The Extremis of Rationality

[Mudhammam]

Where did I go wrong in my argument in the OP? There I argued that an infinite regress of change means that a series of infinite changes have reached the completion of their set, as the present is its end term for which no future time has yet come into existence, and that amounts to saying that it is possible to traverse the whole of an infinite series. But an infinite series cannot have an end term because that is the very definition of infinitude - it has no end or final term.

If the present is the end of the set then you must define the present. what is the present? Even as you ask the question it moves into the past. And when you start to ask the question, the last words of the question are still in the future. The present cannot then be the definite end of the set since the present is not itself definite.

As thinking beings we experience reality in all three phases.
1. past as memory
present as experience
future as anticipation

there is no paradox unless we insist on one.

Well, as you acknowledge, that's not quite so easy... But let's say the "present" is the current calendar day. We can imagine that the amount of time contained within 24 hours could be hypothetically multipled infinitely in both directions, and if I were to tell you that after an infinite number of 24-hour sets are complete, then the birth of X will occur, the question is, will the birth of X ever occur? If you say that an infinite number of such hypothetical 24-hour sets have occurred in the past, then the answer is yes. Today X has been born. To me that's sort of like asking if the series of infinite time-points is an even or odd number. How could it be either?

I suppose one way out of this is to say that no such infinite series actually exists because the past, though conceived to be infinite, doesn't exist in actuality. This won't work for infinite space though...