Infinite Past Time

[pax]

An infinite point is a point that can never be reached, for there is always one more unit of time or space before you get there.

Therefore, an infinite future is a future which can never be reached. It is not an impossibility as it is not yet realized, that is, it has not yet come into existence.

An infinite past, on the other hand, is an entirely different matter. While an infinite past, like an infinite future, can never be reached, it is impossible because an event in an infinite past requires an infinite amount of time for its effects to reach the present, and an infinite amount of time is an amount of time that can never be realized.

Think of a star existing an infinite amount of distance away. Could its light ever reach us? Of course not.

Therefore, a present time dependant upon events which happened in an infinite past simply cannot exist, nor can they ever exist, for in order for them to exist an infinite amount of time must first pass.

Ergo, to propose a universe which has an infinite past is to propose a universe which cannot exist.

Ergo, because we know the universe does indeed exist, we also know the universe does not have an infinite past.

[fredonly]

My position is similar to Aristotle's. Aristotle believed an actual infinity is impossible, but a potential infinity is possible. Aristotle decided this before the development of calculus and set theory, which make use of mathematical infinities – so within the realm of mathematics, Aristotle was wrong: there are coherent mathematical concepts of infinity. However, within the realm of temporal reality, I think he was correct.

What about actual infinities in general, do you think it's impossible? I disagree with Aristotle, I think they are possible, even in our universe. Last I check, cosmologist haven't shown the size of the universe is finite or not. If it is not, that would be a actual infinite.

I don't know if it is feasible for the universe to be actually infinite. My argument against a temporal infinity does not apply. I think an actual temporal infinity is impossible.

I agree. The past, were it to be infinte, would be an actual infinity.

OK, but compare this to a future infinity. We cannot actually count to infinity, right? The mirror image of this, for the past, is the assumption that we are counting DOWN from –infinity. This is no more possible than counting TO infinity.

I don't understand why you and pax insist an infinite past would involve counting down from –infinity. You had previously agreed that a day infinitely remote in time doesn't exist, even given infinite past. If such a day doesn't exist, why would it matter that I cannot go from that non-existent day to the present?

When I said that a day infinitely remote in time doesn’t exist, that was part of the argument that the past cannot be infinite. If the past is infinite, there would have to be days that are infinitely remote in the past that have been actualized. An infinite past implies infinitely many days have been actualized.

I cannot reach from infinity but I can however reach from any day, even if there infinitely many of them.

That just means we can't establish a past temporal boundary by logic alone. We can't establish a future temporal boundary either, nevertheless we know we can't actually reach a future infinity.

Reaching to an infinity is not possible, and conversely it is impossible to reach from a past infinity. To think of time being infinite, requires a coherent definition of what it can mean – not contradicting the unreachable-ness. I have provided such a definition for the future: the unending process. There is no analogous process for the past – which is why I suggest an infinite past is an incoherent concept.

[Bust Nak]

I don't know if it is feasible for the universe to be actually infinite. My argument against a temporal infinity does not apply. I think an actual temporal infinity is impossible.

Well shouldn't the fact that we are still waiting for cosmologists to find enough evidence to say one way or the other about the size of the universe, mean that an actural infinite in the from of a universe infinite in size, cannot be ruled out by on logical gounds? i.e. Actual infinities are logically consistent?

When I said that a day infinitely remote in time doesn’t exist, that was part of the argument that the past cannot be infinite. If the past is infinite, there would have to be days that are infinitely remote in the past that have been actualized.

This is not true. Going back to my original proof. I've shown a day infinitely remote in time does not exist, even if the past is infinite.

An infinite past implies infinitely many days have been actualized.

This I agree with, but there being infinitely many actualized days in no way implies there are actualized days that are infinitely remote in time.

That just means we can't establish a past temporal boundary by logic alone.

No, it means your objection weren't valid.

We can't establish a future temporal boundary either, nevertheless we know we can't actually reach a future infinity.

And I am telling you we cannot actually reach from a "past inifinity," not because the past is finite, but because it simply doesn't exist anywhere in the infinite past.

Reaching to an infinity is not possible, and conversely it is impossible to reach from a past infinity.

Correct. And this is not a problem since a past infinity is not in the infinite past, just as a future infinity, is not in the infinite future.

To think of time being infinite, requires a coherent definition of what it can mean – not contradicting the unreachable-ness. I have provided such a definition for the future: the unending process. There is no analogous process for the past – which is why I suggest an infinite past is an incoherent concept.

But I provided such a coherent definition of what it can mean - a past without a beginning.

[fredonly]

I don't know if it is feasible for the universe to be actually infinite. My argument against a temporal infinity does not apply. I think an actual temporal infinity is impossible.

