2000 years. But it never came into existence.) Fortunately, we can also add the plausible thesis:

3c. The universe did not suffer from gappy existence.

Another tricky thing in 3 is that a reference frame needs to be specified in the antecedent. After all, a spacetime trajectory could be of finite length in one reference frame and of infinite length in another. We could do:

i. If there is a reference frame F such that x has not existed for an infinite amount of time in F, then ... or x came into being some time ago in F.

ii. If there is a reference frame F such that x has not existed for an infinite amount of time in F, then ... or x came into being some time ago simpliciter.

iii. If in every reference frame F it is the case that x has not existed for an infinite amount of time in F, then ... or x came into being some time ago simpliciter.

iv. If in x's reference frame it is the case that x has not existed for an infinite amount of time, then ... x came into being some time ago simpliciter.

I don't know exactly what I mean by "reference frame" in general. In the special case of a world governed by general relativity, a reference frame will be a foliation by spacelike hypersurfaces, but when we're dealing with metaphysical principles, it would be better to have a notion of reference frame independent of a particular physical theory, unless we want to hold (and that's not so crazy) that time, like water, couldn't exist if the laws were different.

If we take (i), then the principle that everything that came into being had a cause needs strengthening: if there is a reference frame in which x came into being some time ago, then x had a cause.

I think (iii) and (iv) are also appealing (and compatible with (i), actually). However, then we need an argument that in every reference frame the universe had finite age (in the case of (iii)) or that the universe has "its own" reference frame and in it has finite age. (It seems hard to define an entity's "own" reference frame given general relativity, for reasons due to the fact that substances can jump around in weird ways. See this post. I think the problem can probably be solved by a generalization of the notion of a reference frame that also solves the problem of undue dependence on relativity theory, but the details are not worked out yet.)

Alex (may I call you Alex?), I agree with your last post on this thread except for something I want to add about reference frames.

Joshua, I want to add suggest one more way to intuit ‘coming-to-be’ that also leads into a comment I want to make about the serrated continuum. James Brian Pitts (who you may know because I think you are both at Notre Dame) has a nice criticism of creation out of a General Relativistic singularity that I think can cut both ways. His ‘Cosmic Destroyer’ argument is that, since the mathematics of stellar collapse are the same as those that describe emergence from a Big Bang singularity (except for time reversal), that implies that if there is a ‘creator’, there must also be a ‘destroyer’! If I understand him correctly, he does agree that this would obtain if General Relativity were indeed the fundamental theory of gravity, but he finds it to be ludicrous. I agree that this seems bizarre. Consider the comments of General Relativity pioneer Robert Geroch:

“Recall there is no event available to [an observer headed toward a singularity] on the singularity itself. In particular, there is no possibility for a further extension of [the observer’s] world-line after it hits the singularity. What, then, does “the world-line of [an observer] hits the singularity” mean physically? Mathematically, what happens is that this world-line just stops. Physically, this would mean that [the observer] is “snuffed out of existence”; after some finite time according to himself, he ceases to exist in space-time.” Robert Geroch, pg. 194, “General Relativity From A to B”, Chicago & London, University of Chicago Press 1978

I think he is being literal here; ‘snuffed out of existence’ is not just a facon-de-parler. The power of this example, I think, is that it seems far easier to intuit that an observer on a trajectory toward a black hole singularity will, indeed, cease to exist than it is to intuit the time reversed case of ‘beginning-to-exist’.

But I agree with Pitts’ parallel. Ceasing to exist at a black hole (or a future universe-wide Big Crunch) does imply ‘begins-to-exist’ at an initial singularity. In the Blackwell piece I quote another General Relativity expert, Robert Wald, using the same language (again, I think, not just as a facon-de-parler) for both beginning and ending to exist.

The black hole example helps with the serrated continuum objection to Kalam as well. I think Quentin Smith, Pitts, and others have argued in various ways that the universe need not begin-to-exist because of the nature of the first arbitrary interval of time, which is a half-open interval. I think it is more useful to consider an observer in spacetime, not just the truncated reality of (divisions of) space & time itself. The last interval of time is also a half-open interval. Does it make any difference that the last interval of time has no ‘last moment’, or that one could infinite subdivide that last interval (in the manner of the stadium paradox)? No, an observer will cease to exist within a finite time regardless of the apparent paradox. She will ‘fall off the world’ in just the manner the ancient mariners feared given belief in a flat earth. By extension, beginning-to-exist should also proceed without difficulty from lack of a first moment and/or the infinity of instants. (BTW, I think Quentin Smith has now dropped this line of reasoning and now no longer believes that there are actual infinities in physical reality.)

