"4. History has its end in the present. (The future is not history.) So if the past was of infinite duration, an infinity came to its end. But this is a self-contradiction.".
Basically he's saying that an infinity as a concept is a paradox. He has a diagram of a timeline in his expansion of premise 4 that shows a timeline with 0 at present and infinity in the past and he says if we have an infinite past we can never reach the present. What are the fallacies of this argument, there is obviously at least one.
What I reckon this person is doing is using the concept of
actual as opposed to
potential infinites.
Potential infinity being more like a process e.g like the counting numbers.
Actual infinity is a concept that I haven't really heard outside of a theological or philosophical framework (can't say I ever came across it in the Maths I studied, but then you don't need to study Cantor for a Physics degree). Think of infinity as a number. That's pretty much your actual infinity.
Having made up this concept, the argument runs "can actual infinities exist in our own universe?" to which the answer is "can't really think of any".
Although.....if the Universe were eternal, then time itself would count as an actual infinite.
There are some properties of actual infinity which can be derived, although I've been loathe to look at this in any depth. It is, I'm told, impossible to traverse an actual infinite, meaning that you'd never be able to say "this is now!". You can definitely say "this is now!", therefore the Universe is not itself an actual infinite in terms of time and therefore cannot be eternal.
Myself, I prefer to look at the evidence.
PE
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