# Infinite past... with a beginning?

#### Speakpigeon

Valued Senior Member
Some people seem to view the notion of an infinite past with a beginning as impossible. Anyone can argue this impossibility properly?
EB

Okay. I'll bite.

1. Assume there is an infinite past.
2. An infinite past means that for every instant in time there is an earlier instant.
3. Assume there is a beginning that happened at a particular instant in time.
4. A beginning is an instant in time prior to which there are no instants in time.
5. By (2), there must be an instant in time earlier than the time of the beginning.
7. Therefore, if all of the above is valid, then there can be no infinite past with a beginning, since the notion that both things can exist simultaneously leads to contradiction - a logical impossibility.

I think that's a "proper" argument.

The argument can be attacked on several fronts, of course. One way would be to claim that (3) is false, and that the "beginning" can be at an indetermine time rather than representing a fixed instant in time. Another is to object to one or both of the definitions in (2) and (4).

Okay. I'll bite.

1. Assume there is an infinite past.
2. An infinite past means that for every instant in time there is an earlier instant.
3. Assume there is a beginning that happened at a particular instant in time.
4. A beginning is an instant in time prior to which there are no instants in time.
5. By (2), there must be an instant in time earlier than the time of the beginning.
7. Therefore, if all of the above is valid, then there can be no infinite past with a beginning, since the notion that both things can exist simultaneously leads to contradiction - a logical impossibility.
I think that's a "proper" argument.
It is.
The argument can be attacked on several fronts, of course. One way would be to claim that (3) is false, and that the "beginning" can be at an indetermine time rather than representing a fixed instant in time. Another is to object to one or both of the definitions in (2) and (4).
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.
EB

Speakpigeon:

Do you have a counterargument to show that an infinite past with a beginning is possible?

Speakpigeon:
Do you have a counterargument to show that an infinite past with a beginning is possible?
Sure, but "possible" here can only mean logically possible since no one alive today could possibly be in a position to have a look to check whether there is an infinite past and whether there is a beginning to it.
Logical possibility in this case just means it's not contradicting any fact, i.e. something we know.
So, the argument that an infinite past with a beginning is logically possible is that there are no argument to the contrary.
I know you're not going to like that, but that's all there is to it.
Maybe something better. I would argue that if I can imagine it, then it's possible. It may sound like a foregone conclusion but no. Can you imagine a square circle? Me I can't. But I can imagine an infinite past with a beginning. So, according to this criterion, it's possible. There are sound reasons to accept this definition of possibility, though I'm not going to go into that here. Please also note that while I can imagine an infinite past with a beginning, I can't imagine the more conventional notion of an infinite past without a beginning, or indeed the conventional notion of an infinite future without an end. I also don't believe anyone could. So, here my criterion fails.
Still, for me, an infinite past with a beginning is a logical possibility. Is it for you as well?
EB

So, the argument that an infinite past with a beginning is logically possible is that there are no argument to the contrary.
I gave you an argument to the contrary in my first post to this thread. You haven't refuted it, as far as I can see.

Maybe something better. I would argue that if I can imagine it, then it's possible.
That is another topic for debate.

Can you imagine a square circle? Me I can't. But I can imagine an infinite past with a beginning.
Can you really? I don't think I can. Not according to the terms discussed in my argument above.

There are sound reasons to accept this definition of possibility, though I'm not going to go into that here.
Then it won't be much of a thread, probably. This seems to be a pattern with you: assert that there are sound reasons for X or Y, but then you fail to deliver any.

Please also note that while I can imagine an infinite past with a beginning, I can't imagine the more conventional notion of an infinite past without a beginning, or indeed the conventional notion of an infinite future without an end.
Why not? What's the obstacle, for you?

Still, for me, an infinite past with a beginning is a logical possibility. Is it for you as well?
At this stage of the discussion, I don't think so.

