:roll:

I take that as acquiescence by silence? LOL

Yes, but only from the standpoint that neither P nor its negation not-P can be truly predicated of the existential subject S during that lapse of time. S continues to exist, it just has a lower mode of being in the sense that it is not determinately P or not-P when it is in the real and continuous process of changing from one to the other. — aletheist

Not only that, but it doesn't make sense to ever speak of whether P can be predicated of S, in this case, because it doesn't make sense to say S is P is true at one time, then at a later time S is P is not true, because neither S is P nor S is not-P is true. Saying that S is P is no longer true is equivalent to saying S is not-P. Therefore, at that time after S is P was true we'd have to say S is not-P at that time. But what is being claimed is that S is neither P nor is not-P. Therefore it doesn't make sense to speak of S in terms of P, at any time, if at any time S is neither P nor not P

No, this indicates a misunderstanding. Recall that a fact as signified by a true proposition is only an abstract constituent part of reality; the existential subject S is always changing with respect to some of its qualities and relations, but not all of them. When "S is P" is true, it signifies a real prolonged state of things with respect to that individual existential subject and that general character or relation; likewise for "S is not-P." — aletheist

As explained above, it doesn't make sense to speak of a time when S is P is true, if at a later time S is P is neither true nor false. This would mean that S is P would cease being true at that time, yet we cannot say that S is not P at that time when S ceases to be P, which is incoherent. Therefore we must maintain the categorical separation. To say S is neither P nor not-P implies that it is a category mistake to say that P might be predicated of S.

Yes, "S is P" or "S is not-P" is indeed a sound way of describing the world in most cases, because they signify prolonged states of things that are realized at any instant that we arbitrarily designate within a lapse of time during which the existential subject S is not in an indefinitely gradual state of change from P to not-P, or vice-versa. In other words, it is only during certain events that the principle of excluded middle is false of the relevant proposition; between those events, it remains true. Again, any existential subject is always changing in some respects, but unchanging in others. — aletheist

It's incoherent to say that there is a subject S, and sometimes S is either P or not-P, but at other times S is neither P nor not-P. If S is either P or not-P at sometimes, then what is it about S which would make it suddenly be neither P nor not-P? If S can be either P or not-P, then it is no longer S, but something completely different than S which can be neither P nor not-P.

With that in mind, there is some leeway for marking two particular instants as the commencement and completion of an event-lapse. — aletheist

I don't see how the marking is anything other than completely arbitrary. We could choose any physical indication whatsoever to mark the beginning or end of a time period. The only thing not arbitrary would be that the beginning must be before the end. Care to explain how you think marking could be other than arbitrary?

That is why I define the present as not only the indefinite lapse of time between the past and the future, but also the indefinite lapse of time at which anything is present to the mind; again, in my view these are one and the same. — aletheist

If the present is an "indefinite lapse of time", then that length, or time period which comprises the present is completely arbitrary. The present might be a nanosecond or it might be a billion years. Each of these is "present to the human mind". What would make one of these more "the real present" than the other? That's what I mean when I say that when you have nothing other than "the human mind" to determine the "lapse of time" the determination is arbitrary. The human mind needs a principle, based in something real, by which to determine the lapse of time which comprises the present, in order that the determination of "the present" is other than arbitrary.

Yes, but two boundaries are necessary because events are constantly being realized at the present, which is why we directly perceive the flow of time and the motion of physical bodies. — aletheist

If there are boundaries within a thing, then the thing which has boundaries within it (time in this case), is not continuous. I don't see why you have so much trouble understanding this fact. I used to think that you simply denied this in order to support your metaphysical position, but now I think that you really believe that a continuous thing can have boundaries within it. Do you not recognize that a boundary is the end of one thing and the beginning of another, and therefore, necessarily, a discontinuity?

If the present were itself a single boundary--i.e., an instant--then whenever something changed, two incompatible states of things would be realized at that same instant, violating the principle of contradiction. — aletheist

This is not true. Under this assumption, at one moment S is P is true, and at the next moment, S is P is false. The "instant" acts as a boundary of separation between these two such that one is before and the other is after, and the law of non-contradiction is not violated. The problem, as Aristotle demonstrated is that this does not allow for the existence of "becoming", or "change", because "becoming" is a temporal concept which cannot occur at an instant. Furthermore, if we replace the instant between S is P and S is not-P, with something like S is O, at that intermediate moment to account for becoming, then we'd have to suppose something like S is N to account for the moment of change between S is P and S is O, and so on ad infinitum. So when we talk about "becoming", the activity which is change in the world, it makes no sense to use propositions like S is P, because we are talking about something which is categorically different from "being", which is the type of thing that S is P refers to.

Here's a thought. These arguments about the nature of time go on interminably without clarification, repeated over and over. Why not try a different approach:

Momentum, from physics, is defined as mass times velocity: momentum=mass x ds/dt.
Why not try to define "momentum" and "mass" and "distance" for the evolution of ongoing events, then define an increment of time by: dt=mass x ds/mom? :chin:

Don't ask me how. Someway define the process of multiplication and division in the equation.

Or return to formal logic and proceed.

What does "ds/dt" mean?

What does "ds/dt" mean?

Velocity, p=mv. But we don't need momentum and mass. Velocity = distance / time is sufficient. In either case I think the point is that there is no point of imagining any other concept of time but the one that fits this equation, and I don't see there is much room for interpretation.

Good thought! Any practical examples ?

Saying that S is P is no longer true is equivalent to saying S is not-P. — Metaphysician Undercover

Only when the principle of excluded middle is true. Again, it is false during an indefinitely gradual state of change, when S is in the process of becoming not-P after previously being P, or vice-versa.

Therefore it doesn't make sense to speak of S in terms of P, at any time, if at any time S is neither P nor not P — Metaphysician Undercover

This does not follow, since existential subjects undeniably have different qualities and relations at different determinations of time. If "S is P" is true at an earlier determination of time, and "S is not-P" is true at a later determination of time, and both propositions cannot be true at the same determination of time (principle of contradiction), then there must a determination of time in between at which neither is true.

To say S is neither P nor not-P implies that it is a category mistake to say that P might be predicated of S. — Metaphysician Undercover

This mixes up the modalities of actuality and possibility. To say that neither "S is P" nor "S is not-P" is true does not entail that "S may be P" is false.

If S is either P or not-P at some times, then what is it about S which would make it suddenly be neither P nor not-P? — Metaphysician Undercover

The fact that S is in the process of changing from being P to being not-P, or vice-versa. The only alternative is to claim that such negation is instantaneous, which requires S to be both P and not-P at the same determination of time, thus violating the principle of contradiction.

