It makes perfect sense.
As you are probably aware by now, I do not think that’s how John defines infinity. That’s merely how I define it. I think that John defines it in Sense A. Here is what I mean by Sense A:
viewtopic.php?f=1&t=195793&start=500#p2769185
Perhaps noone realized it but in that post of mine I argued against John’s proof number four: The Beginningless Time Paradox.
I think that the following is an accurate paraphrase of a part of his argument:
If time has no beginning, it follows that the number of events that took place before the present day is equal to a number that is larger than every number (including itself.)
Note that I am replacing his use of the word “infinity” with “a number that is larger than every number (including itself)”.
I believe the above is a non-sequitur. If the universe has no beginning, what follows is that the number of events that took place before the present day is a number larger than every integer. A number larger than every number (including itself) is a number larger than every integer but it’s not the only number of that kind. In other words, there are different kinds of infinities. One of them can’t be exhausted i.e. reduced to zero (and it’s actually a contradiction in terms.)
Basically, what I am saying is that he’s committing a fallacy known as false dichotomy.