Can't speak about Kant. But the physics theory of eternal inflation posits an infinite future. And Penrose's conformal cyclic cosmology posits an endless succession of big bangs. So infinite time, past and/or future, is a part of speculative physics these days.

Maybe I don't quite understand Kant's argument as Popper presents it, but: isn't that as fallacious as arguing that the series of negative integers cannot be infinite because otherwise it could never reach -3? — Amalac

How do you imagine negative time for yourself? Kant spoke of time, which clearly has a beginning and is always positive. And the past for us is also a positive time. Relative to zero

:up:

The idea of an actually infinite past in the extensional sense of actual infinity is incompatible with the beloved premise of asymmetric causality running from past to future. In order to accept the premise of an actually infinite past, one must both theoretically reverse the direction of causality and somehow square that against physics and intuition, and in addition posit a finite future - a situation that is at least as problematic as the original picture. Or else one must entirely reject the notion of causality altogether - with the presumable consequence that having abandoned the doctrine of causality one must accept that one can no longer construct a theoretical or experimental argument for or against one's position.

In physics , the notion of actual temporal infinity is metaphysical in the literal sense of meta-physics, i.e it is a proposition that cannot be falsified, verified or even weakly evaluated through experiments.

However, there cannot be any empirical evidence on the basis of the observable universe to posit a past of any particular length. Therefore, the idea of a potentially infinite past is both perfectly consistent and the least assuming position to adopt. This position is adopted by presentists, who view the past and future as logical constructs that are reducible to sense-data. It's also compatible with quantum mechanics, due to the fact that QM has perpsectivalist retrocausal interpretations.

How do you imagine negative time for yourself? — SimpleUser

I suspend judgement as to the question whether time had an absolute beginning or not.

Kant spoke of time, which clearly has a beginning and is always positive. — SimpleUser

In this antinomy, Kant considered a universe which is infinite towards the past, which by definition has no beginning, and argued that it is logically inconsistent. Leaving aside the fact that later he argued that we cannot apply the notions of space and time to things that we do not experience (which I think is correct), i.e. the universe as a whole, my point is that the argument he used to prove that the universe cannot be infinite to the past doesn't appear valid regardless.

The idea of an actually infinite past in the extensional sense of actual infinity is incompatible with the beloved premise of asymmetric causality running from past to future. — sime

Could you elaborate a bit on how it's incompatible with asymmetric causality? I'm not very well acquainted to the idea.

In order to accept the premise of an actually infinite past, one must both theoretically reverse the direction of causality and somehow square that against physics and intuition — sime

If by “reversing the direction of causality” you mean that we must go back into the chain of causes and arrive at a first cause, why must we? Doesn't that already assume that the universe must be finite towards the past, and thus beg the question?

Whether or not it contradicts our intuition, that is no ground for rejecting physical models with an actual infinite past, since many physical discoveries also contradict our intuitions and are nonetheless true.

and in addition posit a finite future - a situation that is at least as problematic as the original picture. — sime

I mean, it's currently finite towards the future (up to the present moment).

Whether time has an absolute end at some point in the future I do not know, though physicists assure us that the universe very likely will come to freeze completely (such is one of the most plausible theories at present anyway).

I guess one could argue that even in such a completely static universe, time still passes, in which case the future time would be infinite.

But at any rate, why would an infinite future, in the sense I have described, be incompatible with an infinite past?

In physics , the notion of actual temporal infinity is metaphysical in the literal sense of meta-physics, i.e it is a proposition that cannot be falsified, verified or even weakly evaluated through experiments. — sime

Here I probably agree with you: I don't see how such a proposition could be falsified.

However, there cannot be any empirical evidence on the basis of the observable universe to posit a past of any particular length. Therefore, the idea of a potentially infinite past is both perfectly consistent and the least assuming position to adopt. — sime

Hmm, I'm kind of puzzled with regards to this idea of a universe with a “potentially infinite” past.

I mean, the past is either finite or it's infinite, right? What is meant by “potentially infinite” then?

isn't that as fallacious as arguing that the series of negative integers cannot be infinite because otherwise it could never reach -3? — Amalac

Negative integers have a necessary originating condition, so arriving at -3 is not impossible. The totality of the series of integers is infinite, but a particular member of the series is given by the mere assembly of count from whatever arbitrary origin. Now, the infinite divisibility of an aggregate quantity, represented by numbers, on the other hand, would make arriving at -3 impossible.

