What could it mean for a thing to contain parts but these parts are indefinite? — Metaphysician Undercover

If and when you ever come to understand this, you will then finally understand what Peirce and I mean by a true continuum.

There is no point along the continuous line where it is capable of being divided. We already determined, and agreed that there are no points on the continuous line, that would be contradictory. — Metaphysician Undercover

You are now equivocating on "point." I intentionally did not use that word. Any location along a continuous line is a potential point, but it only becomes a point if we mark it as such - for example, by dividing the line at that location.

Such a "real contiuum" is meaningless. It's a set without any members-- an infinite of nothing at all. — TheWillowOfDarkness

A true continuum is not a set or collection at all; it does not consist of discrete members.

Pierce fails to recognise it is a conntuim because he's still stuck trying to account for the infinte by the finite. — TheWillowOfDarkness

Who is Pierce? If you mean Peirce, it is clear from your comments - especially this one - that you are not familiar with his thought at all.

In a sense yes-- at some point I will reject I have a car-- but what is that point? Clearly, not because it's missing a part (I get a replacement part for the car). Nor is it driving function (I get the car fixed). It's not even a question of having a working car yet (I've built the body of my car).

As a whole, the car is not defined by its parts.

Really? You going to play this game of picking on typos and ignoring the criticism made? I know very well how Peirce defines a true contiuum.

The point is this is mistaken. He's failed to understand that a set or collection can be infinite, that it is not defined in a bottom-up manner as a sum of its parts. Consisting of finite members does not mean being finite.

Yes, actually I was wrong to say that you no longer have a car when you no longer have something that functions as a car, because what you have then is a broken-down car. The problem is that when the point is reached due to subtraction of parts, or, say, corrosion, that a car ceases to be a car, whether functioning or broken down, is not precisely definable. But then nothing about the finite is precisely definable, which means that it is actually in-finite, and is modeled as finite only for practical purposes. Finitude is real only insofar as our terms of conception are discrete.

If and when you ever come to understand this, you will then finally understand what Peirce and I mean by a true continuum. — aletheist

Exactly the point, yours and Peirce's concept of true continuum is incoherent and will never be understood. As I said, Peirce was proceeding in the proper direction, but didn't follow through. Instead of adhering to his logical conclusion, that defining parts into a continuum negates its essence as a continuum, and therefore a continuum is necessarily an indivisible whole, he follows his desire to have a divisible continuum. And this produces the incoherent notion of an indefinite part, the part which doesn't exist as a part until it is defined, but this definition renders it as an individual whole itself, rather than as a part because the thing which it was supposed to be a part of is negated by the so-called part's very existence. If he would have only adhered to the logic, he would have discovered Parmenides' indivisible, continuous, whole, and there would have been no need for this incoherent "indefinite part".

Defining space or duration (which is all that matters when talking about the nature of nature) by the infinite of anything is simply a contortionist attempt to give life to symbols. There is no cutting space into parts and there is no cutting duration into parts. It is simply that simple. If you can do such, you have arrows stopping and going for infinity but going no where, and you have Achilles helplessly moving his heart out but unable to get off the starting line. And if I may, by using the same symbolic replacement of nature by numbers you get time travel (heaven help us).

It one is truly interested in understanding nature, one has only to ask is there any experience of any sort in their life on this earth that gives them any reason to adopt a position that space or time can partitioned (and what in heaven's name is left in between??), and that mathematics in any symbolic form can possibly ever model nature that all experiences have shown is an indivisible whole? This is the only question that needs to be addressed insofar as the OP is concerned. After that, what every other symbol ever created (a car?) means. As one might guess, the meaning of each symbol lies in the beholder. And such disagreements create discussion, but gets us no closer to understanding the meaning of duration and space.

I know very well how Peirce defines a true contiuum. — TheWillowOfDarkness

Apparently not, given your subsequent comments.

He's failed to understand that a set or collection can be infinite, that it is not defined in a bottom-up manner as a sum of its parts. Consisting of finite members does not mean being finite. — TheWillowOfDarkness

He understood all of that extremely well. His point was that consisting of members - whether finite or infinite - means being discrete, rather than continuous.

