| Posted 08/25/11 at 04:29 PM||Reply with quote #1 |
|Hello everyone.Im A.J and I have been an admirer of Dr. Craig's work on the Kalam cosmological argument. I say that I have a pretty good grasp of the argument and it makes sense.Recently I came across a paper written by a professor at the university of albany.His name is Josh Dever. He critiqued the Kalam based on the premise that an actual infinite in the real world is not at all absurd any more than it would be absurd in the mathematical. His argument I think can be summarized as follows:There is no reason to believe that there is a discontinuation between the real world and the mathematical world. If it makes sense in the mathematical world it can make sense in the physical world. |
He goes on to demonstrate how in his analysis, there in fact is no absurdity in such paradoxes as the infinite library or tristram shandy paradox and can be properly understood without it being incoherent in the real world.
Here is the link to the paper:
Anyways this seems like a serious objection and not like those banal objections one finds on youtube.I believe it deserves an adequate response.
Now I dont expect to get an answer from Dr. Craig himself since I understand he's very busy and either way Im not even sure he participates in this open forum. But I am aware that ocassionaly James Sinclair visits the open forum.
Indeed I would be content to get feedback from anyone with an above average understanding of the subject, preferably to have a counter rebuttal to the above objections.
| Posted 08/29/11 at 12:15 PM||Reply with quote #2 |
|I think the author succeeds in demonstrating that the apparent contradictions of infinities do not refute the possibility of an actual infinity. It's a mapping problem, and limitation (or misapplication) of cantorian set theory. |
On the other hand, the author fails to show that an actual infinite is possible. Towards the end of the paper, he states:
We thus distinguish two senses in which an actually infinite collection can be created through successive addition:
(A) An actually infinite collection is created particularly through successive addition if some act of addition creates an infinite collection out of a finite collection.
(B) An actually infinite collection is created procedurally through successive addition if the process of successive addition, carried through to completion, creates an infinite collection.He correctly states that (A) is impossible, but his statement (B) is invalid. While it is true that a procedure can be defined to successively perform an addition, such a procedure cannot be "carried through to completion." It is not completeable. In terms of mapping it to reality, what is infinite is the process: it goes on and on without end, never completing. This is precisely what future time is all about: a potential. In the real world, all infinities are just potentials. Therein lies the fundamental problem with a past infinity: the past has no potential; the past is completed.
I noticed one additional bit of handwaving in the paper:
Consider the following example: assume that God by fiat creates an actually infinite collection of objects. He does so en masse to avoid worries about whether even God can create actual infinities by successive addition; Craig's earlier arguments against the mere existence of an actually infinite collection of physical objects being defeated there is no objection to such en masse creation.
The author is overlooking the fact that God can't do the impossible (he can't create a square circle or a married bachelor). He can only create an actual infinity, if it is possible for an actual infinity to exist. So the author is affirming the consequent, assuming an actual infinity is possible, suggesting that God can create one, thus "proving" an actual infinity is possible!
I do think Craig should drop the paradox arguments and focus on the apparent impossibility of a completed infinity. BTW, I say "apparent impossibility" because even this is not a mathematical proof; it is an inductive argument using a vague mapping between the mathematical properties of infinities and the thought experiments we perform with our metaphysical concepts of infinity.
| Posted 07/16/12 at 03:13 AM||Reply with quote #3 |
|After having read the paper again, I believe that the only way out for Craig if he wants to maintain that the paradoxes he presents are truly absurd and agrue from them that the infinite is impossible is for him to deny mathematical legitimacy to the infinite and subscribe to mathematical finitism.|
| Posted 07/16/12 at 02:40 PM||Reply with quote #4 |
Originally Posted by kuartus4
Now I dont expect to get an answer from Dr. Craig himself since I understand he's very busy and either way Im not even sure he participates in this open forum.
Why don't you submit this question (with a link to the paper) to Dr. Craig via the Q&A section of his website? He may find this paper contains interesting objections to the KCA and therefore may find it worthwhile to address in his Q&A.
