An infinite past.

Originally posted by sonship
You made the same comment to me I think.

Yes, I did.

Now WHERE is the starting point that epi is assuming ?
The issue is NO STARTNG POINT in an imagined infinite past time universe.
So WHERE are you seeing a starting point which flaws the argument ?
Both you and epi claim that an infinite amount of time must pass in order to arrive at now. Epi, doesn't explain from when that time must pass (some hypothetical starting point) and if I recall correctly, neither of you give any actual reasoning as to why an infinite amount of time passing might be a problem. After all the suggestion is that time is infinite, so why can an infinite amount of time not pass?

Originally posted by sonship
What was the word you used concerning a post of mine ? "Poppycock?"

No that doesn't sound like a word I would use.

If you cannot explain to me WHERE epi assumed a point of start in his explaining the delimma of a infinite past existing universe, I might be tempted to think your complaint was a bit of "poppycock."
WHERE did epi assume a starting point such that his conclusion was an error ?
You are remarkably impatient. I was outside all day fixing cars.

Both you and epi claim that an infinite amount of time must pass in order to arrive at now.

That is right ... IF ... the universe has always existed.
Don't forget the qualifying condition.

Epi, doesn't explain from when that time must pass (some hypothetical starting point)

I do not see or agree that epi did not explain it. The explanation is FROM INFINITY of past time.

There IS NO POINT there is only infinity. That is NOT epi's problem. That is your problem. It seems that you are trying to make your difficulty the difficulty of the ones who use the argument.

FROM INFINITY PAST is the assumed infinity direction out of which this traversing of time comes.

and if I recall correctly, neither of you give any actual reasoning as to why an infinite amount of time passing might be a problem.

Huh? For a person who was given no reason (in my case) you sure offered a lot of counter reasons in response.

Up to this moment youR complaint makes no sense to me. Seriously.

After all the suggestion is that time is infinite, so why can an infinite amount of time not pass?

Huh? The "suggestion" is that time is infinite because that is the theory which is being examined. IF ... IF ... time extends infinitely in the past we have this problem of how could it be traversed to arrive at now?


In this problem we are SUPPOSED to assume that the universe had no beginning and that its time has infinitely been passing. That is the assumption that the theory demands.

Why are you blaming epi or me for making the assumption which the theory demands that we make ? ? ? ?

Originally posted by vistesd
I’m suggesting that for JS357’s example to hold, the time function [f(t)] is continuous to infinity, and the counter never reaches t=2, so the most that one can say is that “in the limit t approaches 2”; to actually reach 2 (for 2 to be a member of the set, as tw put it), the function has to become discontinuous. However, if that happens, then you will not ...[text shortened]... ll members of the infinite set of integers. (My math education really is impoverished. :'( )

LATE EDIT to my last post: I should have written that f(t) = 1+1/2+1/4+ . . ..

Originally posted by RJHinds
I suggest you just ignore the idea of other universes, because we don't even know how big our universe is and if there is room for more universes.

[b]The apostle Paul wrote, "Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; and the peace of God, which surpasses all understandi ...[text shortened]... hings."

(Philippians 4:6-8 NKJV)

HalleluYah !!! Praise the Lord! Holy! Holy! Holy![/b]

Sure, I'll follow the advice from someone imagination impaired. NOT. You have lost your sense of wonder of the real world and stars and universe a long time ago, having no need for such mundane mental baggage.

Good luck with your god.

Originally posted by sonhouse
Sure, I'll follow the advice from someone imagination impaired. NOT. You have lost your sense of wonder of the real world and stars and universe a long time ago, having no need for such mundane mental baggage.

Good luck with your god.

Thanks, I am certainly going to need it with all the sin I have committed. May God have mercy on both of us.

Originally posted by twhitehead
Yes, I did.

[b]Now WHERE is the starting point that epi is assuming ?
The issue is NO STARTNG POINT in an imagined infinite past time universe.
So WHERE are you seeing a starting point which flaws the argument ?
Both you and epi claim that an infinite amount of time must pass in order to arrive at now. Epi, doesn't explain from when that time ...[text shortened]... er all the suggestion is that time is infinite, so why can an infinite amount of time not pass?[/b]

All of what follows might best be taken as an extended question, even where posed in the form of an argument—

Why is all this logically different (if it is) from the real number line that is infinite in both directions from some arbitrary starting point, r=0? Using just the integers, . . .r=-3, r=-2, r=-1, r=0, r=1, r=2, r=3 . . . .

The analogous argument would then be that, if the real number line is infinite, then an infinite sequence of numbers would have to be “traversed” (in this case from either direction) to “arrive at” r=0; therefore the real number line must be finite (in at least one direction)—or else r=0, and by extension, any other arbitrarily selected point on the number line, is impossible. [But it has been proven that the set of real numbers, and hence the number line, is infinite.]

There seems to be a reductio ad absurdum here, something like—

1. If the real number line is infinite, the occurrence of any real number, r=x, is impossible;

2. The real number line is infinite; therefore

3. There are no real numbers.

—And there goes arithmetic!