With respect to Kant reflected in Popper, the world exists, which makes explicit a necessary origin in time, therefore the time of the world cannot be an infinite series, even if time itself, is, irrespective of phenomena. And while space is infinitely divisible, the world is already a whole conceptual aggregate in itself which immediately defines the limits of its own finitely divisible space. The tacit understanding here is, if divided too far, in order to conform to the infinite divisibility of space in general, but regarding only that space the world inhabits, the world is no longer conceptually identical to its original, hence the incurrence of a “transcendental illusion”.....the very thing the antinomies make apparent.
———————

my point is that the argument he used to prove that the universe cannot be infinite to the past doesn't appear valid. — Amalac

Interesting. Where do he prove that, exactly? I don’t know of it, and couldn’t find a reference in the texts for it. As far as I understand the antinomy, he describes the confines of it, to certain determinations, of which there is the world, and there is nature...not Nature, nor reality in general, just the constituency of whatever is being considered at the moment....but only makes reference to the universe as a object in the refutation of its viability in any argument with respect to the world.

In fact, I don’t think he attempted to prove the universe cannot be infinite to the past, for to do so is to exchange a phenomenal object of sensibility, which is solely determined by the pure intuitions of space and time thus a possible experience, for an intellectual object of understanding, which cannot be so determined at all thus can never be an experience. If anything, he proved the universe cannot be argued to be infinite to the past, or infinite in any relation to time or space, under the same conditions from which the world is so argued.

But...maybe I missed something, so I’d welcome a little help.

So infinite time, past and/or future, is a part of speculative physics these days. — fishfry

Question: is it? Or do they think in terms of unbounded? Or even unending? Or, is the physicist's infinite a term of art that differs significantly from the mathematician's infinity?

Maybe someone in the forum can enlighten me about this. — Amalac

At the risk of.... The Kant is not too difficult to find and read. Why not try that?

I did, I thought the argument seemed fallacious, but figured maybe I was making some obvious mistake in the argument one of you in the forum could point out.

By asymmetric causality, I am referring to either the belief or definition of causality such that causes come before their effects. This is a physically problematic assumption due to the fact that the microphysical laws are temporally symmetric.

mean, the past is either finite or it's infinite, right? What is meant by “potentially infinite” then? — Amalac

The realist interpretation of potential infinity is that it is epistemic ignorance of the value of a bounded variable. For the realist an unobserved variable has a definite value irrespective of it's measurement or observation . Hence for the realist, the value of a variable is either actually infinite or it is finite, with no third alternative.

Likewise, the constructive interpretation of potential infinity also refers to a bounded variable whose value if measured, is necessarily finite. The difference is, it doesn't assert the existence of any value until as and when the value is constructed. In computer programming terms, a potentially infinite natural number in this sense refers to a natural number variable that is lazily evaluated . Only upon evaluation, does the variable possess a definite (and finite) value.

The logic of a potentially infinite past in this constructive sense is superficially demonstrated in the video games genre known as "roguelikes", where a player assumes the role of an adventurer who explores a randomly generated dungeon that is generated on the fly in response to the player's actions.

The existence of the games are effectively a demonstration of the coherence of retro-causation that is conditioned upon the players present choices. Of course, a realist will be quick to point out that the implementation of such games demonstrates nothing of the sort, being as it is an ordered sequence of instructions with a beginning and end. The deficiency of the realist interpretation of the game must therefore be argued by other means, such as by the Quantum Mechanical refutation of local causation + counterfactual definiteness + no conspiracy.

In the current context regarding the truth of past-contingent propositions , a constructive interpretation of history is that a past cause of an event does not exist over and above the construction of presently existing historical information. For example, if the present state of the universe is compatible with Jack the Ripper having any number of historical identities, then according to historical constructivism Jack the Ripper did not exist and does not exist until as and when his/her identity is constructable from historical information. And because historical evidence is rarely conclusive, the constructivist is forced to reject the assignment of a definite truth value to most, if not all, past-contingent propositions.

With respect to Kant reflected in Popper, the world exists, which makes explicit a necessary origin in time — Mww

Doesn't seem that explicit to me, how does that follow? (1. The world exists, 2.???, 3. Therefore, the world has an origin in time)

Where do he prove that, exactly? — Mww

I meant as in “apparently prove”, since by Kant's reasoning one can also “prove” that the universe cannot be finite towards the past.

