Infinite past... with a beginning?

I wrote:

Yazata said:
Certainly each time interval, no matter how small, would still be infinitely divisible and contain an infinite number of pointlike instants, assuming that we model our concept of a temporal interval with the real number line.
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Speakpigeon complains:

Speakpigeon said:
That's not what I am talking about.
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It seems to have been what you were implicitly assuming when you wrote this:

Speakpigeon said:
Last example: think of an infinite series S starting from 0 and with a limit, for example -2000: S = {-1000/1; -1000/1 - 1000/2; -1000/1 - 1000/2; -1000/4; etc.}. It has an infinite number of elements so it is infinite. And there is no element in the series inferior to the limit.
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Speakpigeon said:
Some people seem to view the notion of an infinite past with a beginning as impossible. Anyone can argue this impossibility properly?
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JamesR did precisely that in post #2. At least he argued in such a way that I agree with his argument.

Of course, if 'arguing properly' means producing an an argument that Speakpigeon is willing to agree with, then it would seem to be an impossible task.
 
Sarkus said:
Eternity has no endpoint.
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I would prefer not to use the word 'eternity' because it's ambiguous between (1) infinite duration, and (2) outside time entirely. So I prefer 'an infinite or unbounded temporal interval' or something like that.

An infinite past with a beginning, however, has two end points: "now" at one end and "the beginning" at the other.
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Yes, that's my primary objection to Speakpigeon's assertion. We have a bounded temporal interval with the Beginning (the Big Bang, lets say) at one end, and 'Now' at the other. In the case of our universe, that's something like 15 billion years, I guess. Not infinite at all.

A series with closed ends is finite, not infinite. Thus any past with a beginning is finite.
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I can imagine a line with one fixed end extending in an unbounded infinite manner. (The positive integers.) Time may or may not extend infinitely into the future subsequent to its origin at the Big Bang. So we can still have an infinite temporal interval with one end point. But not two, unless we introduce some infinite divisibility idea or something like that.
 
Yazata said:
I would prefer not to use the word 'eternity' because it's ambiguous between (1) infinite duration, and (2) outside time entirely. So I prefer 'an infinite or unbounded temporal interval' or something like that.
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Hmmm, I'd never have considered notion 2. For that I'd use "atemporal". But "eternity" only has, for me, the idea of the passing of time without end. But your alternative works for "eternity".
I can imagine a line with one fixed end extending in an unbounded infinite manner. (The positive integers.) Time may or may not extend infinitely into the future subsequent to its origin at the Big Bang. So we can still have an infinite temporal interval with one end point. But not two, unless we introduce some infinite divisibility idea or something like that.
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He has already introduced that (post #13) and I rejected it for being an unsatisfactory sojourn into semantic gamesmanship. Such a notion is not of an infinite past but of a finite past, albeit one that is then infinitely divisible. They are sufficiently different notions, and in my view it was, and would be, dishonest to try to reframe the question, or to try to answer the question, in that direction.
 
Sarkus said:
Hmmm, I'd never have considered notion 2. For that I'd use "atemporal".
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I've been thinking too much about theology, I guess. That's where the 'atemporal' usage is most common these days. I think that it comes from the ancient Platonic tradition, the kind of existence that the Platonic forms (arguably) have. Numbers, mathematical relationships, the laws of physics, and stuff like that.

He has already introduced that (post #13) and I rejected it for being an unsatisfactory sojourn into semantic gamesmanship. Such a notion is not of an infinite past but of a finite past
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Yes, I agree. The idea of the universe's time-line having one end-point (the Beginning, the Big Bang or whatever) but extending without limit into the future, does deliver an infinite time-line. (I guess that mathematically speaking, that would be a ray.) But it doesn't produce an infinite past, since if we arbitrarily select any point on the time-line to be 'Now', we have just selected the second end point for our 'past' time interval and created a line-segment.

The mathematics of infinity may or may not allow us to pick a 'now' that lies an infinite temporal distance from the Origin, but the mathematics of infinity is well above my pay-grade. The idea of an infinitely long line segment doesn't seem all that intuitively plausible though. However mind-bogglingly large we want to make our temporal interval, specifying a second end-point seems to me to render it finite.
 