Care to explain how you think marking could be other than arbitrary? — Metaphysician Undercover

I already did--it is not completely arbitrary, given our purpose of distinguishing the lapses of time at which two incompatible prolonged states of things are realized by marking off a lapse of time between them, during which an indefinitely gradual state of change is realized. There is some leeway, since whatever is realized at any given instant is also realized at other instants beyond all multitude that are "near" it, within its immediate neighborhood or "whenabouts."

If the present is an "indefinite lapse of time", then that length, or time period which comprises the present is completely arbitrary. — Metaphysician Undercover

"Indefinite" is not synonymous with "arbitrary."

The present might be a nanosecond or it might be a billion years. Each of these is "present to the human mind". What would make one of these more "the real present" than the other? — Metaphysician Undercover

This is a valid point from a strictly mathematical standpoint, which comes into play as soon as we introduce measurement. According to Peirce, Josiah Royce suggests in The World and the Individual that the present is a "time-span" of two seconds for humans, and "points out that a consciousness for which the events of a millionth of a second should exceed the time-span and another consciousness for which the events of a million years should be present at a glance would both be so utterly unlike our own that we should not easily recognize them as conscious beings at all." However, Peirce himself takes a very different approach. On the one hand, the present cannot mathematically be an instant with zero duration:

The true conception is, that ideas which succeed one another during an interval of time, become present to the mind through the successive presence of the ideas which occupy the parts of that time. So that the ideas which are present in each of these parts are more immediately present, or rather less mediately present than those of the whole time. And this division may be carried to any extent. But you never reach an idea which is quite immediately present to the mind, and is not made present by the ideas which occupy the parts of the time that it occupies. Accordingly, it takes time for ideas to be present to the mind. They are present during a time. And they are present by means of the presence of the ideas which are in the parts of that time. Nothing is therefore present to the mind at an instant, but only during a time. The events of a day are less mediately present to the mind than the events of a year; the events of a second less mediately present than the events of a day. — Peirce, 1873

On the other hand, the present also cannot mathematically be a lapse with finite duration:

It has already been suggested by psychologists that consciousness necessarily embraces an interval of time. But if a finite time be meant, the opinion is not tenable. If the sensation that precedes the present by half a second were still immediately before me, then, on the same principle, the sensation preceding that would be immediately present, and so on ad infinitum. Now, since there is a time, say a year, at the end of which an idea is no longer ipso facto present, it follows that this is true of any finite interval, however short. — Peirce, 1892

Instead, the present must mathematically be a moment with infinitesimal duration:

But yet consciousness must essentially cover an interval of time; for if it did not, we could gain no knowledge of time, and not merely no veracious cognition of it, but no conception whatever. We are, therefore, forced to say that we are immediately conscious through an infinitesimal interval of time. — Peirce, 1892

The problem is that the mathematical term "infinitesimal" implies "too small to be measured," while our phenomenological experience is such that the present moment is not amenable to measurement at all. Measurement requires comparison with an established standard, and there is obviously nothing else with which we can compare our ongoing experience of the present, since it is sui generis. That is why it is better to characterize it as "indefinite"--a qualitative description, rather than a quantitative one.

If there are boundaries within a thing, then the thing which has boundaries within it (time in this case), is not continuous. I don't see why you have so much trouble understanding this fact. — Metaphysician Undercover

I understand it just fine, but it is not a fact, unless we define a boundary in this context as a discontinuity--which you evidently do, but I do not. Again, there are no real boundaries within a true continuum; we artificially introduce them for various purposes, including marking and measuring.

... I conceive that a Continuum has, IN ITSELF, no definite parts, although to endow it with definite parts of no matter what multitude, and even parts of lesser dimensionality down to absolute simplicity, it is only necessary that these should be marked off, and although even the operation of thought suffices to impart an approach to definiteness of parts of any multitude we please.*
*This indubitably proves that the possession of parts by a continuum is not a real character of it. For the real is that whose being one way or another does not depend upon how individual persons may imagine it to be. It shows, too, that Continuity is of a Rational nature. — Peirce, c. 1906

Specifically, real time has no boundaries (instants) or parts (lapses) except those that we create, and we can mark off as many such limits and corresponding portions as we want or need. For some purposes, those boundaries and parts are quite arbitrary; examples include designating one particular revolution of the earth around the sun as year 1, designating one particular rotation of the earth about its axis as January 1, dividing the lapse required for each rotation into 24 hours, designating one particular hour as 1:00, dividing each hour into 60 minutes, and dividing each minute into 60 seconds. For other purposes, there are constraints.

Under this assumption, at one moment S is P is true, and at the next moment, S is P is false. The "instant" acts as a boundary of separation between these two such that one is before and the other is after, and the law of non-contradiction is not violated. — Metaphysician Undercover

Under this assumption, which proposition is true at that instant? If only "S is P" is true or only "S is not-P" is true, then that instant is obviously not the boundary between the two moments; it is within one or the other. If both "S is P" and "S is not-P" must be true--as I maintain, since I understand a limit to be what two adjacent portions have in common; an immediate connection, rather than a discontinuity--then the principle of contradiction is violated. But you deny this; is it your view, then, that neither "S is P" nor "S is not-P" is true at that boundary-instant? This would amount to McTaggart's assumption--events/changes are only realized at discrete instants, rather than continuous lapses--which (he argues) entails the conclusion that time is self-contradictory, and thus unreal.

So when we talk about "becoming", the activity which is change in the world, it makes no sense to use propositions like S is P, because we are talking about something which is categorically different from "being", which is the type of thing that S is P refers to. — Metaphysician Undercover

On the contrary:

... we may speak of the state of different things at the same time as well as of the states of the same thing at different times and, of course, of different things at different times and of the same thing at the same time. At different times a proposition concerning the same things may be true and false; just as a predicate may at any one time be true and false of different things. — Peirce, c. 1904-5

[Time] is certainly a law. It is simply a unidimensional continuum of sorts of states of things and that these have an antitypy is shown by the fact that a sort of state of things and a different one cannot both be at the same time. — Peirce, 1908

The principle of contradiction is indispensable, but the principle of excluded middle is not. Because classical logic insists on enforcing the latter, it indeed cannot handle the reality of temporal change (becoming).

Only when the principle of excluded middle is true. Again, it is false during an indefinitely gradual state of change, when S is in the process of becoming not-P after previously being P, or vice-versa. — aletheist

But that's arbitrary. All change all the time is "an indefinitely gradual state of change", so it doesn't make sense to say that S is P or S is not-P are applicable in any real way.