But what if one believes in the reality of points and thus there is an infinite number of moments in the first arbitrary interval of time? It strikes me that this actual infinite is irrelevant to Kalam’s 2nd premise. The actual infinite that plays in the stadium and dichotomy paradoxes does not seem to be the type of infinity that Bill Craig is concerned with. Bill is interested in refuting the notion of a beginningless infinite. But, in the dichotomy paradox, there is an infinitely distant beginning point. So if there is a real physical boundary (the singularity) out of which matter/energy emerges (I think the black hole example implies its reality), and the infinite timeline is fully traversable from that boundary to the present, then how does that falsify the premise? (BTW, there is a nice cosmological model called ‘the Mixmaster universe’ that has this type of behavior)

It seems likely to me, as well, that quantum gravity is going to quantize time. So there might be a finite number of moments after all.

Now, to address one of Alex’s points, what about the fact that one can change one’s time measure such that a finite interval can become infinite (and visa-versa)? Well, I recall that J.P. Moreland once referenced a theorem in philosophy that goes something like ‘if A & B both have identical properties, then A is B’. So suppose I have two dissimilar physical descriptions that purport to describe the same universe. Here we are starting with the assumption that ‘A is B’. But if one description includes a physically real boundary such as a singularity, and the other doesn’t that is a problem. I can’t drop a property just because I am changing the physical description. Here one should remember that models by definition are incomplete (otherwise they would be emulations). So the fact that a conformal transformation changes the age of the universe from finite to infinite cannot imply that the universe is beginningless. Rather, one is putting the beginning off to an infinite distance. It seems to me that we have the same situation as the dichotomy paradox. I have a real beginning, followed by a traversable timeline to the present. That is perfectly in accord with Kalam’s 2nd premise.

I know that Howard Sobel and J.L. Mackie have, in the past, accused Bill of illicitly smuggling an infinite distant beginning point into argumentation on actual infinities. So I’ll point out that this line of reasoning is purely my own speculation. If I’m wrong, I would not mind at all having it pointed out where I am in error.

Joshua Rasmussen’s post “More Reflections on Bill Craig and Wes Morriston on the Kalam Cosmological Argument” (April 29, 2009) has initiated many interesting comments about the merits of the KCA disclosing a wide variety of views concerning it. But Josh remarked in his initial post: “My sense is that the Kalam argument is more likely to appeal to the common man or woman than to your average philosopher. From the common man’s perspective, beginnings obviously have causes; science reveals a beginning to our universe; and surely only God would be the cause of our entire universe[].” (JR, April 29, 1:30 PM)) Wes Morriston “totally agree[d] that the kalam argument ‘is more likely to appeal to the common man or woman than to your average philosopher.’ I think that’s why it’s so rhetorically effective in public debates. I received a post the other day from an agnostic who’d been listening to a lot of Bill Craig’s debates. He said that the kalam argument was the one that nobody seemed to have an effective reply to. He thought he was about to become a theist on account of it.” (WM, May 3, 10:09 AM) Au contraire, there is available an effective reply to the KCA likely to appeal to the intelligent common man or woman (whether theist or not), and even perhaps to some philosophers whose noetic structures have not been too severely damaged due to original sin. I believe I have provided that effective reply.

I, a commonsensible naturalist, should therefore like to refer the reader to my refutation of the Kalam Cosmological Argument (hereafter KCA). Although I am not a professional philosopher, I have written two peer-reviewed articles about the KCA in philosophy journals. ["The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities," Philo 5 (2002) 196-215; republished in Philo Online (and The Secular Web Library); "A Critical Examination of Mark R. Nowacki's Version of the Kalam Cosmological Argument," Philosophia Christi 10 (2008): 377-91.] I have also authored two additional articles for the modern library of the Secular Web (http://www.infidels.org/library/modern/arnold_guminski/). [“The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Temporal Series” (2003, updated 2005); “The Kalam Cosmological Argument as Amended: The Question of the Metaphysical Possibility of an Infinite Temporal Series of Finite Duration (2004, updated 2005).]