C C
I gave you an argument to the contrary in my first post to this thread. You haven't refuted it, as far as I can see.
I certainly did. I objected to your assumption that an infinite past means that for every instant in time there is an earlier instant.
I object to this assumption because there is no dictionary definition of the expression "infinite past".
So, all you can do is interpret the expression from the meaning of it component terms.
Here are a few examples of the definitions given for "infinite":
infinite
1. limitless or endless in space, extent, or size; impossible to measure or calculate.
2. extending indefinitely : endless
3. without limits; extremely large or great
4. unlimited or unmeasurable in extent of space, duration of time, etc.
5. Having no boundaries or limits; impossible to measure or calculate.
6. Infinite is defined as endless or limitless.
7. having no limits or boundaries in time or space or extent or magnitude
The point here is that none of these definitions imply that an infinite past has a beginning.
EB

The point here is that none of these definitions imply that an infinite past has a beginning.
So your purpose here is to argue semantics?

2. An infinite past means that for every instant in time there is an earlier instant.
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...

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.
Why does it matter that the notion of infinity is a bit larger? If the property "for all x there is a greater x" is necessary and sufficient for something to be infinite, irrespective of any other properties, then any argument that utilises this property surely speaks to the infinite?

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So your purpose here is to argue semantics?
???
Why does it matter that the notion of infinity is a bit larger? If the property "for all x there is a greater x" is necessary and sufficient for something to be infinite, irrespective of any other properties, then any argument that utilises this property surely speaks to the infinite?
But "for all x there is a greater x" is not necessary. And that's not even the case for any notion of infinite past. So, I'm not sure what's your point.
EB

How is it not necessary? Can you offer an example of the infinite where that does not hold true? If x is "moment in the past" then it would be that for all moments in the past there is a greater moment in the past - i.e. a moment further back in time. So please provide an example where the notion is not necessary for something to be considered infinite? You may well be correct, but I'd like you to actually support your assertion.

The idea of an infinite past with a beginning would seem to violate the etymology of the word 'infinite'. It derives from the Latin 'in-' (not) and 'finitus (finished or concluded). A beginning would be a conclusion to a timeline in the pastwards direction.

Addressing the definitions from post #7, all of them seem to me to agree with this and hence exclude the idea of an infinite past with a beginning.

"limitless or endless in space, extent, or size; impossible to measure or calculate." A beginning would be a limit and an end to the timeline in the pastward direction.

"extending indefinitely; endless without limits; extremely large or great" Again, a beginning in time would be an end and a limit to the timeline in the pastward direction.

"unlimited or unmeasurable in extent of space, duration of time, etc." A beginning would be a limit on duration.

"having no boundaries or limits; impossible to measure or calculate" The same.

"infinite is defined as endless or limitless having no limits or boundaries in time or space or extent or magnitude" The same.

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.

How is it not necessary? Can you offer an example of the infinite where that does not hold true? If x is "moment in the past" then it would be that for all moments in the past there is a greater moment in the past - i.e. a moment further back in time. So please provide an example where the notion is not necessary for something to be considered infinite? You may well be correct, but I'd like you to actually support your assertion.
0 is greater than -1. The past ends at the present time.
Still, if you don't like it, think of the set S of all the Real numbers inferior or equal to zero. It is has an infinite number of elements so it is infinite. The greatest element is zero. There is no "greater" x in S.
If you still don't like it, think of the set S of all Real numbers x the interval [0, 1]. It is has an infinite number of elements so it is infinite. It has both a beginning and end. And 1 is an element of S with no greater element in S.
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.
You can also represent an infinite past with a beginning simply as a set of times in the interval of Real numbers [-1; 0].
My preferred representation is different. Think first of a beginning in the past. Then, independently, of the present time. Then, think of an infinite number of times in between. That's "the past". It's infinite. It has a beginning.
I'm not sure why this is so very hard to understand.
EB

