Actual Infinity in Reality?

[polymath257]

I'd point out that *finite* sets in mathematics are just as 'abstract'. mathematics is the study of formal axiom systems. So of course it is all abstract.

The idea that axioms are 'intuitively obvious' is another outdated idea. Euclid tried that with Euclidean geometry, but we have found that his system, even of geometry, was far from unique. Non-euclidean geometry is equally consistent, but gives different answers.

Which leads to the point: when there are different axioms systems that are all consistent, there is nothing to say which is correct and which is not correct except to go to observation and testing.

So, the fact that introducing actual infinities does bring a contradiction shows that there is no *logical* reason to exclude actual infinities.

And I agree--the actual existence of actual infinites has not been proven. But that isn't my claim. My claim is that there is no *logical* issue with them and that they should be considered as one *possibility*. And that is quite enough to destroy the Kalam argument. There is no *contradiction* with having an infinite regress of causes. It is internally consistent and so cannot be dismissed out of hand.