He understood all of that extremely well. His point was that consisting of members - whether finite or infinite - means being discrete, rather than continuous. — aletheist

Consisting of finite members means being discrete. Consisting of in-finite members means being continuous.

Exactly the point, yours and Peirce's concept of true continuum is incoherent and will never be understood ... And this produces the incoherent notion of an indefinite part ... — Metaphysician Undercover

Your failure to understand it does not render it incoherent. I understand it, I just seem to be unable (so far) to explain it in a way that you will accept. Is this, in the end, the substance of our disagreement here? If you were to wake up tomorrow and decide that the notion of an indefinite part makes sense to you after all, would you have any other objections remaining?

No, consisting of members - no matter how many of them there are - means being discrete, not continuous. There are infinitely many natural numbers, integers, and rational numbers, and yet no one claims that any of these are continuous. Many will claim that the real numbers are continuous, but Peirce (and others) disagreed, for the reasons that I have been citing throughout the thread.

I was talking about the quality, not the quality of the members. I wrote "in-finite" rather than "infinite", to hopefully avoid that misunderstanding. Finite entities are finite only in the sense that we conceive them as such. Of course in saying that, I don't mean to suggest that entities are infinitely large, either! Infinitely large is itself an incoherent notion, because the notion of largeness implies the idea of 'body' which is itself incoherent without the idea of boundaries.

Ah, thanks for the clarification; maybe we are on the same page after all. By "in-finite," do you mean indefinite, or something else?

In reviewing Fernando Zalamea's paper, "Peirce's Continuum: A Methodological and Mathematical Approach," I came across his explanation of what we have been discussing, which are the properties of a true (Peircean) continuum that he calls reflexivity and inextensibility. Maybe what he has to say will convey the whole idea better than my previous attempts.

One of the fundamental properties of Peirce’s continuum consists in its reflexivity, a finely grained approach to Kant’s conception that the continuum is such that any of its parts possesses in turn another part similar to the whole: "A continuum is defined as something any part of which however small itself has parts of the same kind." We will use the term “reflexivity” for the preceding property of the continuum since, following a reflection principle, the whole can be reflected in any of its parts.

As immediately infers Peirce, reflexivity implies that the continuum cannot be composed by points, since points - not possessing other parts than themselves - cannot possess parts similar to the whole. Thus, reflexivity distinguishes at once the Peircean continuum from the Cantorian, since Cantor’s real line is composed by points and is not reflexive. In Peirce’s continuum the points disappear as actual entities (we shall see that they remain as possibilities) and are replaced - in actual, active-reactive secondness - by neighbourhoods, where the continuum flows ...

We will call inextensibility the property which asserts that a continuum cannot be composed of points. As we mentioned, a continuum’s reflexivity implies its inextensibility (Peirce’s continuum is reflexive, thus inextensible), or, equivalently, its extensibility implies its irreflexivity (Cantor’s continuum is extensible, thus irreflexive). The fact that Peirce’s continuum cannot be extensible, not being able to be captured extensionally by a sum of points, retrieves one of the basic precepts of the Parmenidean One, “immovable in the bonds of mighty chains,” a continuous whole which cannot be broken, “nor is it divisible, since it is all alike, and there is no more of it in one place than in another, to hinder it from holding together, nor less of it, but everything is full of what is.” — pp. 13-14

So Zalamea seems to agree with you that a continuum is not divisible, and even quotes Parmenides to that effect; but he also agrees with me (and with Peirce) that it nevertheless has parts, which cannot be points because those do not themselves have any parts. Instead, he calls them "neighborhoods," and he provides an accompanying illustration that is very similar to my microscope example:



We have already agreed that a continuum does not consist of points, that it is undivided, and that it is indivisible in the sense that once it is divided, it is no longer continuous. It seems, then, that the last hurdle - as I have already suggested - is your insistence that a continuum cannot have parts of any kind, grounded in your rejection of indefinite parts, such as infinitesimals or Zalamea's "neighborhoods." Do you concur with this assessment?

