No, it isn't sound, as Hegel pointed out in his criticism of Kant, one can select any arbitrary chunk, as it were, of infinity and progress from the assigned beginning to the assigned end.

What's really wrong with it is two fold. First of all an infinite universe implies that everything that is possible is actual, even contradictory things. Like an alien that exists that has destroyed an infinite amount of the universe, but there still being an infinite amount left to destroy.

Secondly, it assumes a linearity of time rather than relativity. Without there being some context, some movement, change, space then it makes no sense to talk about time, and certainly not in a linear overarching progressive fashion such as that.

Sample objections:

A more accurate conclusion (sequitur), 5,6, is that now does not have a specific (whole, positive) number.
And that would be the case if there were an infinite amount of prior moments.

You'll notice that items 1,2,3 refer to non-indexical moments (1st, 2nd, 3rd), whereas 5,6 is indexical (now).
This is masked a bit by item 4.
There are examples of indexical and non-indexical information being two classes of knowledge.

With an infinite past, the present, now, does not have any particular number, if you will.
Or, alternatively, any numbering is equally fine.
Item 5 a non sequitur.

Interesting argument, I like it. I'll stick around to see what the others have to say on this. However I suspect it is not solid. It seems to depend on the idea that time moves forward in one direction; an intuition that is theoretically refuted from deduction of scientific observation (I can't remember the specificities, perhaps someone like apo will).

Also, can it not be the case that all of time is already set out? It would go as follows:

1 -> 2 -> 3 -> 4 -> 1 -> ... -> infinite loops. Thus all moments of time are already set in stone, and we just keep looping, like a temporal mobius strip. There was no first cause, because the past, present, and future all exist simultaneously, independent of any sort of tense intra-worldly beings place on them, so there is no progress in the actual sense (only the phenomenal sense). So when we progress forward in time, we are actually just another wakened form of existing. The past self that thinks about the future five seconds ago still exists and is still thinking about the future. And the self existing right "now" will always be thinking of the past self. The feeling that we persist is wholly an illusion, then, but nevertheless an experience that will always be the case in this "moment", and all the other moments of experience. "You" are not "you" five seconds ago - they are separate things entirely, existing in a wholly different temporal (yet static) frame, in no way more or less existing than you are now.

Why a temporal mobius strip would be the way it is, I have no idea. It's just a funny idea I've been toying with.

A better argument is that infinity is paradoxical which is why nobody has ever managed to prove it actually exists. Quantum mechanics can crush Zeno's paradoxes into indeterminate mush and does so by everything remaining both indivisible and infinitely divisible allowing the law of identity to go completely down the nearest convenient rabbit hole or toilet of your personal preference. As a result everything should turn out to be infinitely divisible and indivisible with electrons recently providing the first example. Their particle-like aspect is indivisible and fundamental, while their wave-like is infinity divisible. What a paradoxical infinity should also display is four fold supersymmetry in everything and, I believe, a self-organizing systems logic. The recent proof of the Monstrous Moonshine Conjecture means it is possible to prove that for all practical purposes infinity might as well exist.

It seems to depend on the idea that time moves forward in one direction; an intuition that is theoretically refuted from deduction of scientific observation (I can't remember the specificities, perhaps someone like apo will). — darthbarracuda

You are right the argument would be suspect simply because it depends on a particular notion of time. And while modern science might not be able to offer a concrete "better model of time" right at the moment, it does have plenty of evidence to doubt the kind of simplicities the argument assumes.

Why a temporal mobius strip would be the way it is, I have no idea. It's just a funny idea I've been toying with. — darthbarracuda

But the problem here is that you have just destroyed causality, and causality is something we would expect to be able to extract from "a better model of time". Causality is what we observe in the world - it is why we believe it to be "time-like" - and so at the very least, an arrow of time ought to be the emergent feature of any good model of time.

That was the problem of Newtonian time, and the reason for recent thermal models. Newtonian time could not build in a direction. As a result you can get insane metaphysical notions like "the block universe", or "eternal recurrence".

An odd argument I came across recently: — jorndoe

A modern version of this argument is used to show the Big Bang could never have happened. If eternal Time exists (in big-T Newtonian dimensional fashion), then there would have had to have been an infinite amount of time elapsing before - suddenly, in a bright flash - our Universe got created. So therefore never enough time could pass to arrive at that point.

A better answer is that the Big Bang was the start of time, as well as space. So we can't think of the pre-Bang as a temporal dimension - except in some far simpler metaphysical sense yet to be articulated scientifically.

What it means is infinity is a metaphorical concept that has no clear identity outside of specific contexts which is the kind of thing that quantum mechanics can establish statistically. The Monstrous Moonshine Conjecture will change everything within the next few decades and show just how infinity actually applies observably to the world around us by establishing that some things, for example, are at least 26 dimensional.

That's the kind of "dancing wu li master" nonsense that gives serious systems science such a bad name.

