### Craig on an infinite old universe

I listened to some of the podcast of the Craig-Law debate. Craig's argument is in stages. (1) An argument that the world had a beginning in time. (2) That the world therefore had a creator (3) that this creator is good (4) that this good creator is the very being whose son is the Jesus who was resurrected.

Taking the first, I was surprised by his arguments about an infinitely old universe. He seemed to be arguing that there are parodoxes associated with a denumerable infinity. For example, if you take away all the odd numbers, you are left with infinitely many even numbers, so an infinity subtracted from an infinity still equals infinity. Is this a paradox, or just a feature of infinite domains? He seems to acknowledge this, but then says that this means that infinity is simply a mental construct, and nothing real. Therefore an infinitely old universe, which would have to be real, cannot exist. That is also odd. Most mathematicians, who are Platonists to the core, would hold that the natural numbers are real, but have no difficulty with the 'features' associated with a denumerable infinity.

Did anyone else find this odd?

Taking the first, I was surprised by his arguments about an infinitely old universe. He seemed to be arguing that there are parodoxes associated with a denumerable infinity. For example, if you take away all the odd numbers, you are left with infinitely many even numbers, so an infinity subtracted from an infinity still equals infinity. Is this a paradox, or just a feature of infinite domains? He seems to acknowledge this, but then says that this means that infinity is simply a mental construct, and nothing real. Therefore an infinitely old universe, which would have to be real, cannot exist. That is also odd. Most mathematicians, who are Platonists to the core, would hold that the natural numbers are real, but have no difficulty with the 'features' associated with a denumerable infinity.

Did anyone else find this odd?

Labels: God, infinity, kalam argument

## 6 Comments:

I couldn't be bothered to listen to the podcast, so I'll accept your description at face value.

First of all, current physics doesn't think the universe is infinitely old, so arguing about that aspect doesn't really have any direct bearing on reality, as currently understood. This is smoke-n-mirrors warning sign #1.

There are no paradoxes with infinity. The only problems you run into are if you don't define things carefully. Introducing inf-inf=inf as some kind of confusion or problem is a clear sign of either ignorance or dishonesty on his part.

Infinity is just a mental construct, at least the mathematical one that we discuss is. However, that too tells you nothing about the real world. Numbers like "2" are mental constructs, but that doesn't mean you can't have two sheep.

From what you say, it sounds like he is a great debater, in public, but only on the surface. Everything he says (as you report it) falls apart when examined at leisure.

>> I'll accept your description at face value.

You should never do that.

On his skill in debate and public speaking, absolutely yes. As he was speaking, I continually felt the urge to renounce my sceptical way of life and proclaim my belief in a 6,000 year old universe. Now the sounds have faded to vague echoes, I am not so sure. His picture reminds me of the ‘king of real estate’ played by Peter Gallagher in the film American Beauty

I've always thought it would be more charitable to interpret the argument against infinity of the past to be that it's metaphysically impossible for an infinity to be actualized in the world; that the concept of an *actual infinity* is incoherent, not that the concept of infinity is contradictory simpliciter. I'm familiar with more than a few of WLC's debates and he does use this distinction of Aristotle's between potential and actual infinity. Hopefully my distinction makes sense.

Either way, surely you, Ockham, do not agree with the mathematicians that there are an infinite number of platonic abstract objects, so I'm curious then as to why you would disagree.

As for convincingness, I obviously accept the soundness of his "Kalam cosmological argument": (1) Whatever begins to exist has a cause. (2) The universe began to exist. (3) The universe has a cause. In metaphysical realist fashion I accept 1, and 2 is a de fide dogma of the Church. I'm less sure as to whether 2 can be proved though. Aquinas had similar quibbles of course.

My point was that Craig's argument would not be acceptable to Platonist mathematicians.

On whether it is acceptable to nominalist mathematicians, good point. There was a discussion here about this a while back. I'm agnostic about 'actual infinities'. Not even sure what they are!

I’ve written a Critique of Prof. Craig’s Argument against the existence of an actually (physical) infinite Collection, which could be sent to you if you desire. I have found Craig’s line of Argument both unnecessary (for the other Arguments he uses) and I think not justified.

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