Your failure to understand it does not render it incoherent. I understand it, I just seem to be unable (so far) to explain it in a way that you will accept. Is this, in the end, the substance of our disagreement here? If you were to wake up tomorrow and decide that the notion of an indefinite part makes sense to you after all, would you have any other objections remaining? — aletheist

Perhaps it could make sense to me, but to say that a part is indefinite would be to say that this part is unintelligible, it cannot be known. Unless it can be demonstrated that such a part actually exists, why would I accept this assumption? To arbitrarily designate something as unknowable is contrary to the philosophical nature of human beings, which is the desire to know.

Instead, I know of a much more reasonable way to understand the ideal continuity, and that is as indivisible. Maintaining that the ideal continuity is indivisible, avoids this problem of having to assume unintelligible parts. So I see a reasonable approach, which is that the ideal continuity is indivisible, and an unreasonable approach, which is that the ideal continuity consists of unintelligible parts. So until it is demonstrated to me that there is something wrong with this notion that the ideal continuity is indivisible, why would I be inclined toward an unreasonable ideal, which contains unintelligible parts?

We have already agreed that a continuum does not consist of points, that it is undivided, and that it is indivisible in the sense that once it is divided, it is no longer continuous. It seems, then, that the last hurdle - as I have already suggested - is your insistence that a continuum cannot have parts of any kind, grounded in your rejection of indefinite parts, such as infinitesimals or Zalamea's "neighborhoods." Do you concur with this assessment? — aletheist

Yes I think I concur. But there is still another option which we haven't yet explored, and this is what I stated in my first post, that it is possible that an ideal continuity is just a fiction. The only way I can conceive of an ideal continuity is as Parmenides did, as an indivisible whole, without parts. However, it is possible that the only real continuities, are those physical, spatial entities which can be divided, but not divided infinitely. The fact that we divide continuous things, objects, wholes which we can cut up, inclines us to believe that there is some sort of thing (space or time for example) which may be capable of being divided infinitely. From this, we create the notion of an ideal continuity, one which could be divided infinitely. But this idea proves to be logically unsound, and we are forced toward the realization that the only ideal continuity is the indivisible whole, having no parts. Now we started with the fact that a continuous thing is divisible, and have ended with an opposing conclusion concerning the ideal continuity, that it is indivisible. Is it the case that we need to include divisibility in the ideal continuity? Perhaps we are just chasing an impossible dream, and an ideal continuity is just a logical impossibility. Maybe continuity is just not a real thing, and that's why it's impossible to understand.

There isn't a conflict. Ideal continuity is present. Any infinite can't be divided such that it said to begin or end. We don't divide continuous things, such as objects and wholes at all. Our "cutting" of a whole is merely picking out something specific. It doesn't affect continuity. If I pick out a rock, it doesn't make the whole of the world go away. The whole remains, uncut and indivisible, no matter how many times we might suggest we separate it, an all together different object to the individual states we pick out.

A whole has or is no parts, even as parts belong to it. When we pick out a part, the whole remains and is undivided (and is indivisible).

The mistake people make is thinking wholes as defined by parts in the first instance, such selecting a part would somehow divide and destroy the whole. It hides the indivisible nature of whole from us and sees us misread the wholes we do encounter as failed continuity.

There isn't a conflict. Ideal continuity is present. Any infinite can't be divided such that it said to begin or end. We don't divide continuous things, such as objects and wholes at all. Our "cutting" of a whole is merely picking out something specific. It doesn't affect continuity. If I pick out a rock, it doesn't make the whole of the world go away. The whole remains, uncut and indivisible, no matter how many times we might suggest we separate it, an all together different object to the individual states we pick out.

A whole has or is no parts, even as parts belong to it. When we pick out a part, the whole remains and is undivided (and is indivisible).

The mistake people make is thinking wholes as defined by parts in the first instance, such selecting a part would somehow divide and destroy the whole. It hides the indivisible nature of whole from us and sees us misread the wholes we do encounter as failed continuity. — TheWillowOfDarkness

This is precisely the question at hand. If we indeed are able to separate duration or space into parts, what the heck is left in-between?