Go to the latest Q&A and at the bottom there is a link to "Submit your question to Dr. Craig"
| Posted 07/16/12 at 09:54 PM||Reply with quote #5 |
|Mazzgolf, I recently submitted an unrelated question to Dr. Craig and he said he would respond in the future. It would be inappropriate for me to send another question I think. But if you think Craig should address this objection perhaps you should submit it to him.|
| Posted 07/16/12 at 10:15 PM||Reply with quote #6 |
Originally Posted by kuartus4
After having read the paper again, I believe that the only way out for Craig if he wants to maintain that the paradoxes he presents are truly absurd and agrue from them that the infinite is impossible is for him to deny mathematical legitimacy to the infinite and subscribe to mathematical finitism.
The implications of a paradoxical, pointless, past-eternal, perpetual motion universe/megaverse/multiverse
are not metaphysically impossible.
...they are just preposterously absurd.
And that's OK.
Sentient beings are allowed to speculate on the absurdity or otherwise of such notions.
It's just weird to see atheists claiming that their extravagant "woo" is a more plausible explanation than a singularity caused by the intent of another sentient Being.
Meaning versus meaninglessness. That is the question.
If we werent sentient beings with volition of our own, it probably wouldnt matter to us.
But we do seek meaning, patterns, purpose....
| Posted 07/19/12 at 10:13 PM||Reply with quote #7 |
|kuartus4 - I submitted this to the Q&A on the RF.org website and though the answer wasn't published on the website, I got a nice reply from one of the folks at RF.org. Here is the reply - I think you will find it interesting as did I:|
Dr. Craig is familiar with Dever’s argument and thinks it is a very powerful and even-handed critique, one of the best he’s seen. Dr. Craig’s claim is that an actual infinite is metaphysically impossible. So if mathematical objects really existed, his argument would, indeed, apply to them as Dever says. But do mathematical objects really exist? Only if Platonism is true. As Dr. Craig wrote in The Kalam Cosmological Argument, “For the nominalist, the conceptualist, and the formalist, the mathematical validity of the Cantorian system implies no commitment to the existence of the actual infinite in the real world. . . . Only for the Platonist-realist, who accepts the independent status of mathematical entities in the real world, do Cantor’s theories have ontological implications for the real world. This means that our argument against the real existence of the actual infinite would contradict Cantor’s work only if the Platonist-realist position . . . were proven to be . . . correct. . . , for our argument would be compatible with any of the other three.” (p. 89)
If there were mathematical objects, there could be only a finite number of them, as Intuitionists believe. But Dr. Craig sees no reason to think there are such objects; hence there really are not two worlds, as Dever infers.
One addendum: In Philosophical Foundations, Dr. Craig did use the language of the impossibility of an actually infinite number of physical things; but that was because his co-author is a Platonist and so he had to accommodate him! Obviously, if an actually infinite number of things, whether concrete or abstract, cannot exist, then an actually infinite number of physical things cannot exist, which is enough to prove the finitude of the past.
I, myself, am also not a Platonist like Dr. Craig (I still don't know what it means to say the number 9,12354x10^342 really, actually exists :-) so this argument doesn't affect me wrt the KCA.
Anyway, I hope this helps.
| Posted 07/20/12 at 07:22 PM||Reply with quote #8 |
|"...an actual infinite is metaphysically impossible..."|
Something is wrong here.
Maybe it's the indefinite article..."an actual"
Maybe its the use of the word "actual" and "metaphysically" in the same sentence.
Maybe it's the implication that God cant be metaphysically infinite -
a day is like a thousand years is like a day is like a.....and so forth.
A past-eternal universe absurd? Yes. Impossible? No.
For God, all things are possible.
| Posted 07/20/12 at 07:51 PM||Reply with quote #9 |
|It's like the notion of an eternity in heaven becoming boring eventually. (Sysiphus)|
One might mistakenly assume that the eternal Kingdom of God would get boring eventually but, metaphysically speaking, "heaven" could conceivably keep on getting more and more interesting to us as ''time'' goes on.
a) God's creativity is unlimited.
b) Our perception of His eternal Kingdom could theoretically keep on developing incrementally as we came to appreciate it all the more, the longer we spent there. IOW. A feedback loop. The longer you stay, the more you have to look "back" on which enriches the whole perception - a bit like a happy marriage.
A similar line of reasoning is used (by CS Lewis?) in relation to the residents of "hell" becoming increasingly
hateful of God the longer they remain there...thereby from the inside, locking themselves more and more securely
behind the gates of hell.