Over in this thread, a number of us have been having a discussion with daveS regarding the alleged possibility of an actually infinite past. DaveS seems to think that an infinite past is a perfectly viable model that does not entail any logical contradictions. Various arguments for the necessary finitude of the past were offered in that thread by myself and others, however, in comment #187 I offered the following argument for the finitude of the past that did not rely on the impossibility of an actual infinite existing in the world:
1) The past consists of moments that were once the present
2) If the past is infinite, then for any given moment there were infinitely many moments that preceded it
3) If an infinite past entails that for any given moment there were infinitely many moments that preceded it, then an infinite past entails that any moment that was at one time the present was preceded by an infinite number of prior moments already constituting the past
4) If an infinite past entails that any moment that was once the present was necessarily preceded by an infinite number of moments already constituting the past then it entails the existence of infinitely many past moments that were never the present
5) Either premise 1 is false and the past does not consist [entirely] of moments that were once the present, or the past is not infinite
6) Premise 1 is not false and the past does consist [entirely] of moments that were once the present
7) The past is not infinite
DaveS disagreed from Premise 4 on, though no specific argument was given for why Premise 4, or anything else, was incorrect or failed to follow as a matter of logical necessity. For the sake of making ongoing discussion easier to understand I’ve created a couple of simple diagrams / infographics to visualize the logic of the argument, comparing a visualization of how we typically view the flow between future, present and past with the flow seemingly required by the necessary characteristics of an actually infinite past.
First, a diagram of how we typically view the flow of time given a finite past:
And now a diagram showing the characteristics and preconditions of an actually infinite past:
All comments on this issue can continue in the other thread after comment #274.