The reader of my essays will discover that I substantially agree with Craig with respect to several important, relevant, principles and doctrines that the intelligent “common man or woman” is likely, upon reflection, to believe to be true. These principles and doctrines include: (1) the A (or tensed) theory of time; (2) the presentist version of the A theory; (3) that every moment or temporal interval is not of zero duration, such that such moments in a temporal series are consecutively sequenced one immediately after another; (4) the metaphysical impossibility of the traversal of an infinite set of events or entities yet to be traversed; (5) the causal principle embodied in the first premise of the KCA, according to which it is metaphysically necessary that whatever concrete entity begins to exist must have a cause, even if indeterministic. I shall not undertake here to further explain, qualify, or defend these propositions which I believe to be properly basic or more probable than not, whatever is the case. Rather I should like to immediately go to the heart of the matter by asserting most emphatically that I agree with Craig that an infinite temporal series of events, whether or not of infinite duration, is metaphysically impossible provided one grants that an infinite temporal series, or any set of concrete entities, is deemed to have the same relevant mathematical properties as a mathematical denumerable infinite (e.g. the set of natural numbers, or negative numbers, or even numbers). For, assuming that each of two infinite sets of concrete entities or events are equipollent (i.e., correspond one-to-one) to the infinite set of natural numbers, it follows that they are equipollent to each other if indeed infinite sets of concrete entities or events have the same relevant mathematical properties as denumerably infinite mathematical sets. Building on this, Craig has argued that infinitely many concrete entities or events are metaphysically impossible.

In my Philo article, I proposed and defended the thesis that infinite sets of concrete entities or events, although each equipollent with the set of infinite numbers and thus having the same cardinality (i.e., aleph-zero), are not necessarily equipollent with each other. Thus in a possible world in which there are infinitely many humans each with two and only two hands it cannot be the case that the infinite set of all humans are equipollent with the set of all hands. To take up Craig’s Hilbert’s hotel scenario, my position is that if all the rooms are and must be occupied by one and only one guest and there are infinitely many rooms, then the hotel management could not possibly accommodate another guest unless another room was provided, unless one of the guests checks out. And so, to take another example, if the temporal series constituting the history of this universe is infinite then the set of infinitely many years ending at midnight, January 1, 1000 is not equipollent with that set of years ending at midnight, January 1, 2009. My Philo article shows that my theory that infinite sets of concrete entities or events do not have all the same relevant mathematical properties as do denumerably infinite mathematical sets does not result in counter-intuitive absurdities.

In no way do I challenge Cantorian transfinite arithmetic. What I challenge is the opinion commonly held among philosophers that the only way to apply Cantorian transfinite arithmetic to the real world of concrete entities and events is to posit that sets (or, if you will, aggregates) of such entities or events have the same relevant properties as do denumerable mathematical infinites.

Quentin Smith, then editor of Philo when I submitted my article, wrote the following in his message of acceptance of July 15, 2002: “Your paper has been studied thoroughly for some time and there is agreement that it is at least an under-cutting defeater of Craig’s beliefs about real infinites, probable even an overriding-defeater. More importantly, it introduces a novel metaphysical theory of the relating of transfinite arithmetic to concrete reality.” To be sure, a successful refutation of the KCA leaves untouched other arguments for God’s existence. Moreover, rejection of the KCA is not limited to naturalists as many Christian philosophers and theologians also reject the argument.

My Philo article was electronically published on the Secular Web, and this version embodies several corrections. My second KCA article, “The Kalam Cosmological Argument Yet Again,” addressed Craig’s second philosophical argument that any temporal series of events must necessarily be finite even if it is assumed that an infinite set of entities is not necessarily metaphysically impossible. My third KCA article, “The Kalam Cosmological Argument as Amended,” addressed the question whether an infinite temporal series of finite duration is metaphysically impossible and concluded that such is the case. In so doing, I showed that Craig in presenting his scientific argument in writings subsequent to his The Kalam Cosmological Argument (1949) has in substance admitted, or appeared to admit, the possibility of an infinite temporal series of finite duration in order to accommodate his second premise of the KCA (i.e., the universe began to exist) with various Big Bang cosmological models.

Although I have expressed the opinion that the deliverances of the natural sciences, or rather the deliverances of some natural scientists, are insufficient to warrant the conclusion that the temporal series constituting the history of this universe is of finite duration. I hope to write a fourth essay addressing the scientific version of the KCA. Suffice it to say for now that if this universe began to exist in the requisite sense, then the nature of whatever caused the universe to exist cannot be determined by reliance upon the alleged metaphysical impossibility of an infinite temporal series.

Alas! Craig has never answered me although it is notorious how ever since the appearance of his The Kalam Cosmological Argument he has otherwise made every effort to refute other critics of his arguments. He has had plenty of time to respond to my writing; and I do not think he can credibly claim that my writings are beyond the pale. I more than suspect that Craig has not answered me simply because he cannot undertake a successful refutation. Of course I could be wrong but I would like to know why.

