Secular philosopher Graham Oppy, whose views on the kalam argument I discussed in a previous post, is author of an interesting book on the infinite, as this concept plays a role in mathematics and cosmological arguments for God's existence.
In the kalam cosmological argument, it is argued that an actual infinite (i.e. a collection or set composed by a infinite numbers of parts) cannot be instantiated in the concrete world (e.g. in the physical world). If this argument is sound (and I think it is) it implies that the universe is not past eternal, because a past eternal universe would be composed by an infinite number of past events, and such infinite cannot exist.
This implies the absolute beginning of the universe (note that this argument, developed in medieval times, is wholly independent of the current scientific-cosmological evidence for the universe's beginning). So both scientific and philosophical considerations support the universe's absolute beginning.
In the kalam argument, it is shown that the existence of an actual infinite in the concrete world would produce absurd and physically impossible situations. A leading defender of the argument, William Lane Craig, comments:
Take, for example, Hilbert's Hotel, a product of the mind of the great German mathematician David Hilbert. Let us first imagine a hotel with a finite number of rooms. Suppose, furthermore, that all the rooms are full. When a new guest arrives asking for a room, the proprietor apologizes, "Sorry, all the rooms are full." But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are full. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. "But of course!" says the proprietor, and he immediately shifts the person in room #1 into room #2, the person in room #2 into room #3, the person in room #3 into room #4, and so on, out to infinity. As a result of these room changes, room #1 now becomes vacant, and the new guest gratefully checks in. But remember, before he arrived, all the rooms were full! Equally curious, according to the mathematicians, there are now no more persons in the hotel than there were before: the number is just infinite. But how can this be? The proprietor just added the new guest's name to the register and gave him his keys—how can there not be one more person in the hotel than before?... suppose some of the guests start to check out. Suppose the guest in room #1 departs. Is there not now one fewer person in the hotel? Not according to the mathematicians! Suppose the guests in rooms # 1, 3, 5 ... check out. In this case an infinite number of people have left the hotel, but according to the mathematicians, there are no fewer people in the hotel! In fact, we could have every other guest check out of the hotel and repeat this process infinitely many times, and yet there would never be any fewer people in the hotel.
Craig's argument is basically a reductio ad absurdum of the existence of the actual infinite in the concrete world.
In the universe of purely conceptual discourse of mathematicians, the actual infinite is a perfectly a logical concept, you're just playing with a bunch of concepts and trying to reason logically about such concepts. But when you try to make it instantiated in the concrete, physical reality, outside of the conceptual realm of mathematics, the actual infinite produces clearly impossible and absurd situations as the ones mentioned above by Craig.
Now, Oppy (who is a sophisticated secular philosopher) understands perfectly the argument and its absurd implications.
To my astonishment, Oppy's reply to it is... to accept such absurd consequences!
Oppy says that we have to "outsmart" the proponent of the argument, that is, "to embrace the conclusion of one's opponent's reductio ad absurdum argument".
But surely this is wrong. If you accept the conclusion of your opponent's reductio ad absurdum argument, then you're accepting that you position was soundly refuted, since it is the main function of any successful reductio ad absurdum, specially in mathematics. (In fact, it is hard to think in a more sound and convincing form of refutation than an reductio ad absurdum argument).
No mathematician would say "Well, you have provided a sound reductio ad absurdum of my argument, and I fully accept and embrace it. Therefore, my argument is right!"
Only an atheist philosopher would dare to suggest something like that, just on behalf of having the upper hand in a debate and trying to appear to be right (to himself) in the face of contrary evidence and sound logical refutation.
By "embracing" the conclusion of the opponent's reductio, Oppy means to accept that if an actually infinite numbers of things exist in the concrete, extra-conceptual world, the absurd situations mentioned by Craig would happen and we should expect and accept them.
Such reply is shocking coming from a philosopher of Oppy's intellectual stature.
Obviously, if an actual infinite exists, then such absurd situations should be expected. This is simply to repeat the conditional "If an actual infinite number of things exist in the real world, then absurd consequences result"
But the conditional is not in dispute (in fact, such conditional is precisely what the proponent of the kalam is arguing for!). What is in dispute is the antecedent of such conditional, namely, the existence of an actual infinite in the real world.
Simply embracing the conclusion of the argument does nothing to show that the antecedent is possible and hence that such absurd situations can be factually instantiated in the real world.
That a philosopher of Oppy's level of sophistication and erudition have defended such mathematically, metaphysically and logically implausible objection to the kalam argument, reinforces our confidence in the soundness of the kalam as a good argument for the universe's absolute beginning, and hence for God's existence.
Contemporary atheists not just are disposed to accept that "the universe came from nothing", but alternatively also that the universe is composed of an infinite number of past events which, if true, would imply the existence of an actual infinite with its absurd and impossible (and never observed!) consequences in the real world.
It is hard to think about a position which requires more faith than this, and which is more contrary to logic and evidence.
Atheists are prepared to accept ANY position, if it provides them with a apparent escape or way out for not accepting God's existence.
In addition to psychological factors, I suspect that spiritual factors play a role and some religious traditions (from several perspectives) have alerted about it.
For example, in the New Testament, in Matthew 13: 10-13, when asked for his continuous use of parables to convey his teachings, Jesus explained:
And the disciples came, and said unto him, Why speakest thou unto them in parables?
11 He answered and said unto them, Because it is given unto you to know the mysteries of the kingdom of heaven, but to them it is not given.
12 For whosoever hath, to him shall be given, and he shall have more abundance: but whosoever hath not, from him shall be taken away even that he hath.
13 Therefore speak I to them in parables: because they seeing see not; and hearing they hear not, neither do they understand.
Did Jesus perhaps know in advance that certain kind of persons (the ones who are fully committed to reject any evidence for God) won't hear, and hence to such persons no correct or straightforward or unambiguous explanation and information about God should be given?
Who knows...
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