Can the definition of infinity disprove an infinite past?

[Rhea]

From a thread in "Existence of God," a poster named "Random Person" said,

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding prior to now.
Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive.

More description of what I believe is his proposed argument is in this post.

Asking this question in mathematics for his benefit:

What are the mathematical principles that make this argument true or untrue?

 

[steve_bank]

Sounds like another creationist argument. If you were talking about a mathematical Real number line it is infinitely dividable. Same with a theoretical clock. You could say now never exists. A moment is a human concept enbling us humans to communicate. The universe is in constant change, subjective moments and objective clocks are used to talk about observed change,

Time does not exist, change exists. If the universe had a beginning then a debate on causality ensues,

I'd say the answer is no.

 

[Wiploc]

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding prior to now.
Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive.

If the universe were ten minutes old, then ten minutes would have passed.

If the universe were a thousand trillion years old, then a thousand trillion years would have passed.

However old the universe is, that's how much time has passed.

But, if Random Person assumes that only a finite amount of time has passed, then we wouldn't have had time to get to infinity, so an infinite past would be impossible.

On the other time, if infinite time had passed, then a finite past would be impossible.

So, what I assume is going on is that Random Person assumes that only a finite time has passed, and his assumption is all that makes him think an infinite past is impossible.

---

Disclaimer: I have made a guess about what someone is thinking, which is always a risk. But in that part of the thread I read, he never came close to giving a reason for his position, which leaves us reliant entirely on guesses.

 

[bilby]

From a thread in "Existence of God," a poster named "Random Person" said,

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding prior to now.
Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive.

More description of what I believe is his proposed argument is in this post.

Asking this question in mathematics for his benefit:

What are the mathematical principles that make this argument true or untrue?

It's logically fallacious, because it assumes its conclusion.

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding have happened prior to now.

The past has happened. It's not 'still unfolding'.

Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive in a finite time. It would need an infinite amount of time.

The conclusion that this moment would never arrive depends upon the assumption that the past is too short to include an infinite number of minutes - which is the same as assuming that the past is finite. Assuming your conclusion is a logical fallacy.

One could express this mathematically, but there's no real need.

 

[fromderinside]

Why all this? Infinity is a construct, defined and all that. Reality is a conjecture imagined.

 

[Speakpigeon]

From a thread in "Existence of God," a poster named "Random Person" said,

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding prior to now.
Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive.

More description of what I believe is his proposed argument is in this post.

Asking this question in mathematics for his benefit:

What are the mathematical principles that make this argument true or untrue?

I believe myself that this is a very good and legitimate point. I don't buy it, but I sort of understand that people should feel aggrieved by the notion of an infinite past. So, there's no use dismissing this argument. We need to find the proper answer.

So, let's assume the past is infinite. Because it's more convenient for discussion, we can also assume there's a beginning to time. This bit may sound contradictory with the notion of an infinite past but that's not the case at all. We could assume there's no beginning but no beginning is even less intuitive than an infinite past. So, the argument above could be framed a bit more explicitly. Suppose we have a techno civilisation that developed after a finite interval from the beginning of time. Scientists there decide to start counting time using atomic clocks, setting the clocks so that the zero corresponds to the beginning of time, assuming they know broadly how much time has elapsed since the beginning of time. An infinite past means that we ourselves are assumed in this scenario to be alive after an infinite interval of time has elapsed after the beginning of time. So, if we could retrieve the clocks set up by this techno civilisation, and assuming they would still be working, we would have to expect that the clocks have run for an infinite amount of time before today. Suppose this civilisation was really ingenious and found a way to ensure that the clocks keep counting and somehow register every second of time since the beginning of time. Then what indication of time could the clock possibly show today? I guess it would have to be somehow that an infinity of second has elapsed since the beginning of time. But how is it even possible to display such an indication and keep counting in a meaningful way?