This does not follow, since existential subjects undeniably have different qualities and relations at different determinations of time. If "S is P" is true at an earlier determination of time, and "S is not-P" is true at a later determination of time, and both propositions cannot be true at the same determination of time (principle of contradiction), then there must a determination of time in between at which neither is true. — aletheist

This is clearly illogical. If "S is P" is true at some time, and then ceases to be true, then "S is not- P" is true at this time. You might posit a time in between, during which the human being is incapable of determining which of these is true, but this is not the same as saying neither is true, it's a case of saying that we haven't the capacity to determine it.

The problem with your position is your claim that "S is P", and "S is not-P" are sound propositions at some times, but are not sound at other times. This is inconsistency. And, it creates the following problem. If at some time, people cannot determine whether S is P or S is not-P is true, they will be inclined to just accept your proposal that neither is true instead of making the effort to determine which is true. This proposal propagates intellectual laziness. Instead of working to determine the truth of the matter we just assume there is not truth to it.

The only alternative is to claim that such negation is instantaneous, which requires S to be both P and not-P at the same determination of time, thus violating the principle of contradiction. — aletheist

As I just explained, last post, which your post was a reply to, instantaneous change does not imply contradiction. S is not P follows directly in time, after S is P. They are separated by the same boundary which separates one instant in time from the next. It is only if you deny the reality of these divisions, as you do, when you attempt to model time as continuous, that the law of non-contradiction is violated.

However, your attempt to model time as continuous is faulty, because you still impose instants as boundaries to separate the periods of time which you have called "event lapses". There is a necessary boundary, an instant, when "S is P" ceases to be true, and neither "S is P" nor "S is not-P" starts to be true.

Therefore your model doesn't solve any of the real problems with the nature of time. You simply replace the one boundary between S is P, and S is not P, the moment of instantaneous change, with two boundaries, one between S is P and S is neither P nor not-P, and another boundary between S is neither P nor not-P, and S is not P. Each of these two boundaries must itself still be a moment of instantaneous change or else you have the infinite regress which Aristotle elucidated.

Any time you replace the instantaneous boundary with an intermediary description, you still have the boundary which marks the end of S is P and the beginning of the intermediary, so you need to posit another intermediary at that boundary, and so on ad infinitum. This cannot be avoided so Aristotle's proposal was that S is P, and S is not-P are applicable to one aspect of reality which is completely distinct from the aspect of reality which neither S is P nor S is not-P is applicable. "Being" and "becoming" are distinct and incompatible aspects of reality, and this is the basis of Aristotelian dualism.

On the one hand, the present cannot mathematically be an instant with zero duration: — aletheist

It is only if you define "the present" in relation to the subjective experience of human consciousness, as you do, that this proposition is true. If you release your desire to define "the present" in this less than adequate way, you will see that it is possible to define "the present" as an instantaneous division between past and future. I realize that this definition does not match up exactly with the way that the human being experiences the present, but the human being is always experiencing a part of the future along with a part of the past, and we may not be capable of apprehending the instantaneous division.

Instead, the present must mathematically be a moment with infinitesimal duration: — aletheist

This is only derived from the faulty definition of "the present" explained above. If we abstract our thoughts from the subjective experience of time, to think about time as it really is, independent from this subjective experience, this conclusion can be seen as completely unwarranted.

Peirce's conclusion is based on this observation, which I accept: "consciousness must essentially cover an interval of time". It is where each of us goes from here which constitutes the difference between us. I say consciousness straddles the division between future and past, and contains part of each. And, I say consciousness has not apprehended the true boundary which is "the present". You insist that "the present" must be defined by this interval of time which constitutes the subjective experience of the present. Your pathway forward is misleading because you have assumed a subjective present, while I am seeking to understand the objective present.

Under this assumption, which proposition is true at that instant? If only "S is P" is true or only "S is not-P" is true, then that instant is obviously not the boundary between the two moments; it is within one or the other. — aletheist

I don't see why you say this. In one period of time S is P is true, and in the next period of time S is not-P is true. The "instant" is the boundary between the two periods of time. There is no time at that "instant", it has no temporal extension, like a dimensionless point in space, except in time, or a line with no breadth, separating one side from the other. You yourself allow that we can impose arbitrary divisions into time, as divisors, so we simply assume that such divisors really exist within time, so that there is a real point in time when S is P ceases to be true, and S is not-P starts to be true. You simply refuse to admit the reality of such divisors, because the human consciousness has not yet been able to determine them. But it makes no sense for you to ask about anything existing at that instant, because it is non-temporal, so there is nothing existing there.

... I understand a limit to be what two adjacent portions have in common — aletheist

Then you simply misunderstand what a limit is. When my glass is the limit which separates the water inside, from the air outside, it is not the place which the air and the water have in common. When the wall of my house is the boundary between the inside and outside, it is not the place that the inside and outside have in common. A limit is a point, or line, beyond which a thing cannot extend. It is distinct from the thing which is limited, so it is not what they have in common.

The future is substantially different from the past, they are completely distinct. Let's say that future and past form a dichotomy, all time must be either future or past, but it is impossible that any time is both future and past. What the "two adjacent portions have in common" is that they are each a distinct part of time. What they have in common is what allows us to class them together, as "time", but what makes them distinct is the separation between them. Since they are distinct, we must posit something which separates them, which forms the boundary. This is the present. Since there is no mixing of future and past, the present must be distinct and therefore non-temporal.

This is the case with the similar opposing terms, up and down, front and back, right and left, etc.. What they have in common is what allows us to class them together. However, there is necessarily a boundary, or limit between them, such that the two opposing things do not mix. To say 'I understand a limit as the place where two opposing portions mix', which is what you are saying when you say that the two have this place in common, is to misunderstand what a limit is. A limit is precisely what prevents the two portions from having that place in common.

This is only derived from the faulty definition of "the present" explained above. If we abstract our thoughts from the subjective experience of time, to think about time as it really is, independent from this subjective experience, this conclusion can be seen as completely unwarranted.

It's a logical conclusion implicit in continuous time, regardless of subjective experience. Present time is interval of time between past and future time, and if time is continuous this interval is not interval but an instant, i.e. infinitely small point in time. This is paradox in itself and one more reason to think time is not continuous, i.e. it is not infinitely divisible, and the present time is interval of unit time with actual defined non-zero duration.

By the way, you're talking to a guy who does not see the paradox in Zeno's paradoxes, so obviously there is a problem in fundamental understanding, not something that can be argued as practically you're two are just not speaking the same language.