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Yazata said:
Yes, that's my primary objection to Speakpigeon's assertion. We have a bounded temporal interval with the Beginning (the Big Bang, lets say) at one end, and 'Now' at the other. In the case of our universe, that's something like 15 billion years, I guess. Not infinite at all.
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How a finite period of time with a beginning could possibly be an objection to my notion of an infinite past with a beginning?!
If that's your "primary objection" you don't have any objection.
Yazata said:
So we can still have an infinite temporal interval with one end point. But not two, unless we introduce some infinite divisibility idea or something like that.
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I would have thought infinity implies infinitely divisible. But you are confusing global divisibility, that of the infinity itself or some part of it, with local divisibility, as is assumed for any finite interval on the Real line. I used the case of an interval on the Real line as an example of how an infinity can be bounded to falsify your claim to the contrary. And then you pile up the confusion by reducing my claim to this one example. No. The case of an interval on the Real line is definitely not what I am talking about. There are in effect an infinite number of possible ways that the past could be both infinite and have a beginning. Maybe an infinite past with two beginnings? Or two infinite pasts with one beginning. Or an infinity of pasts all with the same present but each with an infinity of beginnings.
All logical possibilities
EB
 
Yazata said:
JamesR did precisely that in post #2. At least he argued in such a way that I agree with his argument.
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First, I replied to his objection:
Yeah, I object to No. 2.
First, I agree that for many people an infinite past means No. 2.
But it does not necessarily.
Not necessarily because there is no dictionary definition of the expression "infinite past". So, we have to work from the definition of "infinite".
Here are a few...
infinite
limitless or endless in space, extent, or size; impossible to measure or calculate.
extending indefinitely : endless
without limits; extremely large or great
unlimited or unmeasurable in extent of space, duration of time, etc.
Having no boundaries or limits; impossible to measure or calculate.
Infinite is defined as endless or limitless.
having no limits or boundaries in time or space or extent or magnitude​
These are only examples but they give a good idea I think.
And there I think it is apparent that the notion of infinity is a bit larger than for each x there is a greater x.​

Second, I also replied to your own assertion that each of these definitions contradicted the concept of an infinite past with a beginning.
And now, all you do is just ignore my last reply and assert that James's counterargument convincing to you.
Whoa.
You have a problem, Sir.
And then we don't have much to debate until you solve your problem.
EB
 
Speakpigeon said:
How a finite period of time with a beginning could possibly be an objection to my notion of an infinite past with a beginning?!
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He is saying that we can stipulate that a period of time has a beginning (and thus bound at one end) but that if it is also bound at the other (by Now) then it is a finite period of time, and used our universe as an example of that.
If that's your "primary objection" you don't have any objection.
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It is, and it is one you have yet to overcome.
I would have thought infinity implies infinitely divisible.
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Implies, sure, but so does "finite". Just because two concepts share a property doesn't mean that you can argue one as if it is the other.
But you are confusing global divisibility, that of the infinity itself or some part of it, with local divisibility, as is assumed for any finite interval on the Real line. I used the case of an interval on the Real line as an example of how an infinity can be bounded to falsify your claim to the contrary.
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And this was debunked as semantics given that we are talking about an infinite past and not some finite past that can be infinitely divided. Or do you really think there is an infinite distance between 0 and 1cm?
No, you don't, and as such all you are doing is semantic gymnastics to try and squirm out of a position you don't want to admit that you foolishly took.
And then you pile up the confusion by reducing my claim to this one example. No. The case of an interval on the Real line is definitely not what I am talking about. There are in effect an infinite number of possible ways that the past could be both infinite and have a beginning.
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And you have yet to show how any are possible.
Maybe an infinite past with two beginnings? Or two infinite pasts with one beginning. Or an infinity of pasts all with the same present but each with an infinity of beginnings.
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Throwing words around doesn't turn them into a coherent whole.
All logical possibilities
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So you have asserted with nothing but hot air and bravado.
 
Sarkus said:
He is saying that we can stipulate that a period of time has a beginning (and thus bound at one end) but that if it is also bound at the other (by Now) then it is a finite period of time, and used our universe as an example of that.
It is, and it is one you have yet to overcome.
Implies, sure, but so does "finite". Just because two concepts share a property doesn't mean that you can argue one as if it is the other.
And this was debunked as semantics given that we are talking about an infinite past and not some finite past that can be infinitely divided. Or do you really think there is an infinite distance between 0 and 1cm?
No, you don't, and as such all you are doing is semantic gymnastics to try and squirm out of a position you don't want to admit that you foolishly took.
And you have yet to show how any are possible.
Throwing words around doesn't turn them into a coherent whole.
So you have asserted with nothing but hot air and bravado.
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That's all rhetoric. You're welcome to offer an argument whenever you feel like it.
EB
 
Speakpigeon said:
That's all rhetoric. You're welcome to offer an argument whenever you feel like it.
EB
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If you can't see the content within my post then you're rather revealing your "la la la I can't hear you!" nature. But hey, if you don't want to deal with what has been written, and address the criticisms raised within, that's your prerogative.
 
Yet more rhetoric.
I looked at your post and considered whether you were articulating any argument or not.
So, the best I can infer from that is that you haven't a clue what's an argument or if you do then you can't be bothered.
Either way, you're just a waste of time and that tallies with my overall impression of you.
EB
 
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