Josh: It is good to hear from you. Thanks for your intellectual hospitality. In response to your comment, I offer the following:
(1) The definition of "equipollence" and "one-to-one correspondence." I am puzzled by your need to have more precise definitions since a one-to-one corrspondence is constituted by a pairing of the members of one set with those of an other without any remainder. Given any finite set of humans, each with two and only two hands,then the set of humans is equipollent with the set of pairs of hands. But the set of humans is not equipollent with the set of all of their hands. In my view, the same results obtain were we considering an infinite set of humans, each with two and only two hands. However, the infinite sets of humans, of their pairs of hands respectively, and of all their hands are each equipollent to the set of all natural numbers and hence have the same cardinality of aleph-zero. What's the problem?
(2) The Hilbert Hotel thought experiment. O.K. Let us agree that it is prima facie plausible that the hotel can accomodate one more guest just by having each occupant move to the next room. But this prima facie plausibility is discharged because the proposed scenario is factually impossible. Before the attempted moves of the occupants, there already obtains an equipollence between the set of rooms and their guests, and all the rooms have occupants. Were the hotel management to add one more room, there would then no longer be a one-to-one correspondence between the set of rooms and the set of occupants. It would then be possible to admit another guest to occupy the vacant new room.
(3) Yes, I did read J. P. Moreland's article some time ago, but I can not not presently locate it among presently. I decline to comment about his article since I might well have a faulty recollection of its main points. However, suffice it to say that, according to my metatheory as to how Cantorian set theory applies to a world of concrete entities: (a) Two infinite sets of concrete entities, both necessarily having the same cardinality (i.e., aleph-zero) because each is equipollent to the set of all natural numbers, are not nececessarily equipollent with each other (ex. an infinite set of humans each with two and only two handsand the set of all their hands); (b) Two infinite sets of mathematical entities, both necessarily having the same cardinality (i.e., aleph-zero) because each is equipollent with the set of all natural numbers, are necessarily equipollent with each other (ex., the set of all all negative numbrs and that of all even negative numbers).
(4) As to whether Craig will ever reply to my KCA papers. It is curious that Craig has not already done so because I am not aware of any published critic of his Kalam philosophical cosmological argument who explicitly agrees with him that: (a) a traversal of an infinite yet to be traversed is metaphysically impossible; and (b) that any infinite set of concrete entities or an infinite temporal series is metaphysically impossible assuming that any two such sets or series necessiarly are equipollnet to each other because they have the same cardinality.

Surely if there is a one-to-one pairing between the elements of A and the natural numbers, and between the elements of C and the natural numbers, then there is a one-to-one pairing between the elements of A and the elements of C. If an element x of A is paired with the number f(x), and an element y of C is paired with the number g(y), then we can just pair an element x of A with the unique member y of C such that g(y)=f(x).

But surely, Professor Pruss, equipollence between the elements of A and those of B does not obtain in the domain of concrete entities (and their properties, states, relations, etc.) just because there is a one-to-one correspondence of each with the set of all natural numbers (N).
Yes, although strange enough, there is indeed an equipollence between the set of all even natural numbers (E) and that of all negative numbers (Z)by virtue of a function-equation, or a law of coordination, that orders a unique and reciprocal one-to-one correspondence between the sets (i.e., e=-(2z). Hence what is true of a finite set of negative numbers and its complementary set of negative numbers is equally true of the infinite sets of the same. Here we are operating within the domain of pure mathematics, far above terra firma.
However, whenever an attempt is undertaken to apply Cantorian set theory to a world of concrete entities, some relevant axions and theorems of any plausible metatheory will not be within the domain of pure mathematics. Thus, according to the received metatheory (which Craig skillfully exploits) it is posited (or stipulated) that two denumerable infinites of concrete entities are necessarily equipollent to each other. The underlying assumption is that such infinites have the same relevant mathematical properties as do mathematical infinites. But the metatheory that I advocate denies this assumption.
To take the example of humans and their pairs of hands, the absence of a one-to-one correspondence between an finite set of all humans (each with two and only two hands) and the corresponding finite set of hands (rights and left) also obtains with respect to the infinite sets of humans and their hands. However, to repeat myself, the infinite sets of humans and of all their hands, abeit not mutually equipollent, have the same cardinality (i.e., that of aleph-zero) because each is equipollent with N.
I cordially invite you, Professor Pruss, to read by paper "The Kalam Cosmological Argument" (the Philo article as corrected) at http://www.infidels.org/library/modern/arnold_guminski/kalam.shtml) for a comprehensive exposition of my opinions in this matter in order to see how my metatheory (although not formalized) avoids the numerous counterintuitive absurdities that obtain when the received metatheory is used in applying Cantorian set theory to a world of concrete entities.