It's a logical conclusion implicit in continuous time, regardless of subjective experience. Present time is interval of time between past and future time, and if time is continuous this interval is not interval but an instant, i.e. infinitely small point in time. This is paradox in itself and one more reason to think time is not continuous, i.e. it is not infinitely divisible, and the present time is interval of unit time with actual defined non-zero duration. — Zelebg

To get rid of the paradox, you need only to assume that time is not continuous. And that time is not continuous is supported by the recognition that the past is substantially different from the future. Once the future is recognized as different from the past, the present must be understood as something other than the continuity of future/past, it must be understood as a divisor between them. Then we are left with three distinct things, past, present, and future.

To get rid of the paradox, you need only to assume that time is not continuous.

That's what I said. But you have Aletheist here who thinks continuity is the solution to the paradox, whatever then is the paradox supposed to be.

And that time is not continuous is supported by the recognition that the past is substantially different from the future. Once the future is recognized as different from the past, the present must be understood as something other than the continuity of future/past, it must be understood as a divisor between them. Then we are left with three distinct things, past, present, and future.

Where did you get that? Continuity of time is just about infinite divisibility and nothing else, nothing more, nothing less.

All change all the time is "an indefinitely gradual state of change", so it doesn't make sense to say that S is P or S is not-P are applicable in any real way. — Metaphysician Undercover

Again, any particular existential subject (S) is always changing with respect to some of its qualities and relations (P), but not all.

If "S is P" is true at some time, and then ceases to be true, then "S is not-P" is true at this time. — Metaphysician Undercover

Only if one assumes that the principle of excluded middle is always true.

You might posit a time in between, during which the human being is incapable of determining which of these is true, but this is not the same as saying neither is true, it's a case of saying that we haven't the capacity to determine it. — Metaphysician Undercover

No, I am positing that a state of things is realized during an event-lapse that is objectively indeterminate, such that the existential subject S neither determinately possesses the quality or relation P, nor determinately does not possess the quality or relation P. Consistent with the definition of "real," it has nothing to do with human capabilities.

The problem with your position is your claim that "S is P", and "S is not-P" are sound propositions at some times, but are not sound at other times. — Metaphysician Undercover

There are no sound propositions, only sound (or unsound) arguments and true (or false) propositions. Again, "S is P" and "S is not-P" can each be true at different determinations of time, but neither can be true at a determination of time when S is changing from possessing P to not possessing P. If this change is not realized at some determination of time, then it cannot be realized at all.

S is not P follows directly in time, after S is P. They are separated by the same boundary which separates one instant in time from the next. — Metaphysician Undercover

As you know, I deny that time is composed of instants; but even if it were, there could be no "next" instant after any given instant, just as there is no "next" rational or real number after any given rational or real number. Otherwise, there would have to be an arbitrary and finite number of instants within any measured interval of time.

There is a necessary boundary, an instant, when "S is P" ceases to be true, and neither "S is P" nor "S is not-P" starts to be true. — Metaphysician Undercover

This is a clever bit of sophistry, because it distracts from the primary issue of when states of things are realized (at determinations of time) to the subordinate issue of how states of things are represented (by propositions).

Any time you replace the instantaneous boundary with an intermediary description, you still have the boundary which marks the end of S is P and the beginning of the intermediary, so you need to posit another intermediary at that boundary, and so on ad infinitum. — Metaphysician Undercover

No, the only real boundary is between the lapse of time at which a particular determinate state of things (signified by "S is P") is realized and the lapse of time at which an incompatible determinate state of things (signified by "S is not-P") is realized. Our disagreement boils down to whether that real boundary can be an individual determination of time (instant) or must always be another general determination of time (lapse). In other words, is instantaneous change really possible, or does real change always require a lapse of time?

"Being" and "becoming" are distinct and incompatible aspects of reality, and this is the basis of Aristotelian dualism. — Metaphysician Undercover

What you call "being" and "becoming" are simply two different classes of states of things (prolonged vs. gradual) that are realized at different determinations of time, involving the same enduring existential subject (denoted by S) and one of its innumerable qualities and relations (denoted by P). Paraphrasing Peirce, the being of the quality/relation as form lies wholly in itself, the being of the existential subject as matter lies in its opposition to other things, and the being of the fact as entelechy lies in its bringing qualities/relations and existential subjects together.

I realize that this definition does not match up exactly with the way that the human being experiences the present, but the human being is always experiencing a part of the future along with a part of the past, and we may not be capable of apprehending the instantaneous division. — Metaphysician Undercover

It is precisely because "the human being is always experiencing a part of the future along with part of the past" that the present cannot be an "instantaneous division" between them. Anything that we are experiencing (present progressive tense) is, by definition, in the present.

Now there are great difficulties in the way of supposing that we are immediately conscious of time, and therefore of the past and future, unless we suppose it to possess ... continuity, so that we can be immediately conscious of all that is within an infinitesimal interval from any instant of which we are immediately conscious, without its thereby following that we are immediately conscious of all instants. — Peirce, c. 1894

The consciousness of the present, as the boundary between past and future, involves them both. — Peirce, 1899

The only important thing here is our metaphysical phenomenon, or familiar notion, that the past is a matter for knowledge but not for endeavor, that the future is an object that we may hope to influence, but which cannot affect us except through our anticipations, and that the present is a moment immeasurably small through which, as their limit, past and future can alone act upon one another. — Peirce, c. 1900

Of course, if there is no such thing as an absolute instant, there is nothing absolutely present either temporarily or in the sense of confrontation ... The present moment will be a lapse of time, highly confrontitial, when looked at as a whole, seeming absolutely so, but when regarded closely, seen not to be absolutely so, its earlier parts being somewhat of the nature of memory, a little vague, and its later parts somewhat of the nature of anticipation, a little generalized. It contains a central part which is still more present, still more confrontitial, but which presents the same features. There is nothing at all that is absolutely confrontitial; although it is quite true that the confrontitial is continually flowing in upon us ...
Another plain deliverance of the percipuum is that moment melts into moment. That is to say, moments may be so related as not to be entirely separate and yet not be the same. Obviously, this would be so according to our interpretation. But if time consists of instants, each instant is exactly what it is and is absolutely not any other. — Peirce, 1903

It is logically impossible for a state of things to be realized in the present instant and not to be at all so in the past and future. Were the instants independently actual, as they are in the Time of the analysts, memory would be a perpetual miracle. — Peirce, c. 1904

An event is a gradual state things involving change, so it is logically impossible for it to be realized in the present instant and not be at all so in the past and future. The minimum of time at which any possible state of things can be realized is an indefinite (mathematically infinitesimal) moment.