So the conclusion of the antinomy is that there is no scientific sense in the very question: “is the universe finite or infinite towards the past?”, right?

But my point was that even his “apparent proof” seems invalid.

By asymmetric causality, I am referring to either the belief or definition of causality such that causes come before their effects. This is a physically problematic assumption due to the fact that the microphysical laws are temporally symmetric. — sime

:up:

The universe probably does have an origin, as it appears to have starting conditions, but that doesn't veto counterfactual worlds with infinite histories. The key, as you say, is getting past our everyday intuitions based on a universe that did have starting conditions, and in taking relativity seriously.

The realist interpretation of potential infinity is that it is epistemic ignorance of the value of a bounded variable. For the realist an unobserved variable has a definite value irrespective of it's measurement or observation . Hence for the realist, the value of a variable is either actually infinite or it is finite, with no third alternative. — sime

Ok, I'm fine with this.

The logic of a potentially infinite past in this constructive sense is superficially demonstrated in the video games genre known as "roguelikes", where a player assumes the role of an adventurer who explores a randomly generated dungeon that is generated on the fly in response to the player's actions. — sime

Hmm, ok.

So it's sort of like the universe, in the sense that it is constantly expanding. But supposing one could “catch up” to the expansion (in some possible world), would there be anything beyond the expansion, or would space somehow “end” there? (maybe I'm just very confused about this matter).

By asymmetric causality, I am referring to either the belief or definition of causality such that causes come before their effects. This is a physically problematic assumption due to the fact that the microphysical laws are temporally symmetric. — sime

I'll plead ignorance about this point, I don't know enough physics to comment on that.

But I guess my point is that the notion of “cause” may not be applicable to the total, as Russell pointed out in his famous debate with Copleston.

If we see the universe as a “set” or “collection/bundle of events”, then there may be no sense in asking what its cause is, just as there is no sense in asking what the cause of “the set of all ideas” is, in the same sense as we would ask what the cause of a rock, or of lightning, is.

But then again, Russell did also say that matter could be seen as a way of grouping events into bundles, so maybe there is a sense in asking for the cause of sets after all.

With respect to Kant reflected in Popper, the world exists, which makes explicit a necessary origin in time
— Mww

Doesn't seem that explicit to me, how does that follow? (1. The world exists, 2.???, 3. Therefore, the world has an origin in time) — Amalac

That’s fine; it doesn’t have to be explicit to you. I said with respect to Kant reflected in Popper, in which there is no 2.???. That the world exists and therefore has a necessary origin in time, is an analytic...tautological....truth of logic, insofar as its negation is impossible.

As a matter of dialectical interest, though, how does the statement not follow, from your point of view?

That the world exists and therefore has a necessary origin in time, is an analytic...tautological....truth of logic, insofar as its negation is impossible. — Mww

Seems to me like that would only be true if the universe were finite towards the past, which doesn’t seem tautologically true, since if it were, no philosophers or physicists would argue about it: they would all agree that the universe is finite towards the past.

Or perhaps I’m misunderstanding and you are talking about the other thesis, which holds that the universe did have a beginning, in which case yes: by definition it does, but only because Kant assumes for sake of argument that it does have an origin in time, to show how that assumption leads to a contradiction, as well as the antithesis which holds that it doesn’t have an origin in time.

That the world exists and therefore has a necessary origin in time, is an analytic...tautological....truth of logic, insofar as its negation is impossible.
— Mww

Seems to me like that would only be true if the universe were finite towards the past, which doesn’t seem tautologically true — Amalac

Evidence that the universe is finitely existent in the past is provided by the mathematically logical necessity of singularities. If singularities are real phenomena, then the existence of the universe follows the same logical criteria as is followed by the world. Thing is, experience informs us of the phenomenal reality of the world, but cannot inform us of the phenomenal reality of the universe or of singularities. Can’t use the criteria for what it is possible to know, in determinations for what is not.

I'll plead ignorance about this point, I don't know enough physics to comment on that.

But I guess my point is that the notion of “cause” may not be applicable to the total, as Russell pointed out in his famous debate with Copleston.