We can also describe the pairing procedure directly. Imagine the people in a line side by side, with Sally being the first, and to the left of everyone else. You want to know which hand to pair George with? Well, you take two rocks. You put one beside George and one beside the leftmost hand in the line. One person at a time, you move the rock beside George to the left, and you move the other rock one hand at a time to the right. When the rock that was beside George gets to be beside Sally, you stop, and you pair George with the hand that the other rock is beside. And you don't need to actually do the procedure, because the procedure even as a counterfactual is sufficient to determine which hand George is going to be paired with (i.e., there is a fact of the matter which George would be paired with if the procedure were executed). Nothing explicit about numbers here.

It's easy to show that this hypothetical procedure pairs each hand with a unique person.

Now I could see how there could be philosophical worries in the case of beings that are not actually lined up in a spatiotemporal arrangement.

We can also describe the pairing procedure directly. Imagine the people in a line side by side, with Sally being the first, and to the left of everyone else. You want to know which hand to pair George with? Well, you take two rocks. You put one beside George and one beside the leftmost hand in the line. One person at a time, you move the rock beside George to the left, and you move the other rock one hand at a time to the right. When the rock that was beside George gets to be beside Sally, you stop, and you pair George with the hand that the other rock is beside. And you don't need to actually do the procedure, because the procedure even as a counterfactual is sufficient to determine which hand George is going to be paired with (i.e., there is a fact of the matter which George would be paired with if the procedure were executed). Nothing explicit about numbers here.

It's easy to show that this hypothetical procedure pairs each hand with a unique person.

Now I could see how there could be philosophical worries in the case of beings that are not actually lined up in a spatiotemporal arrangement.

Alex and Josh

Thanks for your welcome comments. I shall first address your Gendankenexperimente and then turn to Josh’s other remarks.

(1) Josh’s scenario. It appears that your scenario has a redundant feature because you first refer to pairing each human to each hand, and then you refer to pairing each hand to each human. In any case your point is that since that if both sets of humans and of their hands (lefts and rights) are equipollent with the set of natural numbers then they are mutually equipollent. The conclusion of the scenario is that each human is paired with only one hand. But we know per hypothesis that each human is naturally paired with a pair of hands. So the conclusion that an equipollence obtains between the infinite sets of humans and their hands remains for me (and Craig) a counterintuitive absurdity. For Craig this and other absurdities warrants the belief that infinite sets of concrete entities are metaphysically impossible. For me, the absurdities warrant the conclusion that there is something radically wrong with the received metatheory of the application of Cantorian theory to the real world.

(2) Alex’s scenario. In this scenario infinitely many people are in a line standing side by side with Sally being the first and to the left of everyone else. You take two rocks, place one beside George and one beside Sally’s left hand. Then “[o]one person at a time, you move the rock beside George to the left, and you more the other rock (beside Sally’s left hand) one hand at a time to the right. When the rock that was beside George gets to be beside Sally, you stop, and you pair George with the hand that the other rock is beside.”
Well let us expand the scenario a bit as follows:

rock
{Sally Alvin Alice Bill Anne Jane George . . . . .}
{lh-rh lf-rh lf-rh lh-rh lh-rh lh-rh lh--rh . . . . .}
rock

Overcoming philosophical inhibitions about completing infinitely many discrete actions yet to be commenced, the completion of the procedure results in the following with respect to the subset consisting of only the seven named persons:

George is paired with Bill’s left hand
Jane is paired with Alice’s right hand
Anne is paired with Alice’s left hand
Bill is paired with Alvin’s right hand
Alice is paired with Alvin’s left hand
Alvin is paired with Sally’s right hand
Sally is paired with her left hand

And Alex’s position is that completing the procedure with respect to the infinitely many persons in the line would result in the pairing of each hand with a unique person.

Well, as already indicated, I do not believe that an operation involving the yet-to-be-begun performance of infinitely many sequentially ordered actions is metaphysically possible. Moreover, I also don’t believe that is procedure can be accomplished in a finite time assuming it could be done at all. But this difficulty is not insuperable because the scenario could be modified by: (1) simultaneously placing a rock beside each person; (2) placing infinitely many rocks lined up under Sally’s left hand; (3) simultaneously moving each rock initially beside each person into a line of rock in front of Sally; (4) simultaneously moving each rock initially below Alice the requisite number of places to a position beside the left hand or right hand of a person in the line.