Your pathway forward is misleading because you have assumed a subjective present, while I am seeking to understand the objective present. — Metaphysician Undercover

Your paragraph summarizing our disagreement is basically accurate, except this last sentence that sets up a false dichotomy. Our phenomenological experience of the present is what calls for an explanation in the first place, and only a hypothesis that adequately accounts for our observations of both its internal ("subjective") and external ("objective") aspects should be considered plausible.

In one period of time S is P is true, and in the next period of time S is not-P is true. The "instant" is the boundary between the two periods of time. There is no time at that "instant", it has no temporal extension, like a dimensionless point in space, except in time, or a line with no breadth, separating one side from the other. — Metaphysician Undercover

This is the fundamental problem with your model. Since there is no time at an instant, an instant is not a real part of time; since there is no space at a point, a point is not a real part of space. We artificially introduce discrete and dimensionless instants and points into continuous time and space for purposes such as marking and measuring.

Then you simply misunderstand what a limit is. — Metaphysician Undercover

No, as usual we just have different technical definitions of a particular term.

Let's say that future and past form a dichotomy, all time must be either future or past ... — Metaphysician Undercover

This is precisely what I deny. The present is neither future nor past; time is a trichotomy, not a dichotomy.

There is no paradox here. — aletheist

Simple relativity will take care of this. Australia is roughly ten hours ahead of London - that is, it is ten hours in London's future. Information traveling from London to Australia travels forward in time by ten hours, and when it travels from Australia to London, it also goes back in time by ten hours. So, this post will go back ten hours in time to be read by a Londoner; and their reply will go forward ten hours to be read by an Australian; giving the perfect illusion of instantaneous communication.

Of course, an Australian cannot tell a Londoner what will happen in London in ten hours time, because it takes ten hours for the news from London to get to Australia.

Continuity of time is just about infinite divisibility and nothing else, nothing more, nothing less. — Zelebg

If you think that continuity is defined by infinite divisibility, then you misunderstand continuity. What is really the case, is that infinite divisibility is proposed as a defining attribute of continuity. The problem though, is that division in itself is contrary to continuity, and this produces its own sort of paradox. "Divisibility" implies possible to divide, but not actually divided. A continuity is proposed as being divisible anywhere, and that's what supports "infinite divisibility". But if it were actually divided anywhere, it would not be a continuity. So the continuity, in theory is divisible anywhere (infinitely divisible), but in practise (in reality) it cannot be divided anywhere or else it would not be a continuity.

There are no sound propositions, only sound (or unsound) arguments and true (or false) propositions. Again, "S is P" and "S is not-P" can each be true at different determinations of time, but neither can be true at a determination of time when S is changing from possessing P to not possessing P. If this change is not realized at some determination of time, then it cannot be realized at all. — aletheist

I can't believe that you do not see the problem with this; saying that there is a time when S is P ceases to be true, but we cannot say S is not-P at this time, and that this is an objective property of S. "S is P", and "S is not-P" are human determinations, propositions, they are judgements made by us, and these fundamental laws of logic are there to guide us in those judgements.

Therefore, when there is a time when it appears like S is neither P nor not-P, this is a time when we do not have the capacity to make that judgement. To make the assertion that there is something about the object which we are judging, rather than accepting the likelihood that there is something deficient in our capacity to make the judgement, which is responsible for this situation, is not only completely unwarranted, but it also kills the desire and inspiration required for further analysis of the object to determine the precise time when S is P becomes S is not-P, through the assertion that there is no such precise time. Therefore it kills our desire to improve our capacity to make a judgement of whether S is P or S is not-P in these situations, by saying that this capacity cannot be improved. But this claim of yours, that our capacity to make the judgement cannot be improved, can never be justified, because no matter how hard we try and fail to make that judgement, this does not prove that we haven't just been trying the wrong approach.

As you know, I deny that time is composed of instants; but even if it were, there could be no "next" instant after any given instant, just as there is no "next" rational or real number after any given rational or real number. Otherwise, there would have to be an arbitrary and finite number of instants within any measured interval of time. — aletheist

You misunderstand my use of "instant". An instant divides two portions of time, and as I said, it is non-temporal, just like a point divides two line segments, but in no way is that point a segment of line, it is non-linear. Therefore it is impossible that time is composed of instants.

This is a clever bit of sophistry, because it distracts from the primary issue of when states of things are realized (at determinations of time) to the subordinate issue of how states of things are represented (by propositions). — aletheist

It's not sophistry, but an attempt to get you to recognize the failure of your proposition. So you clearly recognize the difference between the real state of things, and the representation. Do you accept that "S is P", and "S is not-P" are terms of representation? If so, then let's proceed to look at the problem in this way. You seem to think that these terms make acceptable representations sometimes, but at other times they do not. So we need to establish a principle of separation between which times the terms make acceptable representation, and at which times they do not.

The Aristotelean proposal is that at future times, these terms of representation are unacceptable. This is because future events have not yet been determined. It doesn't make sense to say of S, that S is P, or that S is not-P, at a future time, because this has not yet been determined. We speak of future things as possibilities, and his famous example is the possibility of a sea battle tomorrow. That future event is dependent on free will choices, which have not yet been decided, so it doesn't make sense to use those terms of representation, therefore the law of excluded middle is inapplicable to these future events.

Now we have a distinction between past events, where the law of excluded middle applies, and future events, where the law of excluded middle does not apply. Notice the difference between what "S" refers to when "S" is a representation of the past, and when "S" is a representation of the future. The future event has no real existence. In between these two very distinct aspects of reality we have the present.

No, the only real boundary is between the lapse of time at which a particular determinate state of things (signified by "S is P") is realized and the lapse of time at which an incompatible determinate state of things (signified by "S is not-P") is realized. Our disagreement boils down to whether that real boundary can be an individual determination of time (instant) or must always be another general determination of time (lapse). In other words, is instantaneous change really possible, or does real change always require a lapse of time? — aletheist

We both agree that real change requires a lapse of time. Where we disagree is in how the representations of states "S is P" etc., are related to "change", which occurs over a time lapse. As I've explained already, the only problem with a representation that consists of a time line with a point when S is P is replaced by S is not-P, is that this model cannot represent change. Furthermore, as Aristotle demonstrated, we cannot represent change with these terms at all. However, this does not lead to the conclusion you suggest. Since there is always things remaining the same, represented by "S is P", and there is always things changing, not representable by "S is P", then the proper conclusion is that we need two distinct representations, to represent these two distinct aspects of reality (dualism).