[The absurdity might stand out a bit more if one were to put it in terms of the set, R, of all real numbers: that if R is infinite, then the existence any real number, r, (i.e., as a distinguishable element of the set) is impossible, therefore there are no real numbers (the set is empty).]

In the above, r is any real number (I just used the integers for simplicity). Now, let’s just substitute t for r, and let t stand for any moment of time. Then Epi’s argument would apply to any point on the timeline, not just t=0 (“the present” ). This seems tantamount to saying that if time is not finite in at least one direction (although we’re specifically talking about the past: all t: t<0) there can be no “moments of time” at all. This strikes me as subject to the same kind of reductio as above.*

I think Wolfgang is correct, in that to speak of countable elapsed time, one is implicitly speaking of elapsed time between two, equally arbitrary, chosen points. And no more is necessary. The present moment of time can be identified by reference to any number of past moments of time. A “first moment” seems no more necessary to “arrive at” the present (or any other identifiable) moment than a first real number is necessary to “arrive at” r=0.


However—there might be a nomological argument, based on the actual physics of time-dimensionality and infinity, as opposed to a logical argument (an argument of logical necessity). Is it logically necessary that time be linear?*

_______________________________________________________

* I wonder if, instead of thinking in terms of linear time (countable elapsed time), one can logically think in terms of the set, T, of all moments of time—as in the switch from the real number line to the set of all real numbers? I wonder how much of the argument depends upon the time dimension being actually linear? Again, that is a nomological specification, unless time is taken to be linear by definition. What do the physicists say?

EDIT: I suspect there might be some Wittgensteinian "bewitchment by language" in play here--with terms like "arrive at"--and I might be falling prey to that as well (though that is why I used the "___" around a number of terms).

Originally posted by vistesd


[b]However—there might be a nomological argument, based on the actual physics of time-dimensionality and infinity, as opposed to a logical argument (an argument of logical necessity). Is it logically necessary that time be linear?*[/b]

You might be interested in Brouwer's views ...

Here is a sample:
http://www.marxists.org/reference/subject/philosophy/works/ne/brouwer.htm

(Read it slowly with a Dutch accent).

Originally posted by vistesd
I’m suggesting that for JS357’s example to hold, the time function [f(t)] is continuous to infinity, )

It is not a continuous function of n or t.

t = f(n) = 2- 1/n

therefore 1/n = 2-t

therefore n = 1/(2-t)

therefore apart from t = 2 n is defined for all time and has values for t>2

Time will not stop just because the function is undefined at 2 seconds!

Originally posted by vistesd
LATE EDIT to my last post: I should have written that f(t) = 1+1/2+1/4+ . . ..

incorrect
t = f(n)

Originally posted by wolfgang59
It is not a continuous function of n or t.

t = f(n) = 2- 1/n

therefore 1/n = 2-t

therefore n = 1/(2-t)

therefore [b]apart from t = 2 n is defined for all time and has values for t>2

Time will not stop just because the function is undefined at 2 seconds![/b]

I'm going to thank you for the correction while I ponder further . . .

Originally posted by sonship

You are making the error of assuming a starting point

You made the same comment to me I think.

Now WHERE is the starting point that epi is assuming ?

The issue is NO STARTNG POINT in an imagined infinite past time universe.
So WHERE are you seeing a starting point which flaws the argument ?

This is what epi posted
In a past-infinite universe the present moment would never arrive since an infinite amount of time would have to elapse for it to do so

An infinite amount of time from when?
A starting point is implicit in the statement surely?
Between which 2 points is your "infinite amount of time"??

Originally posted by wolfgang59
incorrect
t = f(n)

I stand corrected in that t = f(n) = 2-1/n.


In any event, I never said that “time stops”; my point was that the apparent paradoxical outcome—“will have counted” an infinite number of positive integers “in two seconds”—depends on the fact that t=2 is never reached, but only approached asymptotically (taking t as the dependent variable). I have no imagining that Achilles would actually never catch the tortoise; only that he cannot catch the tortoise under the conditions specified--on the flip side, one cannot really count an infinite number of positive integers within an actual finite interval like 2 seconds.

Further corrections/explanations appreciated (clearly, I jumped in over my head).

Originally posted by vistesd
I stand corrected in that t = f(n) = 2-1/n.


I have no imagining that Achilles would actually never catch the tortoise; only that he cannot catch the tortoise under the conditions specified--on the flip side, one cannot really count an infinite number of positive integers within an actual finite interval like 2 seconds.

Further corrections/explanations appreciated (clearly, I jumped in over my head).

1. In Zeno's Paradox Achilles does catch the tortoise. (He must!!!)

2. One cannot count an infinite number in any amount of time.

I believe that you are confusing yourself by treating infinity as a number.

Originally posted by vistesd
I stand corrected in that t = f(n) = 2-1/n.


depends on the fact that t=2 is never reached, but only approached asymptotically

Of course t=2 is reached!!!
We are talking about a mathematical model (t = 2-1/n) which considers the amount of steps in an amount of time. Time will progress! We can calculate the number of steps for any amount of time except t=2.

That does not mean that t=2 is never reached! It means that n is undefined at t=2.