OK, that doesn't work and I think that's broadly the equivalent of the perspective Random Person has on the problem of an infinite past. If the past is infinite, how is it possible to start counting at or near the beginning of time and get a meaningful indication today even though an infinite amount of time would have elapsed. We could also imagine that the civilisation I assumed existed at some point near the beginning of time would have continued to exist and develop up until now. These people would have kept records of their past throughout but how could it be possible to register events throughout an infinitely long past? It would have to be an infinite amount of data. How do you even manage that?

Another way to simplify the scenario is to imagine somebody waking up at the beginning of time and in such a good health he would still be alive today, having lived already an infinitely long life. He certainly wouldn't be able to remember his own life, even a tiny part of it, like say just one event every million years, because after an infinite life he would have to remember an infinite number of such events and no brain could possibly do that.

Still, let's grant forgetfulness. The problem for Random Person, I guess, is when we try to imagine this "immortal" going through every moment of his life since the beginning of time. It's easy enough to imagine him doing it for a few minutes, a few hours, a few years, perhaps a few centuries. But even a few millions of years wouldn't be enough. We would need to imagine an infinity of moments of his life and we're unable to do that. We are finite beings so, although we can conceive of infinity, we cannot imagine it.

So I think the bottom line is that Random Person (and untermensche, of course) wants to be able to imagine going through an infinity of time to accept that such can exist. And unlike conceiving of going through an infinity of time, imagining going through an infinity of time would require an infinity of time, something we don't have. The argument I think is literally to imagine that you're setting a clock at zero at the beginning of time and you're asking people to imagine looking at the clock as it counts time, and this from the beginning of time to today, which would be an infinity of time. And we can't do that. We couldn't possibly do that.

So, I would say myself that some people may be suffering from some quirky cognitive preconception bias that stops them from accepting that conceiving of an infinity is legitimate and good enough in itself so that you don't need to think you'd have go you yourself through the infinitely long process of actually imagining every moment of you observing a clock from the beginning of time to today. So, it's a quirk. A frame of mind. A perspective. A different kind of rationality. Neanderthal-still-with-us sort of thing. And we should celebrate this rather than throw our shoes at them. They can't understand something. Let's not do the same thing. Let's try to understand them.

Because they have a point. We can't imagine this process. And we're also used to think in terms of a finite past. Our own lives and our own pasts are all finite. Any period of time we can imagine is finite. We can't imagine an infinite past.

Still, they probably accept the idea of an infinite future. Random Person possibly, and untermensche certainly. The difference is that there's no necessity to think the whole infinity of it. We just think in terms of starting from now and going on for ever without actually having to think the end of time itself. We usually even assume there's no end of time.

Clearly, we think in those terms just because we remember our past lives, most of it anyway, but couldn't possibly remember our future. And we're certainly not going to think in terms of our own dismissal from this Earth. We don't want to think in terms of a specific time when our lives would end. So we think of the future as time without end. That's our default concept of time because we know when we were born but we don't know when we're gonna die. That's just a quirk of our mind. A bias. We all, or nearly all, have it, I think. And apparently, some people don't and can't accept that "conceiving" should be good enough. Perhaps another quirk.

So, there's no convincing them. They can't, they're unable to conceive the idea most people can conceive without any apparent difficulty. Most people accept this idea. Some don't. Maybe it's the DNA that's different, or something else.

Still, I think we should recognise that we ourselves also can't do the "imagining" trick. We have to rely on "conception", abstract thinking, to get a result we accept as good enough and get at infinity. And so we should do well to remember that there's a whole school of thought that's behind this attitude, namely Constructivism, or at least some of it, which seems to ask us to actually imagine infinity, the whole of it, or find someway to construct it, if we are to accept it exists at all.

Maybe it all comes down to accept or not that we are finite beings. Let's also remember that all those people around here who seem to reject Rationalism as somehow in contradiction with their beloved Empiricism can only reject the concept of infinity since infinity is something we definitely could not possibly empirically verify that it exists. Not even that it could exist. So, here we must have fromderinside and a few others around here joining with untermenshe and Random person to reject the possibility of an infinite past.