Again, as with Josh’s scenario, my fundamental problem is that the result of the scenario as amended results in the conclusion that each hand is paired with a unique person although per hypothesis each human has two and only two hands. However, in my view, the counterintuitive absurdity is compounded in Alex’s scenario as amended. This is the case because the realization of the procedure with respect to the subset of the seven named persons results in a striking anomaly. Notice that each human in the subset is paired with one hand. However, not every hand in the subset is paired with a human. That is, the hands belonging to Bill, Anne, Jane, and George are unpaired in the finite subset. I would suppose that Alex’s response would be that such pairing obtains with respect to the infinite sets of humans and their hands. But this possible solution presupposes that every infinite set of concrete entities is equipollent with any other infinite set of concrete entities.

The anomaly in question can be looked at in another way. Let us suppose that initially only the finite subset of the seven named persons exists. Alex’s procedure results in the pairing of a human with one and only one hand such that several hands are unpaired. But God then adds infinitely many humans (each with two and only two hands) to the line up, and adds infinitely many rocks below Sally. Now, God having realized Alex’s hypothetical procedure, pairs each hand with each human in a one-to-one correspondence.

So many learned mathematicians and philosophers have previously assured us: “Yes, it would be true that a finite set of humans would not be equipollent to the corresponding finite set of their hands (given that each human has two and only two hands. But the exigencies of Cantorian set theory are that there would be a one-to-one correspondence between infinitely many humans and infinitely many hands. You think this is bizarre? Just get over it.”

However, Alex’s scenario as amended implicitly reverses the usual relationship between finite and infinite sets of concrete entities because, in the case of first realizing Alex’s hypothetical procedure to a finite set of humans, some hands are not paired to humans; but a one-to-one correspondence obtains in the case of an infinite set of humans with the realization of Alex’s procedure.

Alex’s scenario is a challenging and entertaining exercise that involves the application of Cantorian theory to a gedankenexperiment in which sets (or aggregates, if you will) of concrete entities are deemed to have the same relevant mathematical properties as mathematical sets. But, I’m sorry, I persist in the view that with respect to the real world of concrete entities, a metatheory of the application of Cantorian theory to that world should avoid the creation of utterly preposterous anomalies. And this takes me back to what prompted my initial comment, viz., the remarks by Josh and Wes about how the KCA is more likely to appeal to the so-called common man or woman than to the average philosopher. The appeal of the KCA to the so-called common man or woman is initially aroused by the apprehension of how the application of Cantorian theory results in striking counterintuitive absurdities that have not been effectively answered by so-called average philosophers. But neither Josh nor Alex has as yet addressed the merits of my metatheory, assuming arguendo the A-theory of time, the causal principle in premise 1 of the KCA, the metaphysical impossibility of traversing a yet-to-be traversed infinity.

(3) An additional response to Josh. At the outset I would like to assure you that, although I am a metaphysical naturalist (and a commonsensible one at that), I believe that I would reject the argument even were I a convinced Christian theist who believes that it is divinely revealed that the universe had a temporal beginning.

Turning to the several points you raise. I do not believe that it is possible to complete an infinite series of past events to reach the present if it is assume that there is somehow a starting point. The moving of two particles together side-by-side in the same direction is not impossible based upon mathematical considerations. But two particles moving always away from each other from eternity past appears to be metaphysically impossible. A person climbing out of a bottomless pit without ever having started is not in my view metaphysically impossible based upon mathematical considerations. Yes, I believe that the temporal series of events constituting or including the history of this universe is infinite and of infinite duration. No, I do not think that it is metaphysically possible for there to have been a first event anymore than I think that the causal principle in premise 1 of the KCA is false. Were I to believe in God, I would believe him to be omnitemporal avec ou sans creation. If it is metaphysically possible for an infinite temporal series to obtain and this universe is of finite duration and thus began to exist, then its beginning necessarily had a cause. I, being a naturalist, would hold that it is at least more antecedently probable than not that the cause of the hypothetical beginning of the universe is itself natural rather than supernatural.

You touch on other matters particularly relating to contingency. Discussion of these matters would, as you say, take us off topic and my comment is already very long. However, I look forward to further exchanges with you.