What is happening is space is being reformed and duration is indivisibly evolving. I have absolutely no idea how anyone can possibly understand a space or a unit that is in any manner being spliced up as mathematics would have it. It is all a just symbolism which is being taught in schools. It's not really happening - is it? Is space and time really being partitioned. Does everything stop an infinite amount of times so Achilles can't move - because he can't leap across non-space??

I think indefiniteness or indeterminacy is certainly part of what I mean when I say that all actual entities are in-finite. I guess what I am saying is that entities are finite only in principle, or in other words in terms of our spatio-temporal conceptions of them.

The other side of it is that the identities of entities are not realized in our experience of them, but rather are formulated in purely conceptual terms. What is formulated is finite only insofar as it is as formulated. This is the misleading aspect of Spinoza's notion of substance; it is conceived as being actually, and not merely formally, infinite, but the conception of it, as formulated,is obviously finite. On the other hand our conceiving of it, prior to its formulation, is in-finite.

I suspect I will be accused by someone of producing word salad here, but at least I know what I mean. :)

Our "cutting" of a whole is merely picking out something specific. — TheWillowOfDarkness

I don't think I agree with this part of your statement. An object, as a whole, is something specific. The wholeness, the unity of the object, is something real, and something which is destroyed when we divide that object. Dividing an object is a real activity which has a real effect on the world, one object becomes two objects, and this is a considerable difference. It is not simply a case of choosing some specific parts, over the whole, it is a case of making those apprehended parts, into wholes themselves, through the act of dividing.

So we must have respect for what really happens in division, and that is that one whole becomes two wholes. And we know that it is different to be a whole than it is to be a part, because unity is attributed to the whole, not the part. So when we divide a whole, we take the unity away from it, and give unity to the parts. It is not the case that the unity of the whole is given to the parts, the unity of the whole is destroyed, and a new unity is given to each of the parts. A unity, or continuity is never divided, it simply has a beginning and an end.

If we associate continuity with the whole, with the unity, then each time we divide something, we destroy a continuity, and create new continuities. From this perspective, continuities have temporal beginnings and ends, so we need to be able to determine a cause of continuity. If nothing comes from nothing, there must be some actuality, some act, which causes the beginning of any particular continuity. Likewise, there must be an act which causes the end of a particular continuity.

There isn't a conflict. Ideal continuity is present. Any infinite can't be divided such that it said to begin or end. — TheWillowOfDarkness

I agree that this would be the ideal continuity, an infinite continuity, without beginning or end. We could assign this continuity to "the present" of time, as a working premise, and then we apprehend the whole of existence as one infinite continuity. But when we look at the nature of individual continuities, as I described above, we see that they all begin and end, so by induction, it is probably the case that there is no such ideal continuity, the infinite continuity.

This may be where mathematics misleads metaphysics or ontology, by allowing the possibility of the infinite. It is necessary that we allow infinity in mathematics in order that we can understand the most vast expanse which is possible. We cannot imagine the most vast expanse, because we don't know what it is, so we must allow that mathematics is limitless in order that the most vast expanse can be apprehended. But if we allow that the infinite has real existence within the world which we are trying to apprehend, then we deny ourselves the capacity to understand that world.

If we associate continuity with the whole, with the unity, then each time we divide something, we destroy a continuity, and create new continuities. — Metaphysician Undercover

Absolutely not. When a wave in an ocean transforms in two or more or even dissolves in the ocean, no continuity is lost whatsoever.

Forms of substance are nothing more than waves in the fabric of the universe. They are just more solid by degrees. How does one break continuity in the universe, in space, in duration? With a very fine knife? Exactly how fine? Finer than Planck's constant? Continuity can never be broken. It can only be reformed, as waves reform in oceans.

Which is the reason that mathematics is constantly giving a awful picture of nature. It's layering is own self-induced picture of the universe onto a universe. It's like putting a cardboard full of holes over a picture. It gives an incomplete and quizzical view of the picture itself. If you want to look at the picture and understand the picture, look at the picture itself, not through lots of holes in the cardboard.