OK, I'll come clean. I was trying to do an infinitely long post, just to set a record, but I won't make it. I will have done my best to prove infinity could exist. I can't. Point taken, then.
EB

 

[Random Person]

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding prior to now.
Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive.

If the universe were ten minutes old, then ten minutes would have passed.

If the universe were a thousand trillion years old, then a thousand trillion years would have passed.

However old the universe is, that's how much time has passed.

But, if Random Person assumes that only a finite amount of time has passed, then we wouldn't have had time to get to infinity, so an infinite past would be impossible.

On the other time, if infinite time had passed, then a finite past would be impossible.

So, what I assume is going on is that Random Person assumes that only a finite time has passed, and his assumption is all that makes him think an infinite past is impossible.

---

Disclaimer: I have made a guess about what someone is thinking, which is always a risk. But in that part of the thread I read, he never came close to giving a reason for his position, which leaves us reliant entirely on guesses.

The universe had a beginning according to known physics.

When you advance an eternal universe it comes with a problem that your going to have to explain.

A finite amount of time can pass. An infinite amount of time cannot pass.

 

[Random Person]

Sounds like another creationist argument. If you were talking about a mathematical Real number line it is infinitely dividable. Same with a theoretical clock. You could say now never exists. A moment is a human concept enbling us humans to communicate. The universe is in constant change, subjective moments and objective clocks are used to talk about observed change,

Time does not exist, change exists. If the universe had a beginning then a debate on causality ensues,

I'd say the answer is no.

I'm not making a creationist argument but oddly you are making an atheist argument. Arguing against any infinite past is neither.

Time = change. An infinite universe requires a lot of special pleading.

- - - Updated - - -

It's logically fallacious, because it assumes its conclusion.

If the universe was eternal, then this moment would never exist. An infinite number of moments would still be unfolding have happened prior to now.

The past has happened. It's not 'still unfolding'.

Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive in a finite time. It would need an infinite amount of time.

The conclusion that this moment would never arrive depends upon the assumption that the past is too short to include an infinite number of minutes - which is the same as assuming that the past is finite. Assuming your conclusion is a logical fallacy.

One could express this mathematically, but there's no real need.

The past would indeed still be unfolding if it was infinite.

 

[untermensche]

An infinite amount of time cannot pass.

This idea is a fire that ignites a lot of rage.

 

[PyramidHead]

The past would indeed still be unfolding if it was infinite.

That's an abuse of language. Anything that is "still" anything is happening right now, and the past is not happening right now. If the past were infinite, it would be the same thing as the set of negative numbers being infinite: there is no member of the set that does not have a prior member (i.e. no earliest moment). Every negative number is a finite distance away from zero, just as every point in the past is a finite distance away from now. That does not change if we stipulate infinitely many negative numbers or past moments.

In actuality, it is probably easier to simply adopt a B-series notion of time than to bother with these arguments. The sense that time flows and gradually unfolds is most likely an illusion of subjectivity with no real bearing on the actual nature of things. There are just arrays of coordinates located relative to one another along various axes we call dimensions, of which time is one of several we have so far discovered. A quirk of our consciousness is the post-hoc stitching together of successive points along the time dimension to impress upon us the perception of duration, the "passing" of seconds and hours. But from a higher dimensional perspective, all points are just points. From the perspective of each point, it seems as though it constitutes the whole of reality, but this sensation is not defensible anymore.

Copernicus and Galileo disabused us of a privileged "here", Einstein exposed the lie of a special "now". Personally, I feel that we are on the verge of performing the same surgical excision of the alienated "me". There are just moments of conscious experience, with no identity-enabling connection among them that can survive even the simplest thought experiments. Surely, the natural conclusion is that they are not happening to distinct subjects that must be both accounted for and matched up with physical substrates; that exercise was doomed from the start ever since Parfit. If they are happening to anything at all, they are happening to me, now, here--and that is true regardless of which brain is having the experience, and where it is located in spacetime. From a higher dimensional perspective, all experiences are my experiences. From the perspective of each experience, it seems as though it constitutes the whole of reality, but this sensation is not defensible anymore.