If we see the universe as a “set” or “collection/bundle of events”, then there may be no sense in asking what its cause is, just as there is no sense in asking what the cause of “the set of all ideas” is, in the same sense as we would ask what the cause of a rock, or of lightning, is.

But then again, Russell did also say that matter could also be seen as a way of grouping events into bundles, so maybe there is a sense in asking for the cause of sets after all. — Amalac

Right. As you point out, a notion of causality cannot play a role with respect to any data-set that is regarded as complete and self-contained. This creates a conflict within realism, for realists tend to simultaneously assert i) the transcendental reality of causality, ii) the transcendental existence of a completed universe whether finite or actually infinite, and iii) that counterfactual propositions have a definite truth value independent of actual measurements and observations.

By contrast, if the reality of an inter-subjectively complete universe is denied, then causality can not only retain it's useful meaning as referring to the potential outcomes of an intervention relative to an agent's perspective, but also it's ontological status to a limited extent, albeit not necessarily as a linear ordering of events from "past" to "future". Bayesian networks come to mind here.

Evidence that the universe is finitely existent in the past is provided by the mathematically logical necessity of singularities. — Mww

If you have to look for evidence in support of that proposition, then it's no longer a tautology. It may be logically necessary given the laws of physics that govern the actual universe, but these laws themselves are not logically necessary (as in: they could have been different, and could even change in the future).

As for singularities, if you are talking about gravitational singularities, then I guess you are refering to the Big Bang being one.

Well, I seem to remember that some scientist (was it Sean Carroll? Lawrence Krauss?) said that the Big Bang is a sort of placeholder for our ignorance, the limit to how far back we can know the cosmos.

There are some things that are not too clear to me: Is the Big Bang the cause of the observable universe? Or is it the cause of the universe in an absolute, all-encompassing sense (both the observable and the unobservable universe)?

Because I'm refering to the universe in the second, all-encompassing sense.

Now, I know some people say that time “appeared”, so to speak, with the Big Bang, but that seems problematic to me for many reasons, one of them being that it is not clear that time actually exists outside our minds, and if it doesn't exist outside our minds then there is no sense in saying that time appeared with the Big Bang, since in that case time “appeared” when the first subject who imposed time onto what he perceived appeared. Such was Kant's point of view, for instance.

I don't know how we could know if time exists outside of our minds or not.

Thing is, experience informs us of the phenomenal reality of the world, but cannot inform us of the phenomenal reality of the universe or of singularities. Can’t use the criteria for what it is possible to know, in determinations for what is not. — Mww

Maybe here is where I misunderstood you, I thought you were using the words “world” and “universe” as synonyms.

But I agree with Kant's conclusion: there is no sense in asking such questions about the universe as a whole.

For what it's worth, to think there's a problem with an infinite past in the sense such can't be for the simple reason that infinite anything can't be completed is to assume Aristotle's position that there are only potential infinities and no actual infinities.

It's quite clear why Aristotle thought that way; after all, the definition of infinity is such that the very notion of completion/an end is incompatible with it.

The only supposedly actual infinity I'm aware of is the set of natural numbers {1, 2, 3,...} but then it's an axiom [something arbitrarily assumed as true].

Suppose we do accept that there are actual infinites like in set theory vide infra. If so, an infinite past maybe one of the possibly many actual infinities out there.


Argument A

1. For any given point in time, one can always ask what preceded it temporally? [premise]

2. If for any given point in time, one can always ask what preceded it temporally? then, the past is infinite [premise]

3. The past is infinite [1, 2 MP]

Argument B

4. There is no actual infinity [premise??]

5. If there is no actual infinity then, false that the past is infinite [premise]

6. False that the past is infinite [4, 5 MP]

As you can see, line 6. False that the past is infinite, requires premise 4. There is no actual infinity [in bold]. The problem is the subargument 1 through 3 with the conclusion 3. The past is infinite, seems perfectly sound. If so, one option we have is to abandon the belief, albeit itself reasonable as per the definition of infinity, that 4. There is no actual infinity.

Put simply, an infinite past is an actual infinity [completed].

For what it's worth, to think there's a problem with an infinite past in the sense such can't be for the simple reason that infinite anything can't be completed is to assume Aristotle's position that there are only potential infinities and no actual infinities.

It's quite clear why Aristotle thought that way; after all, the definition of infinity is such that the very notion of completion/an end is incompatible with it.