Well shouldn't the fact that we are still waiting for cosmologists to find enough evidence to say one way or the other about the size of the universe, mean that an actural infinite in the from of a universe infinite in size, cannot be ruled out by on logical gounds? i.e. Actual infinities are logically consistent?

Are you sure actual infinities are logically consistent? Paradoxes, such as Hilbert's Hotel and the Tristan Shandy paradox demonstrate logical inconsistency.

When I said that a day infinitely remote in time doesn’t exist, that was part of the argument that the past cannot be infinite. If the past is infinite, there would have to be days that are infinitely remote in the past that have been actualized.

This is not true. Going back to my original proof. I've shown a day infinitely remote in time does not exist, even if the past is infinite.

I don't see how you conclude that. You showed that if the past is infinite, then it's possible for the number of past days to be any finite number. I don't see that this has any bearing on whether or not there were days actualized in the infinitely remote past. If there's a problem, it seems to me the problem is with the vagueness of the term infinitely remote past. My general issue is that vaguely defined infinities seem plausible, but when you nail it down to a more complete definition, they can become implausible.

That just means we can't establish a past temporal boundary by logic alone.

No, it means your objection weren't valid.

You have to at least agree that logic can't establish a temporal boundary. This is true irrespective of whether or not the past is infinite. So IF I'm right, that the past is finite, it is irrelevant that a past temporal boundary has not been identified.

However it may very well be that the big bang establishes that past temporal boundary.

Note that logic can sometimes be a guide to physical reality. For example, logic establishes the impossibility of time travel to the past: this would entail the grandfather paradox (travel to the past, kill your grandfather, resulting in you never being born, resulting in you never travelling to the past to kill your grandfather…). Stephen Hawking has calculated the probability of time travel to the past as being infinitesimally low (this is noted in his book, The Universe in a Nutshell). Logic led us in the correct direction here. Also recall what I mentioned awhile back: the Borde-Guth-Vilenkin analysis has proven that an inflationary universe (or multiverse) cannot be past eternal. It doesn't actually identify the boundary, but it shows that must be a boundary.

We can't establish a future temporal boundary either, nevertheless we know we can't actually reach a future infinity.

And I am telling you we cannot actually reach from a "past infinity," not because the past is finite, but because it simply doesn't exist anywhere in the infinite past.

But you have to rely on a vague definition of infinity in order to believe that. In effect, this ignores the limitations that are inherent in temporal reality.

Reaching to an infinity is not possible, and conversely it is impossible to reach from a past infinity.

Correct. And this is not a problem since a past infinity is not in the infinite past, just as a future infinity, is not in the infinite future.

But use a rigorous definition of a temporal infinity:

Future: no future day will ever be actualized that is infinitely remote into the future. An infinite future can only mean an unending process of actualizing days.

Past: no past day has ever been actualized that is infinitely remote in the past. An infinite past can only mean…..what?

There is no coherent definition of what a past infinity can be. It obviously can't be an unending process. You can't escape the fact that it would have to entail infinitely many days having been actualized:

1. The past is infinite (assumption)
2. The past consists of all days that have been actualized (definition of the past)
3. The set of all days that have been actualized is an infinite set (1,2)
4. An infinite set has infinitely many members (definition of an infinite set)
5. Therefore infinitely many days have been actualized (3,4)

This proves that if the past is infinite, then infinitely many days have been actualized.

To think of time being infinite, requires a coherent definition of what it can mean – not contradicting the unreachable-ness. I have provided such a definition for the future: the unending process. There is no analogous process for the past – which is why I suggest an infinite past is an incoherent concept.

But I provided such a coherent definition of what it can mean - a past without a beginning.

A past without a beginning is no more complete than a future without end.

[Bust Nak]

Are you sure actual infinities are logically consistent?

Pretty sure, yeah. That's what I am arguing for.

Paradoxes, such as Hilbert's Hotel and the Tristan Shandy paradox demonstrate logical inconsistency.

Counter intuitive, sure. Logical inconsistency, no.

I don't see how you conclude that. You showed that if the past is infinite, then it's possible for the number of past days to be any finite number.

No, that would be my second proof. I was referring to the stuff to do with proving there being a finite number of steps between any two specific points in time.

You have to at least agree that logic can't establish a temporal boundary. This is true irrespective of whether or not the past is infinite. So IF I'm right, that the past is finite, it is irrelevant that a past temporal boundary has not been identified. However it may very well be that the big bang establishes that past temporal boundary.

Ok, I agree. Logic alone cannot establish a temporal boundary regardless of whether the past is infinite or not. And if the fact logic cannot identify this temporal boundary does not mean one can conclude the past is infinite.

Note that logic can sometimes be a guide to physical reality. For example, logic establishes the impossibility of time travel to the past: this would entail the grandfather paradox (travel to the past, kill your grandfather, resulting in you never being born, resulting in you never travelling to the past to kill your grandfather…).