 

[Underseer]

In math, any finite quantity is described as an infinite number of infinitesimal quantities.

So according to his argument, finite quantities are also impossible because if we try to add up all the infinitesimal quantities to reach a finite number, we never reach it, therefore finite numbers are an impossibility, therefore finite numbers don't exist.

QEDuh.

 

[Random Person]

In math, any finite quantity is described as an infinite number of infinitesimal quantities.

So according to his argument, finite quantities are also impossible because if we try to add up all the infinitesimal quantities to reach a finite number, we never reach it, therefore finite numbers are an impossibility, therefore finite numbers don't exist.

QEDuh.

I've noticed people use QED when they don't even understand the argument they are making much less the one they are arguing against.

 

[Random Person]

The past would indeed still be unfolding if it was infinite.

That's an abuse of language. Anything that is "still" anything is happening right now, and the past is not happening right now. If the past were infinite, it would be the same thing as the set of negative numbers being infinite: there is no member of the set that does not have a prior member (i.e. no earliest moment). Every negative number is a finite distance away from zero, just as every point in the past is a finite distance away from now. That does not change if we stipulate infinitely many negative numbers or past moments.

In actuality, it is probably easier to simply adopt a B-series notion of time than to bother with these arguments. The sense that time flows and gradually unfolds is most likely an illusion of subjectivity with no real bearing on the actual nature of things. There are just arrays of coordinates located relative to one another along various axes we call dimensions, of which time is one of several we have so far discovered. A quirk of our consciousness is the post-hoc stitching together of successive points along the time dimension to impress upon us the perception of duration, the "passing" of seconds and hours. But from a higher dimensional perspective, all points are just points. From the perspective of each point, it seems as though it constitutes the whole of reality, but this sensation is not defensible anymore.

Copernicus and Galileo disabused us of a privileged "here", Einstein exposed the lie of a special "now". Personally, I feel that we are on the verge of performing the same surgical excision of the alienated "me". There are just moments of conscious experience, with no identity-enabling connection among them that can survive even the simplest thought experiments. Surely, the natural conclusion is that they are not happening to distinct subjects that must be both accounted for and matched up with physical substrates; that exercise was doomed from the start ever since Parfit. If they are happening to anything at all, they are happening to me, now, here--and that is true regardless of which brain is having the experience, and where it is located in spacetime. From a higher dimensional perspective, all experiences are my experiences. From the perspective of each experience, it seems as though it constitutes the whole of reality, but this sensation is not defensible anymore.

I'm going to stop you at your first sentence, Our language doesn't perfectly adapt to the idea of infinite time.

It's simple. "right now" can't happen if we must wait for an infinite amount of time to unfold first.

 

[PyramidHead]

In math, any finite quantity is described as an infinite number of infinitesimal quantities.

So according to his argument, finite quantities are also impossible because if we try to add up all the infinitesimal quantities to reach a finite number, we never reach it, therefore finite numbers are an impossibility, therefore finite numbers don't exist.

The objection I anticipate here is that people will say that numbers don't have to "pass" in order for the higher ones to be real, which illustrates the illusion I was talking about. The other option is just to say that finite numbers actually don't exist, which is pretty commonly heard among philosophy students entering their second semester. Finally, I'd expect someone to invoke the Planck time, and state that however many slices of time there are between A and B, it must be a finite number if there is such a thing as the smallest possible slice (but they would be mistaking the smallest physically possible slice for the smallest conceivably possible slice).

 

[PyramidHead]

The past would indeed still be unfolding if it was infinite.

That's an abuse of language. Anything that is "still" anything is happening right now, and the past is not happening right now. If the past were infinite, it would be the same thing as the set of negative numbers being infinite: there is no member of the set that does not have a prior member (i.e. no earliest moment). Every negative number is a finite distance away from zero, just as every point in the past is a finite distance away from now. That does not change if we stipulate infinitely many negative numbers or past moments.