Absolutely not. When a wave in an ocean transforms in two or more or even dissolves in the ocean, no continuity is lost whatsoever. — Rich

Of course there's a loss of continuity. The description of the wave as one wave applies no longer, and the description of two waves applies. Therefore the continuity of the one wave ends, and the two distinct continuities begin. You might be thinking that the continuity of energy is not lost, but if you are talking about the energy involved, this is something different than talking about the waves involved. The continuity of energy is a different continuity than the continuity of the wave.

Forms of substance are nothing more than waves in the fabric of the universe. They are just more solid by degrees. How does one break continuity in the universe, in space, in duration? With a very fine knife? Exactly how fine? Finer than Planck's constant? Continuity can never be broken. It can only be reformed, as waves reform in oceans. — Rich

As I explained in my post, it's quite obvious that continuity is broken, this we know. It is not broken in the sense of being divided though, it begins and it ends. But this is not "ideal continuity" this is the continuity of existence of various different things, they have beginnings and endings. And as I said, I don't think we know the cause of continuity. What you call "reforming" of the same continuity, is really the beginnings and endings of various different continuities. We must allow that there are various different continuities to account for the fact that there are various different, individual objects.

Are you arguing that there is no such thing as individual objects?

Of course there's a loss of continuity. The description of the wave as one wave applies no longer, and the description of two waves applies. — Metaphysician Undercover

The description changes, not the intrinsic continuity. And yes, everything is ultimately energy with differing substantially imbued into the fabric of the universe. As with mathematics, descriptions (for communication purposes only) is symbolic. Symbols are not that which is being described. Just because I describe two different events in my life does is constantly starting and stopping. Duration is continuous when observed directly. Symbolics only are necessary for communication or as a tool for manipulation. The important point is that no continuity is ever lost and no symbolic, which is intrinsically formed by individual units can possibly capture this continuity. This thread is basically about the ability for symbolics to adequately describe continuity. It can't. In fact, the description they yield is pretty much totally contrary to experience. The waves never, ever, ever break the continuity of the ocean. The objects are formed and reformed out of the continuity.

The description changes, not the intrinsic continuity. — Rich

The problem is, that according to the laws of logic, when the description changes the continuity which was described, ends, and a new continuity begins. That is why the laws of logic are not compatible with "becoming", and becoming is not compatible with continuity. So logic forces us toward discrete units, states of existence, and becoming occurs somehow in between. The position aletheist was arguing, the one derived from Peirce, takes continuity from the individual things with beginnings and endings, and hands continuity to the "becoming", the spatial temporal continuum. But this may render the laws of logic as useless.

As with mathematics, descriptions (for communication purposes only) is symbolic. Symbols are not that which is being described. Just because I describe two different events in my life does is constantly starting and stopping. Duration is continuous when observed directly. Symbolics only are necessary for communication or as a tool for manipulation. — Rich

The symbol must symbolizes something, and intelligibility depends on the assumption that what is symbolized remains the same. This is the continuity which I am referring to. The description, being symbols, describes something, and what it describes must remain the same. So that which is being described, remains the same, as a continuity. If the description is no longer applicable, then the state intended to be described, has changed, and that continuity no longer exists.

The important point is that no continuity is ever lost and no symbolic, which is intrinsically formed by individual units can possibly capture this continuity. — Rich

The problem with this perspective is that what exists between the described states, is activity, becoming. And since becoming is change, it cannot be understood as continuity, which is a remaining the same. That is why we have had so much difficulty in this thread describing space and time as continuous. These are the principles of flux, and flux is contrary to the continuity of being. I have now opted to describe individual existing objects as wholes, continuities. So "continuity" must be used to refer to each described state which continues to exist without change, and "becoming" is something other. Therefore continuity is always being lost into becoming, as things change.