That's the kind of "dancing wu li master" nonsense that gives serious systems science such a bad name. — apokrisis

LOL, the theory of everything is coming and the world will never be the same again because mother nature's sense of humor is the only rival to her beauty. The problem is modern western science has focused on her beauty to the exclusion of humor which is why Max Planck begged his colleges to explain the joke.

No, it isn't sound, as Hegel pointed out in his criticism of Kant, one can select any arbitrary chunk, as it were, of infinity and progress from the assigned beginning to the assigned end. — Wosret

I don't see how that solves anything with respect to the argument presented in the first post of this thread.

All one would have to do to counter that counter is to change "momemt" to "chunk":

1. if the universe was temporally infinite, then there would be no 1st chunk
2. if there was no 1st chunk, then there was no 2nd chunk,

etc.

Its more argument for argument's sake when the evidence of quantum mechanics says there is no way any length of time can be smaller than 10^-27s. You guys might as well be debating how many angels can dance on the head of a pin for all the respect you show for evidence.

The problem is modern western science has focused on her beauty to the exclusion of humor — wuliheron

So beauty = ideas with mathematical precision, and humour = measurement uncertainty? Where then is there a problem if science has mathematically precise models of measurement uncertainty?

Like the 1960s Batman, the argument is so bad that it's good. Here are some bad/good (nonsensical) things about it that I love:

Line 4 is note even a proposition, as it lacks a verb.

The only justification offered for line 5 is 'then'. Can I apply the same reasoning to the proposition 'You must give me all your money' by putting 'then' in front of it?

The most interesting one though, to me, is that proposition 1 is also insupportable, even though most people would usually accept it. If we map each instant in time to an ordinal that denotes how many years ago it was, we can hypothesise that the collection of all non-fractional instants in time might map to the set of all finite ordinals together with the first infinite ordinal ω. Then the instant of time that maps to ω can be thought of as the first instant of time, even though the past is infinite in this model.

The key point though, is that these days arguments of the impossibility of an infinite past are only made by people that do not understand mathematics well.

Yes, most of the essential equations in physics today can fit on a t-shirt and display what physicists like to call elegant simplicity. Einstein compared Relativity to a Jewel for its symmetry, while Indeterminacy expresses asymmetry because it can be considered paradoxically both symmetrical and asymmetrical. In general, you could say western thinking focuses on beauty to the exclusion of humor with the result that Asian languages have jokes that go right over our heads and use more of their brains than our languages do. We think more mechanically, while they think metaphorically and mechanical perspectives are better for beauty among other things. But it means for science to take the next leap it will have to acquire a better sense of humor that is compatible with all that beauty.

Next generation computers will spit out jokes routinely that go over everyone's heads and the US federal government has finally admitted they have classified a few jokes as "Vital to the National Defense." It requires mathematics that are four times as complex and Contextual philosophies such as the one I am writing. You could say the rise of civilization has so far depended upon digital approaches which are better for error correction and accuracy, but now we are beginning to master analog logic.

But the problem here is that you have just destroyed causality, and causality is something we would expect to be able to extract from "a better model of time". Causality is what we observe in the world - it is why we believe it to be "time-like" - and so at the very least, an arrow of time ought to be the emergent feature of any good model of time.

That was the problem of Newtonian time, and the reason for recent thermal models. Newtonian time could not build in a direction. As a result you can get insane metaphysical notions like "the block universe", or "eternal recurrence". — apokrisis

Right, again, it was just supposed to be a musing idea. In any case, though, the notion of causality has been attacked, many times. So this muse accordingly would destroy the illusory concepts of causality and persistence. Which does seem implausible, as our minds seem to pick up on these sorts of things.

There are some extrapolating arguments from evidence that the universe was not temporally infinite (e.g. Big Bang models, entropy, the Borde-Guth-Vilenkin theorem).
These may vary a bit on the no-boundary hypotheses.

I was mostly interested in the logical argument here.
If someone shows that anything but a definite earliest time is impossible, well, then that's the most rational scientific pursuit, for example.

Personally, I think there are better arguments by intuitive appeal (I can post some if anyone's interested).
Seems to me the argument isn't sound.

these days arguments of the impossibility of an infinite past are only made by people that do not understand mathematics well — andrewk

Yep, especially for logical arguments.

Here are some bad/good (nonsensical) things about it — andrewk

I apologize for any poor wording. :)

Let me try adding details, some of which go one way, others another:

1. if the universe was temporally infinite, then there was no 1st moment
2. if there was no 1st moment, but just some moment, then there was no 2nd moment
3. if there was no 2nd moment, but just some other moment, then there was no 3rd moment
4. ... and so on and so forth ...
5. if there was no 2nd last moment, then there would be no now
6. since now exists, we started out wrong, i.e. the universe is not temporally infinite

As before

• items 1,2,3 refer to non-indexical moments (1st, 2nd, 3rd), but 5 is indexical (2nd last, now), which is masked by 4
• 6 is a non sequitur because the argument only shows that, in case of an infinite past, now does not have a specific, definite number (1st, 2nd, 3rd, ..., now)

US federal government has finally admitted they have classified a few jokes as "Vital to the National Defense." — wuliheron

References please....