In actuality, it is probably easier to simply adopt a B-series notion of time than to bother with these arguments. The sense that time flows and gradually unfolds is most likely an illusion of subjectivity with no real bearing on the actual nature of things. There are just arrays of coordinates located relative to one another along various axes we call dimensions, of which time is one of several we have so far discovered. A quirk of our consciousness is the post-hoc stitching together of successive points along the time dimension to impress upon us the perception of duration, the "passing" of seconds and hours. But from a higher dimensional perspective, all points are just points. From the perspective of each point, it seems as though it constitutes the whole of reality, but this sensation is not defensible anymore.

Copernicus and Galileo disabused us of a privileged "here", Einstein exposed the lie of a special "now". Personally, I feel that we are on the verge of performing the same surgical excision of the alienated "me". There are just moments of conscious experience, with no identity-enabling connection among them that can survive even the simplest thought experiments. Surely, the natural conclusion is that they are not happening to distinct subjects that must be both accounted for and matched up with physical substrates; that exercise was doomed from the start ever since Parfit. If they are happening to anything at all, they are happening to me, now, here--and that is true regardless of which brain is having the experience, and where it is located in spacetime. From a higher dimensional perspective, all experiences are my experiences. From the perspective of each experience, it seems as though it constitutes the whole of reality, but this sensation is not defensible anymore.

I'm going to stop you at your first sentence, Our language doesn't perfectly adapt to the idea of infinite time.

It's simple. "right now" can't happen if we must wait for an infinite amount of time to unfold first.

It's certainly simple, but not all simple things are true. The issue you are having seems to be that you insist your idea of time as an unfolding piece of fabric cannot possibly be due to a perceptual trick or an illusion of perspective, even as experiments have conclusively shown that "right now" does not denote anything of substance.

Actually, language can adapt to talking about time in a meta-sense pretty easily. Just as we would look at a 2-dimensional world such as the one depicted in Edwin A. Abbot's Flatland and say that all points in the world are of equal height (as the shapes only have length and width), we can come up with another word for the property that all points on the timeline possess in equal measure, relative to some higher dimension. It would relieve the strain of having to imagine a block of spacetime existing "now" with its entire history represented as a 4-dimensional object. So: just like all of the shapes on a flat piece of paper have the same height while having different lengths and widths, all points on the timeline of the universe can be said to exist "meta-now" even though not all of them exist now.

 

[steve_bank]

I'm not making a creationist argument but oddly you are making an atheist argument. Arguing against any infinite past is neither.

Time = change. An infinite universe requires a lot of special pleading.

- - - Updated - - -

It's logically fallacious, because it assumes its conclusion.


The past has happened. It's not 'still unfolding'.

Time happens chronologically. If an infinite number of minutes had to pass before this moment could occur, then this moment would never arrive in a finite time. It would need an infinite amount of time.

The conclusion that this moment would never arrive depends upon the assumption that the past is too short to include an infinite number of minutes - which is the same as assuming that the past is finite. Assuming your conclusion is a logical fallacy.

One could express this mathematically, but there's no real need.

The past would indeed still be unfolding if it was infinite.

Neither a theist nor an atheist be. Invoking and misusing infinities are a common creationist approach.

I was answering your question. 'An infinite amount of time' has no meaning. The universe is change, moments and seconds are subjective and objective human creations.

The argument fails.

 

[steve_bank]

Somebody is time tripping.

 

[Random Person]

I'm not making a creationist argument but oddly you are making an atheist argument. Arguing against any infinite past is neither.

Time = change. An infinite universe requires a lot of special pleading.

- - - Updated - - -




The past would indeed still be unfolding if it was infinite.

Neither a theist nor an atheist be. Invoking and misusing infinities are a common creationist approach.

I was answering your question. 'An infinite amount of time' has no meaning. The universe is change, moments and seconds are subjective and objective human creations.

The argument fails.