This thread is basically about the ability for symbolics to adequately describe continuity. It can't. In fact, the description they yield is pretty much totally contrary to experience. The waves never, ever, ever break the continuity of the ocean. The objects are formed and reformed out of the continuity. — Rich

What is described by the symbols, what the symbols refer to is something which doesn't change in time, therefore the thing described is a temporal continuity. But if we want to describe "continuity" itself, what it means to be continuous, that is something different from what the symbols refer to, it is this unchangingness. There is nothing "contrary to experience", about describing what it means to be continuous, as a state which doesn't change in time. We observe all sorts of objects to be like this. We also observe that these continuities can be ended, as is the case when we divide up an object, and when an object is constructed, a continuity begins. The aspect of reality which is difficult to describe with symbols is the "becoming" the means by which these various continuities which may be described, begin and end. That is because our symbols are intended to have a static, fixed meaning, while becoming is a changing.

The problem with this perspective is that what exists between the described states, is activity, becoming — Metaphysician Undercover

There are no states in nature. Everything is continuously evolving. Problems arise when attempting to describe this and replacing the existence with the symbolics. For this reason I do not utilize discrete symbolics, but rather I attempt to utilize imaginative metaphors such as the ocean and the waves. Problems in communication and description should not interfere with the actual experience. For the most part, Bergson also used metaphors in his books. Metaphors are good because the macro reveals itself in the micro and vice-versa.

Perhaps it could make sense to me, but to say that a part is indefinite would be to say that this part is unintelligible, it cannot be known. — Metaphysician Undercover

Not really. To say that a continuum has no definite parts just means that it does not have any distinct, discrete, or indivisible parts. With this qualification, I might even be willing to grant that a continuum has no parts at all, as long as it remains undivided. After all, we agree that the act of dividing a continuum breaks its continuity; so what "infinitely divisible" means in this context is that if we start dividing a continuum, we will never reach the point (literally) of reducing it to an indivisible part. In other words, a continuum is indivisible in the specific sense that if it were divided into parts, and thus made discontinuous, then none of those parts would be indivisible. What do you think?

However, it is possible that the only real continuities, are those physical, spatial entities which can be divided, but not divided infinitely. — Metaphysician Undercover

Again, whether there are any real continua is a separate question from what it means to be continuous. Per my definition, something that can be divided, but not divided infinitely (as described above), is not continuous. In any case, I think that the first thing to establish is whether space and time are themselves continuous. If not - if they are discrete - then presumably all spatio-temporal entities are also discrete. However, if we establish that they are continuous, then we can investigate whether anything within space and time is also continuous.

However, if we establish that they are continuous, then we can investigate whether anything within space and time is also continuous. — aletheist

This should be interesting, finding anything that is within space and duration (real time) that is not continuous.

The only candidates for non-continuity that I can imagine are the unconscious state (including death), and the sleep state. Perhaps dreams themselves have duration, but certainly of a different type, which symbolically is almost impossible to describe. But then again it appears that even within a sleep state, and I would include daydreaming in this, duration seems to pop in and out. Consciousness seems to have an ability to exit memory when it is unconscious. Interestingly, Bergson had very little to say on this rather perplexing switch in states. It is sort of a mini birth/death cycle. Without question, mathematics cannot be applied to this activity.

There are no states in nature. — Rich

I disagree. I can look around my room and describe the positioning of the objects, and this will stay the same until it is changed, therefore it is a state that naturally persists. That's what Newton's first law describes, the state which things are in, will persist until a force causes that to change.

Not really. To say that a continuum has no definite parts just means that it does not have any distinct, discrete, or indivisible parts. With this qualification, I might even be willing to grant that a continuum has no parts at all, as long as it remains undivided. — aletheist

Yes, that is what I was arguing, if the parts are not distinct, or discrete, it doesn't really make sense to think of them as parts. So why not just say that the continuum has not parts?