The idea of an infinite past with a beginning would seem to violate the etymology of the word 'infinite'. It derives from the Latin 'in-' (not) and 'finitus (finished or concluded). A beginning would be a conclusion to a timeline in the pastwards direction.
I already agreed that the original notion of an infinite past was without a beginning. But most definitions don't specify "without a beginning".
In fact, it is the notion of infinite itself which has evolved. It was initially conceived in the same way as our ordinary notion of an infinite future, hence "infinite", without an end.
Today, mathematicians think of the infinite in all sorts of way, including infinite with boundaries, which was anyway already implicit in the interval of Real numbers [0, 1].
Addressing the definitions from post #7, all of them seem to me to agree with this and hence exclude the idea of an infinite past with a beginning.
No, they don't.
"limitless or endless in space, extent, or size; impossible to measure or calculate." A beginning would be a limit and an end to the timeline in the pastward direction.
Read again: "limitless or endless in space, extent, or size; impossible to measure or calculate."
Limitless in extent or size. Impossible to measure.
An infinite past with a beginning is limitless in size and extent. And it is impossible to measure.
"extending indefinitely; endless without limits; extremely large or great" Again, a beginning in time would be an end and a limit to the timeline in the pastward direction.
An infinite past with a beginning is "extending indefinitely".
"unlimited or unmeasurable in extent of space, duration of time, etc." A beginning would be a limit on duration.
An infinite past with a beginning is "unmeasurable in extent, duration of time".
"having no boundaries or limits; impossible to measure or calculate" The same.
Impossible to measure.
An infinite past with a beginning has a number of points in time which is infinite, so it is an infinite past.
"infinite is defined as endless or limitless having no limits or boundaries in time or space or extent or magnitude" The same.
In extent.
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.
That's not what I am talking about.
EB

0 is greater than -1. The past ends at the present time.
You are being deliberately disingenuous, given that you are not stupid enough to equate "greater the" simply with a movement along the positive number line toward the more positive. E.g. a greater negative number than -1 is -2. You know this, you understand this, but due to the weakness of your chosen position you now opt to be disingenuous.
Fair enough. And you questioned me as to whether or not you were simply here to argue semantics. Heck, next you'll be questioning the meaning of "is".
Still, if you don't like it, think of the set S of all the Real numbers inferior or equal to zero. It is has an infinite number of elements so it is infinite. The greatest element is zero. There is no "greater" x in S.
If you still don't like it, think of the set S of all Real numbers x the interval [0, 1]. It is has an infinite number of elements so it is infinite. It has both a beginning and end. And 1 is an element of S with no greater element in S.
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.
You can also represent an infinite past with a beginning simply as a set of times in the interval of Real numbers [-1; 0].
So you really are here to argue semantics until everyone gets bored of you. Fair enough. Consider me bored of you.
My preferred representation is different. Think first of a beginning in the past. Then, independently, of the present time. Then, think of an infinite number of times in between. That's "the past". It's infinite. It has a beginning.
I'm not sure why this is so very hard to understand.
What you are imagining is no more an infinite past than the gap between 0cm and 1cm is an infinite distance. Sure, you can argue semantics until you're blue in the face, if that is your intent. Meanwhile the grownups will be speaking, okay?

OK, but I still don't know what you think would be logically impossible about the idea of an infinite past with a beginning.
Appart from being inconceivable for you.
Nothing very new here, though.
EB

OK, but I still don't know what you think would be logically impossible about the idea of an infinite past with a beginning.
Appart from being inconceivable for you.
I do struggle to imagine the logically impossible, yes.

Let the beginning exist at t=0, and the current time t=X.
Now imagine the universe progressing through time, from t=0 to t=1, to t=2 etc.
For there to be an infinite past there must be an infinite amount of time between t=0 and t=X.
So the universe can never actually reach t=X, because no matter how many time intervals have progressed since t=0, there are always an infinite more to t=X.

But the current time is t=X.
Thus at least one of the premise must be wrong.
We know the current time is t=X (i.e. non-zero), so either the past is finite, or there is no beginning. You can't have both.
Logically impossible.