When then it fails for those proposing an eternal universe.

 

[Wiploc]

The universe had a beginning according to known physics.

I'm skeptical. But I'm not up to date on the subject, so I'm willing to be surprised if you want to defend that claim.

I know that when Asimov said that the universe began at the big bang, he then added a hedge, something like, "At least we can call that the beginning, since we don't know what happened before that." And I know that Hawking did a similar move in A Brief History of Time. And I've seen the same move elsewhere by other scientists.

On the internet--at least when Creationists are talking--sometimes the hedge is omitted.

Hawking used "imaginary time" (time measured in terms of the square root of minus one) to claim that the universe may be "finite but unbounded," neither begun nor infinitely old. Did he change his mind? Or has a scientific consensus repudiated his claim? Or do you have something you want to reveal, a compelling argument that will change the scientific consensus?

Some years ago, a creationist told me that my knowledge was out of date, that the current (as of that time) scientific consensus was that the big bang was the beginning. So I went on campus, and found a cosmologist, and put the question to him: Is it true that there exists a scientific consensus that the universe began at the big bang? The cosmologist said, "Nobody knows what happened before the big bang. Nobody knows what happened before the big bang. Nobody knows what happened before the big bang."

Bertrand Russell wrote that when the experts are agreed, the layman does well not to take the opposite position. And when the experts disagree, the layman does well not to hold any opinion at all. On this subject, I am definitely a layman.

If you are claiming that the experts are agreed, then I definitely want to know about that. And I want substantiation; I want you to explain why I should believe in this scientific consensus. Why do you believe in it?

Or if you are claiming to have an irrefutable argument, something so strong that the opinions of the experts cannot stand against it, then I'd like to hear about that too.

Or maybe you have a personal theory that is flavored with a little scientific or pseudo-scientific language. I'm even willing to listen to that.

But I'm not willing to just take your word for it without seeing your justification.

I therefore invite you to support your claim that "The universe had a beginning according to known physics."

When you advance an eternal universe it comes with a problem that your going to have to explain.

The choices that I'm aware of:

- A universe infinitely old and unbegun.
- A universe that began without cause.
- A finite but unbounded universe, whatever that means.

I can't explain any of them.

You are the one fielding a theory, so you are the one who needs to explain.

I haven't read the whole of the other thread, but my impression was that you were just going to keep repeating your claim, without ever trying to explain, support, defend, or justify it.

If you have justification for your claim, I'd like you to present it now.

A finite amount of time can pass. An infinite amount of time cannot pass.

A finite amount of time can pass in a finite amount of time.
An infinite amount of time can pass in an infinite amount of time.
A finite amount of time cannot pass in an infinite amount of time.
An infinite amount of time cannot pass in a finite amount of time.

If you reject an infinite past, you will be stuck with an uncaused beginning, which is one more thing you won't be able to explain, support, defend, or justify. (I'm not saying that it isn't true; I'm just saying that it doesn't make sense to me (no more than an infinite past makes sense) and, based on past experience, I feel justified in assuming that you won't offer support for the claim.)

 

[Speakpigeon]

In math, any finite quantity is described as an infinite number of infinitesimal quantities.

So according to his argument, finite quantities are also impossible because if we try to add up all the infinitesimal quantities to reach a finite number, we never reach it, therefore finite numbers are an impossibility, therefore finite numbers don't exist.

QEDuh.

Your conclusion that "according to his argument, finite quantities are also impossible" doesn't follow since you can have finite quantities without the "infinite number of infinitesimal quantities" assumed to make them up.

Still, I think you do have a point, which is that we seem to have an intuitive sense of a continuous interval as indeed being made up of an infinity of points (although not so much of "an infinite number of infinitesimal quantities"). And Zeno's Paradox notwithstanding, most of us think nothing of going from one end of any interval to the other end. So, apparently, we can accept the notion of going through an infinity of points. So, your "logical" argument here doesn't work but it seems that we don't have any problem with the idea of going through an infinity of things.
EB