Surely branching time line, as envisaged by many si-fi writers, would deal with this paradox.

Stephen Hawking has calculated the probability of time travel to the past as being infinitesimally low (this is noted in his book, The Universe in a Nutshell). Logic led us in the correct direction here. Also recall what I mentioned awhile back: the Borde-Guth-Vilenkin analysis has proven that an inflationary universe (or multiverse) cannot be past eternal. It doesn't actually identify the boundary, but it shows that must be a boundary.

Sure, I have no problems with that. As I mentioned before, there is a difference between the past being finite because there is scientific evidence to show it, and the past being finite because an infinite past is logically impossible. I am more interested in the latter in this thread.

But you have to rely on a vague definition of infinity in order to believe that. In effect, this ignores the limitations that are inherent in temporal reality.

I don't think "unbound" is vague at all. And we can throw in actualized days into "a past without a beginning" to convey the idea of arrow time too if you like.

But use a rigorous definition of a temporal infinity:

Future: no future day will ever be actualized that is infinitely remote into the future. An infinite future can only mean an unending process of actualizing days.

Past: no past day has ever been actualized that is infinitely remote in the past. An infinite past can only mean…..what?

It can only mean there is no beginning.

There is no coherent definition of what a past infinity can be. It obviously can't be an unending process. You can't escape the fact that it would have to entail infinitely many days having been actualized:

...

This proves that if the past is infinite, then infinitely many days have been actualized.

This is trival. If the past is infinite, then of course there are infinitely many days that have been actualized. I agree with that. What I am contesting is whether any of these actualized days is infinitely remote in time.

A past without a beginning is no more complete than a future without end.

And I would suggest that a "future without end" is a coherent definition for what an infinite future is.

[Bust Nak]

Are you sure actual infinities are logically consistent?

Pretty sure, yeah. That's what I am arguing for.

Paradoxes, such as Hilbert's Hotel and the Tristan Shandy paradox demonstrate logical inconsistency.

Counter intuitive, sure. Logical inconsistency, no.

I don't see how you conclude that. You showed that if the past is infinite, then it's possible for the number of past days to be any finite number.

No, that would be my second proof. I was referring to the stuff to do with proving there being a finite number of steps between any two specific points in time.

You have to at least agree that logic can't establish a temporal boundary. This is true irrespective of whether or not the past is infinite. So IF I'm right, that the past is finite, it is irrelevant that a past temporal boundary has not been identified. However it may very well be that the big bang establishes that past temporal boundary.

Ok, I agree. Logic alone cannot establish a temporal boundary regardless of whether the past is infinite or not. And if the fact logic cannot identify this temporal boundary does not mean one can conclude the past is infinite.

Note that logic can sometimes be a guide to physical reality. For example, logic establishes the impossibility of time travel to the past: this would entail the grandfather paradox (travel to the past, kill your grandfather, resulting in you never being born, resulting in you never travelling to the past to kill your grandfather…).

Surely branching time line, as envisaged by many si-fi writers, would deal with this paradox.

Stephen Hawking has calculated the probability of time travel to the past as being infinitesimally low (this is noted in his book, The Universe in a Nutshell). Logic led us in the correct direction here. Also recall what I mentioned awhile back: the Borde-Guth-Vilenkin analysis has proven that an inflationary universe (or multiverse) cannot be past eternal. It doesn't actually identify the boundary, but it shows that must be a boundary.

Sure, I have no problems with that. As I mentioned before, there is a difference between the past being finite because there is scientific evidence to show it, and the past being finite because an infinite past is logically impossible. I am more interested in the latter in this thread.

But you have to rely on a vague definition of infinity in order to believe that. In effect, this ignores the limitations that are inherent in temporal reality.

I don't think "unbound" is vague at all. And we can throw in actualized days into "a past without a beginning" to convey the idea of arrow time too if you like.

But use a rigorous definition of a temporal infinity:

Future: no future day will ever be actualized that is infinitely remote into the future. An infinite future can only mean an unending process of actualizing days.

Past: no past day has ever been actualized that is infinitely remote in the past. An infinite past can only mean…..what?

It can only mean there is no beginning.

There is no coherent definition of what a past infinity can be. It obviously can't be an unending process. You can't escape the fact that it would have to entail infinitely many days having been actualized:

...

This proves that if the past is infinite, then infinitely many days have been actualized.

This is trival. If the past is infinite, then of course there are infinitely many days that have been actualized. I agree with that. What I am contesting is whether any of these actualized days is infinitely remote in time.

A past without a beginning is no more complete than a future without end.

And I would suggest that a "future without end" is a coherent definition for what an infinite future is.