I would think the following would be a sufficient condition for a pairing between two collections A and B of concrete objects: There is a clearly defined procedure P such that, given a member x of A, it would unambiguously generate a member P(x) of B, with the properties that (a) the procedure P as applied to distinct members of A would yield distinct members of B, and (b) for every member y of B, there is a member of A which would generate y with P.

It is necessary for this that for every member x of A, the procedure could be applied to x. It is not necessary for this that the procedure could be applied (sequentially or simultaneously) to all the members of A. For instance, suppose A is a collection of seven solvents, and B is a collection of seven objects made of different plastics. Suppose, further, that the following is true: if we take any of the seven solvents and put all of the seven objects in it, all but one will dissolve. Moreover, the one that wouldn't dissolve is different for different solvents. So, here is my procedure P. Given a solvent x, dump all the objects from B in x, and then let P(x) be the survivor. This has the requisite properties. But it would not be possible to apply this procedure, sequentially or simultaneously, to all the members of A. This is fine, however.

Josh. You ask whether I would "accept a definition of pairing in terms of sets."
Alex. You set forth a procedure as constituting "a sufficient condition for a pairing between two collections A and B of concrete objects." The statement of the procedure that immediatley follows would, I agree, establsh a pairing between two collections A and B of concrete objects and hence an equipollence between the two collections.

Perhaps I'm wrong. However, it seems to me that both of you think or suspect that I believe that it is metaphysically impossible for two infinite sets of concrete entities to be equipollent. But that is not at all my position. What I am urging is that a one-to-one correspondence between two infinite sets of concrete entities is a sufficient but not a necessary condition for having the same cardinality (i.e., that of aleph-zero). Two infinite sets of concrete entities, whether mutually equipollent or not, have the same cardinality because each is equipollent with the set of all natural numbers--and therefore with every denumerably infinite mathematical set.

Arnold:

Well, if you accept my sufficient condition, then you have to accept an equipollence between the hands and the people. For I've described a procedure for telling which hand a given person is paired with, and it's easy to prove that every hand gets paired by this procedure, and that no hand gets paired with more than one person.

Alex:

When I accepted your "sufficient condition" I did not understand to mean that I have to accept an equipollence between the hands and the people. For I did not understand you to describe a procedure for telling which hand a given person is paired with. What I understood you to describe in the first paragraph was a scenario that resulted in every member of B being paired with every member of A because the procedure was applied to every member of A and there is no member of B lacking the property of having been an object of the procedure. However,it appears that I may have grossly misunderstood your first paragraph.

Yes: I was giving a procedure for telling which hand a given person is paired with. Doesn't the procedure work?

Alex:

First, my thesis is that any pairing procedure (licit though it may be the domain of pure mathematics), that would entail or result in the pairing of all members of an infinite set of humans (each with two and only two hands) with the infinite set of all human hands (lefts and rights), is metaphysically (but not logically) impossible. So if acceptance of your "sufficient conditon" means that I must accept that an equipollence would obtain between the infinite sets of humans and of their hands then I do not accept your sufficient condition as licitly applicable to the domain of concrete entities.

Second, as to your proposed scenario. I should have written the second last paragraph of my last post of October 20 as follows: "What I understood you to describe in the first paragraph is a scenario that results with every member of B being paired with every member of A because: (a) the procedure P could be applied to every member of A; (2) the application of procedure P to distinct members of A would result in distinct members of B being 'y with P'; (3) for every member of B there is a member of A that could (you wrote 'would') generate 'y with P'." Although I wrote that "it appears that I may have grossly misunderstood your first paragraph," perhaps I rightly understood what you wrote but not what you meant.

Third. let us assume arguendo that you were indeed "giving a procedure for telling which hand a given person is paired with." So my answer to your question, "Doesn't the procedure work?" is "No, not in the world of concrete objects." It works, however, only in some pickwickian sense when it is claimed that one can also add infinitely many new guests in Hilbert's Hotel where all of the infinitely many rooms are occupied with one and only one guest. But in both cases (humans and their hands, and Hilbert's Hotel) we have scenarios involving counterintuitive absurdities. Recognition that these obtain grounds the conviction (of Craig and myself) that these scenarios pertain to metaphysical impossibilities.

Evidently we are at an impasse. But "Hier stehe Ich. Ich kann nicht anders."

Josh: Thanks for your latest comment. However tardy it is welcome.