So where we disagree is in how these two distinct aspects of reality relate to each other. I am arguing, that the aspect of reality referred to by "S" as a past object or event, is always describable in the terms of "is P", and "is not P". But there is another aspect of reality which is not describable in those terms, and we cannot refer to this as "S", in the same way, because what "S" signifies has no real existence, only possible existence. You want to say that the same "S" is sometimes describable by these terms, and sometimes not. But I think that this is irrational, because "S" signifies an intelligible object, a subject, it does not signify a physical object. And, to say that neither P nor not-P is applicable to S is to render S as unintelligible, which is inherently contradictory.

What you call "being" and "becoming" are simply two different classes of states of things (prolonged vs. gradual) that are realized at different determinations of time, involving the same enduring existential subject (denoted by S) and one of its innumerable qualities and relations (denoted by P). Paraphrasing Peirce, the being of the quality/relation as form lies wholly in itself, the being of the existential subject as matter lies in its opposition to other things, and the being of the fact as entelechy lies in its bringing qualities/relations and existential subjects together. — aletheist

This is exactly what I'm talking about as the problem with your proposal. Instead of upholding the division, or distinction between the aspects of reality which can be described as "is P", and "is not P", which we refer to with "S" (subject), and the aspects of reality which cannot be described as "is P" and "is not P", which when referred to as "S" (subject), give "S" a different meaning, you want to talk about some sort of "existential subject". That is fundamentally irrational, because "S" as subject refers to something different when talking about a past object, from what it refers to when talking about a future object. There is a need to separate two distinct types of subject, rather than conflating them as "existential subject".

This is the fundamental problem with your model. Since there is no time at an instant, an instant is not a real part of time; since there is no space at a point, a point is not a real part of space. We artificially introduce discrete and dimensionless instants and points into continuous time and space for purposes such as marking and measuring. — aletheist

Right, an "instant" is not a real part of time, and that is why time cannot be continuous. There is something which breaks the continuity, which is called the "instant". You however, start with an unjustified premise, that time is continuous, and conclude that instants cannot be real, therefore you argue that all instants are unreal. But just because the human being has not yet developed the means to determine the real instants in time, does not mean that there are not such real instants. So your argued position is nothing but a vicious circle. Human beings have not been able to determine real instants in time, therefore there are no real instants, and time is continuous. Since time is continuous, there are no real instants, therefore human beings ought not seek to determine the real instants in time. I think they call that argument a fallacy of reification, or misplaced concreteness.

This is precisely what I deny. The present is neither future nor past; time is a trichotomy, not a dichotomy. — aletheist

You claim to deny it, but your definition of "limit" supports it. That is contradiction. You said a "limit" is "what two adjacent portions have in common". If time is truly a trichotomy, as you say, then "the present", as the limit, and a third distinct thing between future and past, would prevent the two adjacent portions, future and past, from having anything in common. And, time could not be continuous.

So, the problem with your proposal is that you want to inject a third distinct thing, into time, between future and past, a lapse of time when neither "S is P" nor "S is not-P" is true, and despite the positing of the intermediary, you want to claim that time is continuous. Clearly, if this third thing which separates future from past has real existence, then time is not continuous.

If you think that continuity is defined by infinite divisibility, then you misunderstand continuity.

It’s not a matter of opinion, but of speaking the same language as the rest of the world. The defining and most relevant aspect of continuity when talking about space and time is infinite divisibility. You have the whole internet to see that for yoursel, where do you get your information?

So the continuity, in theory is divisible anywhere (infinitely divisible), but in practise (in reality) it cannot be divided anywhere or else it would not be a continuity.

Continuous / analog is defined by infinite divisibility, it means “composed of no parts”, it does not mean “composed of infinitely many parts”. Discrete / digital is defined by already being divided into unit parts which can not be further divided.

There is no theory / practice distinction here, we are talking about the most general logical categories to differentiate two possible ontologies - analog vs. digital. Then we test both via thought experiments such as Zeno’s paradoxes.

So yes, we can divide continuity and we get two continuities plus one paradox, but there is nothing “real” or practical about any of it, all is just a thought experiment and semantic / logical conclusions.

Once again I attempt to get the conversation about time moving in a slightly different direction:

Wiki: "With an incomplete theory of quantum gravity, it is impossible to be certain what spacetime would look like at small scales. However, there is no reason that spacetime needs to be fundamentally smooth. It is possible that instead, in a quantum theory of gravity, spacetime would consist of many small, ever-changing regions in which space and time are not definite, but fluctuate in a foam-like manner.[3]

Wheeler suggested that the Heisenberg uncertainty principle might imply that over sufficiently small distances and sufficiently brief intervals of time, the "very geometry of spacetime fluctuates".[4] These fluctuations could be large enough to cause significant departures from the smooth spacetime seen at macroscopic scales, giving spacetime a "foamy" character."

"S is P", and "S is not-P" are human determinations, propositions, they are judgements made by us, and these fundamental laws of logic are there to guide us in those judgements. — Metaphysician Undercover

There is an important difference between a proposition and a judgment. A true proposition signifies a real state of things--i.e., a fact--so it is true regardless of what anyone thinks about it. A judgment is one person's belief that a certain proposition is true, which is fallible.

To make the assertion that there is something about the object which we are judging, rather than accepting the likelihood that there is something deficient in our capacity to make the judgement, which is responsible for this situation, is not only completely unwarranted, but it also kills the desire and inspiration required for further analysis of the object to determine the precise time when S is P becomes S is not-P, through the assertion that there is no such precise time. — Metaphysician Undercover

This cuts both ways. To make the assertion that there is a precise time when S changes from being P to being not-P, rather than accepting the likelihood that a state of change is only ever realized at a lapse of time rather than at an instant, is not only completely unwarranted, but it also kills the desire and inspiration required for further analysis of the reality of time, through the assertion that there must be such a precise time.

Therefore it is impossible that time is composed of instants. — Metaphysician Undercover

Indeed, and if time is not composed of instants, then it must be continuous. Instants in time, like points on a line, are artificially imposed.

Do you accept that "S is P", and "S is not-P" are terms of representation? — Metaphysician Undercover

Of course, they signify two different prolonged states of things that are incompossible; i.e., they cannot be realized at the same determination of time.

Notice the difference between what "S" refers to when "S" is a representation of the past, and when "S" is a representation of the future. The future event has no real existence. — Metaphysician Undercover

No, "S" does not refer to an event at all, it denotes an existential subject; i.e., an enduring concrete thing. An event is the gradual state of things when a change is realized, which is signified by "S became not-P" (past) or "S is becoming not-P" (present) or "S would become not-P under such-and-such circumstances" (future). That is why neither "S is P" nor "S is not-P" is true during the lapse of time at which the event is realized.

