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My friend claimed that time cannot extend infinitely into the past. He explained:

"If an event A will happen in 10 years, when do you expect it to happen? In 10 years. But if event A (such as the event of our conversation) will happen in infinitely many years, when do you expect it to happen? Never. Therefore, if time was infinite into the past, this conversation would never occur."

First, I find this argument extremely weak and totally unconvincing. Just because something doesn't make sense to us is only "infinitesimal" evidence that it is false.

Secondly, there is another issue that I find with it that I don't fully understand myself, but I have a hunch it is right. Basically in his argument he is implicitly assuming that he can pick a point P on a timeline and view any other point from the POV of point P, including points that are infinitely far away from P (which doesn't really make sense by itself). But I have a hunch that this ability to pick a specific point P on the timeline is exactly what he is trying to disporove.

Can somebody please help me understand and flesh out my own argument, and/or offer a better alternative?

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  • Could you edit the quoted sentence. Does "you expect event A to happen 10 years" mean "you expect event A to happen every 10 years"? And what is "such out existence"? Currently I do not understand what it means, let alone if it is an argument, weak or strong. Does it mean that we "expect" our existence to happen "never" if the universe existed for infinitely long time? If so, the response is that our "expectations" are irrelevant, and somebody like "us" might have been happening every quadrillion years anyway. – Conifold Jan 27 '17 at 19:18
  • @Conifold Apologies. I edited it, is it more clear now? To answer your specific questions: I made typos in both of those sentences. The first phrase should've been "you expect event A to happen in*10 years", and the second phrase should've been "such as *our existence". To make it more understandable, I have replaced this second phrase with "such as the event of our conversation". – Ovi Jan 27 '17 at 19:35
  • Your objection (I think) can be rephrased as follows: there are no points "on the timeline" that are infinitely far from each other, even if the timeline itself is infinite, so there is no point P from which "infinitely many years" can be counted. But there are far more basic issues with this "argument", like analogizing infinite to finite (for continuous probability all individual outcomes have probability 0, yet one of them still happens), or even the initial non-sequitur "if an event A will happen in 10 years, we expect it to happen in 10 years"??? – Conifold Jan 27 '17 at 19:50
  • I like the mathematical example of the real line, which extends indefinitely in both directions. Put a big tape flag at the point marked "2017". Here we are, with unboundedness in the directions of both past and future. Works for me. Note that even if the past is infinite (or more accurately, unbounded) the distance between any point in the past and now is a finite interval of time. Maybe that's just how the universe works. – user4894 Jan 28 '17 at 2:21
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Whether or not time can extend infinitely into the past depends on the truth of a particular theory of time.

Parmenides denied the reality of space and time, which is a metaphysic that begot Zeno's paradox. "If time extends infinitely into the past, this conversation would never occur" is a variant of Zeno's paradox because, in order for the hypothetical proposition to be true, time cannot be real. If the proposition is true and time is unreal then the occurrence of the conversation is an illusion.

Presentism denies the reality of past and future (but affirms the reality of the present) such that nothing real is referred to by the statement "time extends infinitely into the past". Therefore, presentism can accept that time truly can extend infinitely into an illusionary past and the conversation truly can occur in the very real present, because the present is the only time anything real happens.

Perdurantism and B-theory of time affirm the reality of past, present, and future but deny that there is any objective location in any B-series (or C-series) ordering of time. These metaphysics of time suggest that time is a 4-dimensional object, but not necessarily finite in its dimensions. It is possible that aleph null is the cardinality of the set of a all B-series (or C-series) statements completely describing a 4-dimensional object.

An endurantist non-presentist A-theory of time affirms the reality of past, present, and future and it affirms that there is an objective location in an A-series, B-series, and C-series ordering of time. Yet, the aforementioned point about cardinality applies here as well.

What would make an infinite past impossible? Why would statements about a real infinite past necessarily not be true?

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