Well good! We agree “that the argument for a finite past based upon the impossibility of an actual infinite fails (to convince us).” But you take a latitudinarian view that “[w]e just have different reasons for thinking it fails.” Here I beg to differ because the grounds upon which we differ have significant ramifications. You complain “that there are procedures (which [you] take to be abstract propositions) that pair the hands with the people and the people with the hands.” You write, “it seems to me that the procedure does indeed apply to the humans and the hands precisely by being about the humans and the hands.” But the underlying fallacy of your approach is to presuppose that modern set theory includes among its definitions and axioms that the theory applies to concrete entities and events such that any two infinites of concrete entities equipollent to the set of natural numbers are necessarily equipollent to each other. What is needed is a bridging or interpretive rule positing such application to the real world. The absurdity of the received opinion, which you and Craig share, is that although every finite subset of humans is not equipollent to the subset of their hands it is nevertheless the case that the infinite set of humans is equipollent to the infinite set of their hands. In my view, infinitely many humans, each with two and only two hands, cannot be in one-to-one correspondence (i.e., paired) with their infinitely many hands.

It seems to me that so much discussion of these issues involves very far-fetched possible-world scenarios. Some writers assert that in such cases the metaphysical impossibility of infinites obtains not because of transfinite mathematical considerations but rather because of other reasons (e. g., the factual impossibility of Hilbert’s Hotel, or of infinitely many humans in one physical universe). But the received opinion obviously applies to situations that do not involve prima facie factual impossibilities. For example, let us suppose that are infinitely many physical universes the contents of each of which are not spatially related to the contents of any other. I do not believe that this is metaphysically possible but I think this is epistemically possible. Let us suppose that each such universe has only finitely many physical substances. It is quite evident that, according to my metatheory of the application of transfinite arithmetic to the real world, the set of infinitely many universes is not equipollent to the set of all the physical substances in these universes. You would disagree professing that you “don’t know what ‘pairing’ or ‘equipollence’ (as they are ultimately defined in terms of a procedure that applies to …).” You do not say to what the ellipsis refers. However, the answer is that in the domain of pure mathematics the ellipsis refers to only mathematical entities (sets, numbers, points, lines) and not to concrete entities. It takes a metatheoretical proposition to make the ellipsis to also pertain to concrete entities and events.

According to you, there is a one-to-one correspondence, assuming the temporal series of events successively constituting or including the history of our universe is infinitely many and of infinite duration, between the series of years ending at midnight December 31, 2008 and the series of years ending at midnight December 31, 1008. According to me, there is no such one-to-one correspondence although both are equipollent to the set of all natural numbers. And it is upon your view of things that Craig and his allies mount their very plausible philosophical argument that it is metaphysically impossible for there to obtain an infinite temporal series of successively instantiated events or moments of infinite duration. Perhaps the “average philosopher,” not yet awakened from his dogmatic slumbers, will not agree that the argument in question based upon supposed counter-intuitive absurdities is plausible given the received opinion as to the application of transfinite arithmetic to the real world. But the intelligent “common man or woman” will likely think otherwise. So if the alternative to theism is some version of metaphysical naturalism that is not sufficiently commonsensible it is likely that the Craig version of the KCA will appeal to many persons, whether philosophically sophisticated or not.

When people, such as we, disagree as to philosophical fundamentals having done their best to understand opposing views, the best course for us is to heed the counsel of John Henry Cardinal Newman in his Apologia Pro Vita Sua (Part VII. General Answer to Mr. Kingsley): “Be large-minded enough to believe, that men may reason and feel very differently from yourselves; how is it that men fall, when left to themselves, into such various forms of religion [or irreligion], except that there are various types of mind among them, very distinct from each other?” (bracketed matter added). In the mean time we have much to learn from each other since we agree sufficiently on some matters to disagree profitably as to others.

Josh:
Of course, your bridging rule involves a procedure that applies to humans and hands. So I don’t have a different understanding of the meaning of ‘x applies to y.’ But the question is whether your bridging rule results in the counter-intuitive absurdities that bother both Craig and myself, and whether we should be looking for an alternative bridging rule that obviates the possibility of counter-intuitive absurdities. Evidently you don’t think any alternative bridging rule, such as what I propose, is needed.

Josh: Of course, Alex's pairing procedure results in the conclusion that the set of hands and the set of humans are equipollent. But this conclusion is absurd since each human has two and only two hands. Therefore the set of humans and the set of their hands cannot possibly be equipollent--although each is equipollent to the set of natural numbers. So we must reject the bridging rule, exploited by Craig to have transfinite arithmetic generate counter-intuitive absurdities concerning the real world, and replace it with another bridging rule, i.e., that proposed by yours truly.