I do struggle to imagine the logically impossible, yes.
Let the beginning exist at t=0, and the current time t=X.
Now imagine the universe progressing through time, from t=0 to t=1, to t=2 etc.
I don't have to accept the assumption of "the universe progressing through time" and I don't have to assume time to be countable.
For there to be an infinite past there must be an infinite amount of time between t=0 and t=X.
That's the idea.
So the universe can never actually reach t=X, because no matter how many time intervals have progressed since t=0, there are always an infinite more to t=X.
But the current time is t=X.
Thus at least one of the premise must be wrong.
We know the current time is t=X (i.e. non-zero), so either the past is finite, or there is no beginning. You can't have both.
Logically impossible.
The premise that seems wrong to me in this instance is that we would know time as you implicitly specify it.
Thus, first, "the universe"?! Why do we have to have "the universe"? I accept to assume a number of things, but to call that "the universe" seems too much.
For example, we could have one universe at the beginning and an infinity of other universes spread at different times throughout the infinity of time. So, not one universe would need to start at the beginning of time and reach now.
The other premise that seems unacceptable to me is to assume that something, anything, would actually "progress" through time. We don't step into the same river twice and I certainly don't believe we know that anything literally progressing through time, not even ourselves.
So, my understanding here is not that the notion of an infinite past with a beginning would be contradictory with what we know about time but instead that it is contradictory with whatever you happen to believe about time.
For me, all we know about time is what we know about the past, and that is that, first, as we reminisce about the past, things then looked different from what they look now.
Second, I accept the assumption that what happens now is determined by what happened at some point in the past.
Anything else? I don't think.
Given that, I can still imagine an infinite past with a beginning, and maybe it looks somewhat like what you suggest yourself:
1. There was something at the beginning;
2. There is something now;
3. There was something at all times in between;
4. At each point in time except the beginning, the state of whatever existed then has been determined by the state of whatever existed before that time.
Isn't that good enough?
EB

OK, but I still don't know what you think would be logically impossible about the idea of an infinite past with a beginning.
Appart from being inconceivable for you.
Nothing very new here, though.
EB
I see no logical impediment to the concept of a specific beginning with an infinite future, or even an infinity of beginnings with finite futures before the new beginnings.

I don't have to accept the assumption of "the universe progressing through time" and I don't have to assume time to be countable.
Then you're not talking about time, and the notion of "infinite past" becomes meaningless. But if you really are here simply to try to redefine "is" to suit your needs, then I'll happily leave that to you and yourself.
The premise that seems wrong to me in this instance is that we would know time as you implicitly specify it.
"It depends on what the meaning of 'is' is" -- Bill Clinton.
Thus, first, "the universe"?! Why do we have to have "the universe"? I accept to assume a number of things, but to call that "the universe" seems too much.
"Universe" is really nothing more than a placeholder for the thing being referenced that is said to have a beginning. Call it whatever you want.
For example, we could have one universe at the beginning and an infinity of other universes spread at different times throughout the infinity of time. So, not one universe would need to start at the beginning of time and reach now.
Then you're talking about the multiverse, and as such that is what is deemed to have a beginning. The term "universe" that I offered is simply a placeholder for whatever it is you think has a beginning.
The other premise that seems unacceptable to me is to assume that something, anything, would actually "progress" through time. We don't step into the same river twice and I certainly don't believe we know that anything literally progressing through time, not even ourselves.
The passage of time is implied through the notion of "past". For something to be past it has to have happened (passage of time). To talk of "past" without that inherent implication is meaningless. So either you accept the passage of time, or you can't talk of an infinite past.
So, my understanding here is not that the notion of an infinite past with a beginning would be contradictory with what we know about time but instead that it is contradictory with whatever you happen to believe about time.
No, it is contradictory to what is implied about time within the word "past". Past implies the passage of time.
For me, all we know about time is what we know about the past, and that is that, first, as we reminisce about the past, things then looked different from what they look now.
And this rebuts the analysis... how, exactly?
Second, I accept the assumption that what happens now is determined by what happened at some point in the past.
Anything else? I don't think.
And this rebuts the analysis... how, exactly?
Given that, I can still imagine an infinite past with a beginning, and maybe it looks somewhat like what you suggest yourself:
1. There was something at the beginning;
2. There is something now;
3. There was something at all times in between;
4. At each point in time except the beginning, the state of whatever existed then has been determined by the state of whatever existed before that time.
Isn't that good enough?
No. To talk of the past implies the passage of time. This, per the analysis provided, leads to the conclusion of the logical impossibility of an infinite past with a beginning.

Or are we really going to have to define what "is" means?