In any case, though, the notion of causality has been attacked, many times. — darthbarracuda

That's a little hand-wavy. Where do we have evidence that on the whole causality fails the locality principle?

Yes, we definitely also have good evidence that "at the quantum scale" causality breaks down in a particular fashion. But we rely on causality being pretty conventional at an emergent classical scale.

So this is why we would want an emergent model now. It is not a reason to just throw away classicality. That still "works".

1. if the universe was temporally infinite, then there would be no 1st moment — jorndoe

Time is continuous. To assume that there are moments in time is to contradict "time is continuous". Therefore either my assumption that time is continuous, or the posted argument's assumption that time consists of a succession of moments, is false. Or both are false, and time is neither.

A quick observation:

If we argue from Big Bang models, i.e. extrapolate to a definite earliest time, then other infinites just show up instead, infinite density and temperature.

Temperature may be a better label than time for the evolution of the universe

Perhaps time is the wrong marker.
Perhaps what we call time is merely a labeling convention, one that happens to correspond to something more fundamental.
The scale factor, which is related to the temperature of the universe, could be such a quantity.
In our standard solutions, the scale factor, and hence the temperature, is not a steady function of cosmic time.
Intervals marked by equal changes in the temperature will correspond to very different intervals of cosmic time.
In units of this temperature time, the elapsed interval, that is, the change in temperature, from recombination till the present is less than the elapsed change from the beginning to the end of the lepton epoch.
As an extreme example, if we push temperature time all the way to the big bang, the temperature goes to infinity when cosmic time goes to zero.
In temperature units, the big bang is in the infinite past!

In an open universe, the temperature drops to zero at infinite cosmic time, and temperature and cosmic time always travel in opposite directions.
In a closed universe, on the other hand, there is an infinite temperature time in the future, at some finite cosmic time.
A closed universe also has the property, not shared by the open or flat universe, of being finite in both cosmic time and in space.
In this case, the beginning and end of the universe are nothing special, just two events in the four-geometry.
Some cosmologists have argued for this picture on aesthetic grounds; but as we have seen, such a picture lacks observational support, and has no particular theoretical justification other than its pleasing symmetry.

If we are looking for clues to a physical basis for the flow of time, however, perhaps we are on the right track with temperature. — Foundations of Modern Cosmology by John F Hawley and Katherine A Holcomb

The no-boundary hypotheses do not have any of these, but are sometimes dismissed as counter-intuitive.

If we argue from Big Bang models, i.e. extrapolate to a definite earliest time, then other infinites just show up instead, infinite density and temperature. — jorndoe

I certainly agree with a thermal approach to time. But other infinities don't show up at the beginning. Instead, all things have the same Planckian scale.

So even temperature or energy density is not infinite at the Planck scale. It has a size - at least when measured against an extrapolated version of a Newtonian system of clocks and rulers with scales that go "all the way up" to zero (just like Spinal Tap's amps!).

time is continuous — Metaphysician Undercover

Maybe.
I don't think the argument intended zero-dimensional "moments", or a particular quantification, as such.
It was given to me in a much less formal format; it's also possible my rendition remains a bit hokey. :)

Indeed, it still works, but it might not be an accurate picture of reality. Hume tried to ground all metaphysics in experience. And Russell thought causality was the common man's myth, as did some of the logical positivists.

I'm not saying I agree with them. Causality isn't my best topic. But in any case, just because something works does not mean it actually is the case. A convenient explanation need not always be the correct explanation.

A convenient explanation need not always be the correct explanation. — darthbarracuda

But also if you advance a positive doubt here, it needs to be constrained by what appear to be the facts, dontcha think?

You seem to be claiming that causality fails in some generic sense. I ask where are the facts that suggest that?

You seem to be claiming that causality fails in some generic sense. I ask where are the facts that suggest that? — apokrisis

I am saying that what we experience is all we ever actually know, and that causality may or may not be needed in order to understand the world. I consider it to be likely that causality is indeed real (as is the outside world) but it's not straightforward either.

Huh? You are confusing an epistemological point with an ontological question. Hume ain't relevant here as this was about specific models, not the underlying possibility of modelling.

Again I wasn't making an ontological claim, just pointing out the fact that the the reality of causality is not altogether obvious or straightforward.

I think a better argument is that: all temporal events are finite, if time was infinite, everything would be finished already.

It's worse than that, time like space is a result of extension. Pondering the products of extension doesn't tell us anything about the nature of the origin of the extension. Chattering about notions like infinity in relation to extension, or what is beyond this extension(our world) is pie in the sky.

. . .(just like Spinal Tap's amps!) — apokrisis

:D