The Extremis of Rationality

[Rhondazvous]

Why then does the set have to be empty? Or rather, why does it make superior sense to insist that it was empty?

Infinity is more descriptive of a volume rather than a line. One of the terms is doomed to be undefined. Chad argued as much earlier.

Then would you say that time is a series of units within that volume?

[houseofcantor]

Infinity is more descriptive of a volume rather than a line. One of the terms is doomed to be undefined. Chad argued as much earlier.

Then would you say that time is a series of units within that volume?

No. 

The problem with infinite time is that there is either an undefined quantity at the beginning or at the end of "the series" in which you try to contain it, making it "not a series." 

[Anomalocaris]

Empty universes don't experience time, as there is nothing for it to impinge upon, and that makes empty universes unstable, and they tend to decay immediately into universes that are not empty.

Both may be true, but one does not lead to the other.

[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...

[Thumpalumpacus]

Given that in our experience today is followed by tomorrow, it seems to me that a problem in your argument is the assumption that today is the end of eternity.

It's just that it takes time to get here, not that time has stopped.

[RoadRunner79]

An excellent post, and I think that you stated the issues well.  And a large part of the problem, is that we do not understand time very well.  If we could figure it out, we would be famous. 

I would love to study more deeply into the subject however as Einstein said "If you cannot explain it simply, you don't understand it well enough".  As I said, I don't think anyone understands it well, so therefore any study is going to be anything but simple.  As with anything before the beginning of the universe, it is going to also get into a lot of theoretical assumptions.

It does seem that many in cosmology do tie time in relation to matter, and the space-time dimension.  With this, it is theorized, that physics and even time itself break down if the singularity model is correct.  Also if time does have a relation to matter then is there any time, if there is not any matter?

[Rhondazvous]

Then would you say that time is a series of units within that volume?

No. 

The problem with infinite time is that there is either an undefined quantity at the beginning or at the end of "the series" in which you try to contain it, making it "not a series." 

Infinity is not the opposite of time. That would indeed be a paradox, for infinity would have to stop when time begins and then start again when time ends. If infinity has to stop and start then it's not infinite. But then if infinity doesn't have to stop and start then there needn't be a time when matter and energy did not exist and interact to create measurable changes that we call time.

[TheoneandonlytrueGod]

There are points at which rational thought must break down and admit the fundamentally absurd. One such paradox is found in the origin of change, or time. Either time began or it is eternal, both of which seem impossible to swallow. The problem with a beginning of time is that it requires there to have been a time in which there was no time. This is absurd. That is, to say that time began to exist is to say that its non-existence preceded the moment at which it began. What else can "began to exist" mean other than that time was non-existent, and then - voila! - it existed? Furthermore, if time did not - at one time - exist, there was always the potentiality for time to come into existence, and so time always existed potentially before it existed in actuality. So, time was actually non-existent but not potentially non-existent (in other words, the existence of time was not an impossibility). If actual time had a beginning, then prior to actual time there was an eternity of potentially existent time. This is absurd. So, either the actuality or potentiality of time must be eternal. This amounts to nothing other than the observation that there has always been change, either actually or potentially. If there was a state in which change did not occur, then such a state could not but remain in stasis. For, if change did occur, then the conditions upon which the prior inactivity [of the state in stasis] were necessitated must have changed. But if those conditions were unmoved prior to moving, or unchanged prior to changing, then they must have begun to move or change as a result of those very conditions which necessitated stasis - a contradiction in terms - or as a result of an external force or mover. But the same reasoning applies to the external force or mover. Either that moved as a result of the conditions upon which its prior inactivity were necessitated, and in that case, the original problem surfaces, or it must have begun to move or change as a result of another external force or mover, ad infinitum. So, change then must either be eternal, à la an infinite regress of change, i.e. there has never been a state which was not preceded by another, or change does not exist. But 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. Again, this is absurd. And if we accept that change exists, this is the bullet we must bite when it comes to the question of origins: Either the universe (or multiverse) is eternal, and there is an infinite amount of past time, or the beginning - the something for which we ask ourselves "Why?"- arose from nothing, and there is no time preceding the first cause - the first cause being neither temporal nor eternal, but self-actualization from non-existent potentiality. THIS IS ABSURD. Of course, positing God as an uncaused cause does not allow one to escape the paradox for the reasons suggested in blue. Three options: No change exists, there is an infinite regress of past change, or change spontaneously arose from nothing. With respect to the latter two choices, the same dilemma, in a slightly different context (where change is substituted for cause) that faces the macrocosm (the universe) confronts the microcosm (man) when it comes to the issue of free will. That, however, is a different topic. This, I contend, is the extremis of rationality: it refutes itself.

There must be more than one paragraph but I'll be damned if I can sort them out.

I think there should be a law/requirement that posts of over five lines should be re-written so that there be at least two paragraphs.

When I see a long "paragraph" like this one I just skip to the follow up posts to find out what the heck the OP? is up to.

[Neo-Scholastic]

He used colors to distinguish concepts. I found in clever. He can refer back to 'text in blue' and that's more clear than saying paragraph two.

[Neo-Scholastic]

The OP's puzzle would not have bothered the Schoolmen. They made the distinction between what someone can imagine versus what one can conceive. For example, people cannot imagine a set of 3,543,672 objects; however, people can conceive such a set. Likewise, no one can imagine a truly formless substance or a substance completely devoid of form. And yet it is possible to consider each in concept. I say Man's rationality is not limited by his imagination.