The only supposedly actual infinity I'm aware of is the set of natural numbers {1, 2, 3,...} but then it's an axiom [something arbitrarily assumed as true]. — TheMadFool

What about the series of negative integers? It has no first term of course, but it ends in -1, so that it is “completed” in that sense. Why can't the timeline of the universe be like that (with -1 being the present, so to speak)?

If being “completed” means that one must be able to write down all of the elements of the series, then why should we accept that criterion as the one which determines whether a series of elements can “exist” or not?

What about the series of negative integers? It has no first term of course, but it ends in -1, so that it is “completed” in that sense. Why can't the timeline of the universe be like that (with -1 being the present, so to speak)?

If being “completed” means that one must be able to write down all of the elements of the series, then why should we accept that criterion as the one which determines whether a series of elements can “exist” or not? — Amalac

I'm afraid you misunderstood me or did I not get what you're saying?

The past is infinite and an actual infinity at that; after all, we're at some point in time (this now) that can be only if infinite time did pass [another way of saying completed/actual infinity].

I like what you said :point: "...if being "completed" means that one must be able to write down all the elements of the series..." I think you're on the right track.

Evidence that the universe is finitely existent in the past is provided by the mathematically logical necessity of singularities.
— Mww

If you have to look for evidence in support of that proposition, then it's no longer a tautology. — Amalac

I’m not supporting the proposition, but merely stating it. The solutions to the field equations support it, which are not subject/copula/predicate propositions, but mathematical formulations, and while not analytical, are nonetheless true. If otherwise, the entire human system for knowledge certainty is in serious jeopardy, regardless of its adaptability to changes in observational data.
—————-

It (mathematically logical necessity) may be logically necessary given the laws of physics that govern the actual universe, — Amalac

Laws don’t govern the universe; they are human constructs representing how the universe appears to govern itself. In that regard, I agree you are correct, in that they are only as certain as the observation data from which they are derived. Mathematical certainty is not predicated on the apparent operation of the universe, in that they must be certain under any conditions whatsoever, no matter what we discover about the universe. Mathematics is our creation; the world is not.
—————

I thought you were using the words “world” and “universe” as synonyms. — Amalac

Nope. Using the concepts....the words.... as you are.
—————

I don't know how we could know if time exists outside of our minds or not. — Amalac

Nor do I. Theoretically it cannot, but you know what they say about theories.

The past is infinite and an actual infinity at that; after all, we're at some point in time (this now) that can be only if infinite time did pass [another way of saying completed/actual infinity]. — TheMadFool

But when someone says an infinite amount of time “passes”, if they don't mean that it passes from some moment in time to some other moment in time (which clearly cannot be the case), then I do not understand what is meant by “passing”. In the case of a universe with an infinite past, the idea that time must “pass” from a beginning moment all the way to the present seems false, since by definition such a universe has no beginning moment:

The statement that the universe cannot be infinite towards the past because that would imply going through or traversing an infinite number of events to get to the present seems false to me, since it seems to assume that in traveling such a series of events one goes through or traverses from an initial moment to the present, while this infinite universe towards the past by definition has no initial moment.

If, on the contrary, the journey begins at some point in the past which is not an initial moment, it does not matter how much one goes back in the timeline, the events and time from that moment to the present will always be finite, and there is therefore no impossibility in a universe whose time is infinite to the past.

And it makes no sense to say "but the journey begins before the temporal events begin", because there is no point in time in which they begin according to this model (again, by definition). — Amalac

I like what you said :point: "...if being "completed" means that one must be able to write down all the elements of the series..." I think you're on the right track. — TheMadFool

If that's what you mean, that what's your response to this?:

If being “completed” means that one must be able to write down all of the elements of the series, then why should we accept that criterion as the one which determines whether a series of elements can “exist” or not? — Amalac

Meaning: Why is whether it is “enumerable” or not the way to determine if it's possible or not?

The solutions to the field equations support it, which are not subject/copula/predicate propositions, but mathematical formulations, and while not analytical, are nonetheless true. If otherwise, the entire human system for knowledge certainty is in serious jeopardy, regardless of its adaptability to changes in observational data. — Mww

Ok, but you said before that it was a tautology, which seems untrue: the universe is not by definition finite towards the past, which would be the case if you could deduce that from the definition of “universe” alone, there would be no need for empirical observation.

you said before that it was a tautology, which seems untrue — Amalac

I said that the world exists and therefore has a necessary origin in time, is a tautology, a analytic truth.