But I think that this is irrational, because "S" signifies an intelligible object, a subject, it does not signify a physical object. — Metaphysician Undercover

On the contrary, it is an assertion like this that is irrational and unintelligible. "S" denotes an enduring concrete thing, which is an intelligible object.

And, to say that neither P nor not-P is applicable to S is to render S as unintelligible, which is inherently contradictory. — Metaphysician Undercover

It is perfectly intelligible once we recognize that the enduring concrete thing denoted by "S" is changing from possessing the quality or relation denoted by "P" to no longer possessing that quality or relation, or vice-versa.

That is fundamentally irrational, because "S" as subject refers to something different when talking about a past object, from what it refers to when talking about a future object. — Metaphysician Undercover

Nonsense, in this context "S" denotes the same enduring concrete thing. What changes over time are the qualities and relations that it possesses, such as the one denoted by "P."

Right, an "instant" is not a real part of time, and that is why time cannot be continuous. — Metaphysician Undercover

This is backwards; time would only be discontinuous if a discrete instant were a real part of it.

Human beings have not been able to determine real instants in time, therefore there are no real instants, and time is continuous. Since time is continuous, there are no real instants, therefore human beings ought not seek to determine the real instants in time. — Metaphysician Undercover

The fallacy here is that of a straw man--neither of these sentences accurately expresses any assertion or argument that I have actually offered.

If time is truly a trichotomy, as you say, then "the present", as the limit, and a third distinct thing between future and past, would prevent the two adjacent portions, future and past, from having anything in common. — Metaphysician Undercover

No, my whole point is that the present is a third portion, not a limit at all. The past and present are not adjacent portions, because the present is another lapse of time between them, not an instant.

So, the problem with your proposal is that you want to inject a third distinct thing, into time, between future and past, a lapse of time when neither "S is P" nor "S is not-P" is true, and despite the positing of the intermediary, you want to claim that time is continuous. Clearly, if this third thing which separates future from past has real existence, then time is not continuous. — Metaphysician Undercover

In my terminology (and Peirce's), a determination of time is not a thing and it does not exist. Time is a real law that governs existents, like the enduring concrete thing denoted by "S." The present is not distinct from the past and the future, it is an indefinite moment such that we directly perceive the continuous flow of time.

Indeed, and if time is not composed of instants, then it must be continuous. — aletheist

Would that imply time is also "smooth?" Or space/time?

It’s not a matter of opinion, but of speaking the same language as the rest of the world. The defining and most relevant aspect of continuity when talking about space and time is infinite divisibility. You have the whole internet to see that for yoursel, where do you get your information? — Zelebg

I get my information from studying philosophy, where continuity is the feature of an undivided existence. So when mathematicians look at the divisibility of the undivided, it produces the paradox I described. The paradox is maybe easier to understand in Zeno's terms.

There is no theory / practice distinction here... — Zelebg

Are you familiar with Zeno's paradoxes. The substance of his paradoxes is that what is described in theory does not occur in practise. In theory Achilles cannot reach the tortoise in the race, in practise this is not so. The paradox is resolved by realizing that the theory is based in faulty premises, the infinite divisibility of space and time.

There is an important difference between a proposition and a judgment. A true proposition signifies a real state of things--i.e., a fact--so it is true regardless of what anyone thinks about it. A judgment is one person's belief that a certain proposition is true, which is fallible. — aletheist

This is irrelevant, because it is impossible to determine what "is true regardless of what anyone thinks". All determinations of truth are judgements, and judgements are human. So you are suggesting that there is a judgement independent of human judgements, which is somehow more reliable than human judgements. That there is a God may or may not be true, but it is irrelevant to this discussion because we are talking about human judgements concerning propositions.

This cuts both ways. To make the assertion that there is a precise time when S changes from being P to being not-P, rather than accepting the likelihood that a state of change is only ever realized at a lapse of time rather than at an instant, is not only completely unwarranted, but it also kills the desire and inspiration required for further analysis of the reality of time, through the assertion that there must be such a precise time. — aletheist

As I explained, what this assumption does, is force the necessary and proper conclusion that reality consists of two distinct and incompatible aspects, that which "being" refers to, and that which "becoming" refers to. It does not force us to exclude "becoming" as unreal, it simply encourages us along the pathway toward accepting as true, some propositions of dualism.

You, have come to the point of realizing that the fundamental laws of logic appear to be applicable at some times, but at other times not. However, you refuse to take the analysis further, to determine which aspects of reality they apply to, and which they do not. Instead, you say that the same aspect of reality, represented as "S", is subject to predication at some times, and at other times not. Then you insist that there is nothing real (no real markers in time, as "instants") to indicate when predication is valid and when it is not. So all we are left with is completely arbitrary decisions as to when predication is valid and when it is not.

If you would take the analysis further, you would see that what is referred to by "S", varies depending on the circumstances of use. Sometimes "S" is substantiated by a physical object, and sometimes "S" is substantiated by a rational principle, a possibility, or even something imaginary. Therefore we need two distinct types of substance (what validates "S" as referent). And, we find that the one type of substance, which validates the imaginary, but rational subject, is grounded in logical possibility, where the law of excluded middle is not applicable.

But you refuse to get out of the muddled mess you are in, holding that the same substance is both subject to the law of excluded middle, and not subject to the law of excluded middle, depending on what time you look at it, while insisting that there is no valid markers in time to determine the one time from the other. All you need to do, to escape from this mess, is to recognize that the substance of the past is completely distinct from the substance of the future (dualism), and the that present is a valid marker to separate the one part of time from the other.

Indeed, and if time is not composed of instants, then it must be continuous. Instants in time, like points on a line, are artificially imposed. — aletheist

This is a blatant conclusion by equivocation. You are not adhering to how I defined "instant". An instant separates one period of time from another, but consist of no time. Therefore the conclusion that time is not composed of instants does not force the conclusion that time is continuous. Your misunderstanding of the nature of a "limit" which you demonstrated earlier, is showing here again.

No, "S" does not refer to an event at all, it denotes an existential subject; i.e., an enduring concrete thing. An event is the gradual state of things when a change is realized, which is signified by "S became not-P" (past) or "S is becoming not-P" (present) or "S would become not-P under such-and-such circumstances" (future). That is why neither "S is P" nor "S is not-P" is true during the lapse of time at which the event is realized. — aletheist

I reject your notion of "existential subject" for the reasons given already. It does not account for the separation between the logical subject, and the object which is sometimes represented as a subject. The fact that only sometimes an object is represented, and sometimes an object is misrepresented, are sufficient evidence to exclude the notion of "existential subject". We cannot limit "subject" in the way you want. Furthermore, because of this conflation, you do not recognize the two distinct types of objects recognized in philosophy, material objects and immaterial objects. This refusal to distinguish between the two types of things which might be referenced by "the subject", insisting on an "existential subject" as a conflation of these two, appears to be at the root of your confusion.

