If there's an infite past, it would take an infinite time to reach this point. The countdown to my arrival would never stop, and so I would never arrive.
I did arrive. Conclusion: past events are finite in temporal expansion.
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4Zeno's Paradoxes– Mauro ALLEGRANZACommented Mar 18 at 9:50
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4This is the same fallacy as in the Achilles and the Tortoise. Achilles does catch up to the tortoise nonetheless. And whether time is finite or infinite is just a matter of measuring convention, we can rescale it so that finite intervals according to our current convention are infinite and vice versa. Such rescaling happens even under the standard conventions for local times of observers near black holes.– ConifoldCommented Mar 18 at 9:52
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2Ill-formed: you assume you've existed forever. If you would do the same with space, you'll occupy the whole universe. Wrong. You (and me) are a dot in space, and in time.– RodolfoAPCommented Mar 18 at 10:20
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6I don't believe the OP is describing Zeno's paradox. They're talking about the case where Achilles has to travel an infinite distance at finite speed, not merely an infinitely divisible finite distance.– RayCommented Mar 18 at 20:22
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3What if you counted down really fast though– causative ♦Commented Mar 19 at 0:05
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6 Answers
"It would take an infinite time to reach this point"...reach it from where? By assuming a countdown you assume a point where the countdown begins, i.e. a beginning of time, and so your argument is circular.
Whether or not time is infinite is an empirical question. It's logically possible that there is no first point in time, just as there is no smallest integer
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Are you looking for "smallest nonzero real number" or "most negative integer"? en.wikipedia.org/wiki/Integer– g sCommented Mar 18 at 14:50
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despite what your computer might think -2147483648 isn't in fact the smallest integer– OganMCommented Mar 18 at 21:10
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2I am a mathematician, and I chose the words "smallest" and "integer" with their mathematical meanings, e.g. -2 is an integer, and -3 is a smaller integer. Given any integer, one may construct a smaller integer by subtracting one from it. Hence, there is no smallest integer. Commented Mar 19 at 12:20
If a number line extends infinitely in either direction, that does not prevent us from using finite numbers, even though you cannot count from the lowest possible value to the highest possible value (or even from one set value to the lowest/highest possible value).
We can still use finite references in an infinite line, why wouldnt that work with time? You arent measuring time in relation to some absolute beginning, just relative to other events.
This is, as Kant explains in his discourse on antinomies of space and time, a natural line of argument against an infinite past. The problem is that an equally natural line of argument can apparently be conjured for the opposite conclusion, viz. that past time must be infinite (since an empty time would for ex nihilo, nihil fit reasons not give rise to any determinate change of its (absent) content).
So one might be a dialethist and conclude that time is both finite and infinite as to its past extent. Kant's conclusion, though, was that there is a subtle premise being omitted in such arguments, the premise that space and time are determinate wholes of some sort. One can read Kant as offering not a paraconsistent, but a paracomplete, picture of the extent of past time and the "edge" of outer space: if the forms of intuition (forms of givable particulars) are not transcendentally real, then their object, the "whole" world, is either determinately not a whole or is indeterminately a whole.
answered Mar 18 at 22:46
No. You could make the exact same argument even if there were a finite past. So long as time is continuous you get the exact same result (suppose the universe is 10,000 years old but continuous, i.e. any unit of time can be further divided– so any traversal of some unit of time will require half of that and half of that and half of that...So, how could we have arrived at this moment!?). It follows that you "arriving" at a certain time is no evidence for whether time before was infinite or finite.
Further, contemporary physics seems to have a clean way of dealing with the issue of "beginning the count". We live in a (at least) four dimensional universe. Literally construed, it means that time is a dimension within a 4-dimensional manifold that just exists. Time is "within" it, so it doesn't even make sense to utter phrases like "counting down".
But suppose your argument is against the continuity of time. The generic response would be the generic response to Zeno's paradox: the formalization of the notion of the limit in calculus. The limit of adding these infinite intervals reaches your desired outcome of a specific unit. Of course, it is a controversial matter of whether calculus does resolve Zeno's paradox.
Infinity is not a number. It's a process. As long as time continues in a forward direction the "present" is not a fixed number and the "distance" from past to present is not fixed but is always increasing. This is how time can be described as infinite. Even if the past began at zero, time (the present) continues to increase in an unending process.
When the process of time stops, the timeline becomes finite.
answered Mar 18 at 23:40
If the past is infinite (which is contradictory, because 'the past' implies the passage of time, which is a limitation, and therefore not infinite. Infinity has no limitations.) you are already in everywhere and every time at once. Infinite time is contradictory. 'Where' and 'when' lose all relevance and really cannot be logically discussed in terms of infinity. One of the reasons I have described infinity and singularity as descriptions of the same condition.