But when someone says an infinite amount of time “passes”, if they don't mean that it passes from some moment in time to some other moment in time (which clearly cannot be the case), then I do not understand what is meant by “passing”. In the case of a universe with an infinite past, the idea that time must “pass” from a beginning moment all the way to the present seems false, since by definition such a universe has no beginning moment — Amalac

Review my arguments below.

Argument A

1. It makes sense to ask about a time before any given moment in time

2. If it makes sense to ask about a time before any given moment in time then, the past is infinite

Ergo,

3. The past is infinite [1, 2 MP]

Argument B

4. We are in the present, the now

5. If we're in the present, the now and the past is infinite then, the infinite past (has passed) is an actual/completed infinity

6. We're in the present, the now and the past is infinite [3, 4 Conj]

Ergo,

7. The infinite past (has passed) is an actual/completed infinity

You're bothered by how if the past is infinite, time has no beginning and ergo, you contend that time couldn't possibly pass. This, if you really think about it, is just another way of expressing the idea that the past is finite. In other words, there has to be a beginning for time = the past is finite. Simply put, a petitio principii - you can't claim the past is finite because the past is finite.

As for the passage of time, we're here, in the now, right? Considering the past is infinite (see proof above) and we're here, in the now, time has passed.

If you are not using the words “world” and “universe” as synonyms, then what's the difference between the two?

I said that the world exists and therefore has a necessary origin in time, is a tautology, a analytic truth. — Mww

Right, but that would mean that we could deduce the proposition “The world has a necessary origin in time” without experience, merely by analysis of the concept “world”, right? I don't think that's the case, but maybe you could show me how that proposition is analytic.

world” and “universe" — Amalac

It appears this "world" or "universe" isn't a simulation after all. Infinite computing power is required for an infinite past. I don't know if I should laugh or cry.

Argument A

1. It makes sense to ask about a time before any given moment in time — TheMadFool

If there is no beginning in time, then yes.

2. If it makes sense to ask about a time before any given moment in time then, the past is infinite — TheMadFool

If 1 is true, then yes.

Ergo,

3. The past is infinite [1, 2 MP] — TheMadFool

That does follow if 1 and 2 are true.

Argument B

4. We are in the present, the now

5. If we're in the present, the now and the past is infinite then, the infinite past (has passed) is an actual/completed infinity — TheMadFool

If the past is infinite, then the infinite past is an actual/completed infinity, if by that one means merely that it is the case in reality. But that does not imply that an infinite amount of time has “passed” up to the present moment.

For I ask: From/since when to when did it pass? You can't say “From the beginning of the universe to the present day”, Because there is no “beginning of the universe” in this model.

And if you say, it passes from some moment in the past that wasn't the beginning up to the present moment, then a finite amount of time has passed, not an infinite amount, and that poses no problems.

You're bothered by how if the past is infinite, time has no beginning and ergo, you contend that time couldn't possibly pass. This, if you really think about it, is just another way of expressing the idea that the past is finite. — TheMadFool

No, did you read my OP? I'm trying to show that there is nothing logically inconsistent about a universe with an infinite past, against what Kant tried to “prove” with one of his theses.

I'm saying an infinite amount of time has not “elapsed”, but also that that doesn't contradict a universe with an infinite past.

In other words, there has to be a beginning for time = the past is finite. Simply put, a petitio principii - you can't claim the past is finite because the past is finite. — TheMadFool

No, what I'm rejecting is Kant's argument which states that the universe couldn't have been infinite towards the past because that would imply that an infinite amount of time would have elapsed up to to the present moment.

That one would be the one that begs the question, by assuming tacitly that the universe must have had a beginning in time: It assumes that such an infinite universe both has and doesn't have a beginning in time, which is just a way of creating a strawman of the person who holds that the universe is infinite towards the past.

As for the passage of time, we're here, in the now, right? Considering the past is infinite (see proof above) and we're here, in the now, time has passed. — TheMadFool

If you look at my previous posts again, you'll see that I don't have a problem with the idea of time passing, but with the idea that “if the universe has an infinite past then an infinite amount of time must have passed”.

So, if you are saying that, that's what I'm rejecting.

But if you insist: From/since when to when did it pass? It must have passed from some moment in time to some other moment in time, right?