It is perfectly intelligible once we recognize that the enduring concrete thing denoted by "S" is changing from possessing the quality or relation denoted by "P" to no longer possessing that quality or relation, or vice-versa. — aletheist

This is a blatant denial of the fact that "S' signifies a subject, and a subject is in no way defined as an "enduring concrete thing". You show complete disregard for disciplined philosophy, and blatant denial of fundamental principles.

No, my whole point is that the present is a third portion, not a limit at all. The past and present are not adjacent portions, because the present is another lapse of time between them, not an instant. — aletheist

Three portions of the same type of thing does not make a trichotomy, which requires three different types of things. So you are only trudging forward in denial of your own contradiction. Furthermore, you have already denied that there are any real divisors within that thing which is supposedly portioned, so you don't have any real portions at all.

Time is a real law that governs existents... — aletheist

Utter nonsense.

So you are suggesting that there is a judgement independent of human judgements, which is somehow more reliable than human judgements. — Metaphysician Undercover

No, there are states of things independent of human judgments--namely, facts. These are signified by true propositions, which are likewise independent of human judgments. Again, a judgment is a human decision to adopt a certain proposition as a belief.

You, have come to the point of realizing that the fundamental laws of logic appear to be applicable at some times, but at other times not. However, you refuse to take the analysis further, to determine which aspects of reality they apply to, and which they do not. — Metaphysician Undercover

On the contrary, I have consistently maintained that the principle of excluded middle applies to propositions signifying prolonged states of things (what you call "being"), but not to propositions signifying indefinitely gradual states of change (what you call "becoming"), both of which are only realized at lapses of time (not instants).

If you would take the analysis further, you would see that what is referred to by "S", varies depending on the circumstances of use. — Metaphysician Undercover

I stipulated from the very beginning that in my example, "S" denotes an existential subject, an enduring concrete thing; and "P" denotes one of the innumerable qualities or relations that it possesses at some determinations of time, but not at others. I have never been talking about any other possible referent of either term.

But you refuse to get out of the muddled mess you are in, holding that the same substance is both subject to the law of excluded middle, and not subject to the law of excluded middle, depending on what time you look at it, while insisting that there is no valid markers in time to determine the one time from the other. — Metaphysician Undercover

The principle of excluded middle does not apply to subjects at all, it applies to propositions; and what matters in this context is whether the state of things signified by a given proposition is prolonged (unchanging) or gradual (changing). These are necessarily realized at different determinations of time for the same subject.

This is a blatant conclusion by equivocation. You are not adhering to how I defined "instant". — Metaphysician Undercover

The pot is calling the kettle black.

Utter nonsense. — Metaphysician Undercover

I have the same opinion of your responses at this point, so maybe it is time (no pun intended) for us to call it quits.

The event is the //W//existential junction of states//W// (that is, of that which in existence corresponds to a statement about a given subject in representation) whose combination in one subject would violate the logical law of contradiction. //W//The event, therefore, considered as a junction, is not a subject and does not inhere in a subject.//W// What is it, then? Its mode of being is existential quasi-existence, or that approach to existence where contraries can be united in one subject. Time is that diversity of existence whereby that which is existentially a subject is enabled to receive contrary determinations in existence.//W// — Pierce

I've marked with //W// where I think Pierce is wrong, but time is real in my opinion, and Pierce supports the right argument.

(universe) Time is the 4th dimension generated by all mass(hence constellations) and the impartial speeds(hence solar systems) of primarily gravity and rotation, but of all matter.

Time is not 'diversity of existence', all universe phenomenon are related. Humans are related to stars. Even if just time-wise.

Why do electrons not form a single group - why are they separate?

Elemental mass, and all their relative speeds, determine the electron-locale; we do not crunch together because of harmonious mass and we all exist through the speed of primarily rotation and other spin.

Like being 'on' - the disc planet spinning.

Would that imply time is also "smooth?" Or space/time? — jgill

If by "smooth" you mean that any function with respect time is differentiable arbitrarily many times, then yes, that is my understanding (and Peirce's) of true continuity.

Not only must any given instantaneous value, s, implied in the change be itself either absolutely unchanging or else always changing continuously, but also, denoting an instant of time by t, so likewise must, in the language of the calculus, ds/dt, d^2s/dt^2, d^3s/dt^3, and so on endlessly, be, each and all of them, either absolutely unchanging or always changing continuously. — Peirce, 1908

Note that instants and instantaneous values are perfectly acceptable within mathematics as "the study of what is true of hypothetical states of things" (Peirce's definition, emphasis mine).

Time is not 'diversity of existence', all universe phenomenon are related. Humans are related to stars. Even if just time-wise. — xyzmix

This seems like a misinterpretation of what Peirce meant by "diversity of existence." Consider his other definition, which I also quoted in the OP.

Time is a certain general respect relative to different determinations of which states of things otherwise impossible may be realized. Namely, if P and Q are two logically possible states of things, (abstraction being made of time) but are logically incompossible, they may be realized in respect to different determinations of time. — Peirce, c. 1905

"Diversity of existence" simply refers to the reality that the same existential subject (enduring concrete thing) possesses different qualities and relations at different determinations of time.

I get my information from studying philosophy, where continuity is the feature of an undivided existence. So when mathematicians look at the divisibility of the undivided, it produces the paradox I described. The paradox is maybe easier to understand in Zeno's terms.

We agree about Zeno and divisibility in that sense. The problem was you then started talk about divisibility in terms of past, present, and future - where did you get that, some reference?

Are you familiar with Zeno's paradoxes. The substance of his paradoxes is that what is described in theory does not occur in practise. In theory Achilles cannot reach the tortoise in the race, in practise this is not so. The paradox is resolved by realizing that the theory is based in faulty premises, the infinite divisibility of space and time.

Explain that to Aletheist. That's where his confusion is, and anything else you two are talking about is beside that essential point.

Does fire exist in the same way a human exists?

How do elements exist?

Time is a real law that governs existents

Can you translate that into English? What is "real law", how is it different than "not-real law", and how is it different from conteporary understanding of time?

Indeed, and if time is not composed of instants, then it must be continuous.

True, which means "infinitely divisible", hence the paradox.