After all, we agree that the act of dividing a continuum breaks its continuity; so what "infinitely divisible" means in this context is that if we start dividing a continuum, we will never reach the point (literally) of reducing it to an indivisible part. In other words, a continuum is indivisible in the specific sense that if it were divided into parts, and thus made discontinuous, then none of those parts would be indivisible. What do you think? — aletheist

I think that the ideal continuum cannot be divided at all, because it has no parts. And to give it parts would deny its existence as a continuum, so the ideal continuum must be indivisible. Therefore it makes no sense to talk about dividing an ideal continuum. But now I've been talking to the others about real existing continuums, and these are physical objects which display the quality of continuous existence. We can divide an object, or change an existing state, but in doing so we end its continuity, and start new continuities, as the divided parts are now objects which display continuous existence. But I believe these objects are not infinitely divisible. Infinite divisibility seems like an impossibility.

Again, whether there are any real continua is a separate question from what it means to be continuous. — aletheist

This is the same type of point that we are always disagreeing on. If we want to know what it means to be continuous, we need to refer to real things which are continuous. You seem to think that we can just stipulate the meaning of a word, regardless of whether there are any real examples of this. What good does that do us? If we want to know what it means to be continuous, we need to look at real examples of continua and determine what they have in common.

I think that the first thing to establish is whether space and time are themselves continuous. If not - if they are discrete - then presumably all spatio-temporal entities are also discrete. However, if we establish that they are continuous, then we can investigate whether anything within space and time is also continuous. — aletheist

OK, if we are going to venture into this subject we need to agree on some fundamental principles in order that we can understand each other. I believe that there are real existing things in the world, physical objects. And I also believe that we have concepts of space and time, and that these concepts have been produced to help us deal with, and understand the physical objects. So if we are to understand what the concepts of space and time refer to, we must relate them to physical objects, because that is where these concepts are abstracted from, the assumed existence of objects. They are not abstracted from the observations of real space, and real time. We cannot start to talk about space and time, as if they are real things in the world, because they are just concepts derived from our study of objects. Therefore if we assume that there is a real space, and a real time, because we have concepts of these, our understanding of these things is limited by our understanding of objects, so that any misunderstanding of objects which we have, will also manifest as a misunderstanding of space and time. Our only means to understanding real space, and real time, is through our understanding of objects.

So if we assume that discrete objects are continuous, as things, perhaps beings, we can proceed to analyze how this relates to space and time. First, I would suggest that an object appears to be discrete in relation to other objects. They may overlap, as gravity overlaps, and substances overlap in solutions, but the objects appear to be generally discrete in space. Therefore space appears to be discrete. However, objects appear to obtain their continuity from having continuous temporal existence. So we might consider that time is continuous.

To describe to you what I mean by the indivisibility of the continuous, consider that time is continuous. We can mark points in time, and durations in time all over the map. any where we want. But these are marked on the map, they are not within time itself. These points and segments are not part of time itself, they are part of the grid, the map, or marking system, which is independent of time itself.

disagree. I can look around my room and describe the positioning of the objects, and this will stay the same until it is changed, therefore it is a state that naturally persists. — Metaphysician Undercover

Actually, it is constantly changing. Some quite overtly others very subtly. But everything is constantly changing in one manner or another. Energy never stands still. Heraclitus was right and my guess is that he intuited it. If you were correct, then a whole new problem is created, like how does all quanta stop long enough, in concert with each other, to create your state. That would be interesting.

I think that the ideal continuum cannot be divided at all, because it has no parts. — Metaphysician Undercover

That which cannot be divided at all is an individual, not a continuum - e.g., a point rather than a line. There has to be a way to distinguish these two concepts. What would you call something that satisfies the following definition of a continuum? That which has potential parts, all of which would have parts of the same kind, such that it could be divided (but would then cease to be continuous), and none of the resulting parts would ever be incapable of further division.

If we want to know what it means to be continuous, we need to look at real examples of continua and determine what they have in common. — Metaphysician Undercover

This just seems completely backwards to me. How can we identify any real examples of continua without first defining what it means to be continuous? What interests me is whether there is anything real that satisfies my definition of continuity, even if you want to call it something else. That means beginning with space and (especially) time as the framework for our phenomenal experience - examining whether they seem to exhibit the characteristics that I mentioned. If so, we can then move on to whatever spatio-temporal objects we deem the best candidates for also being continuous in that sense.

The whole doesn't get divided in instances where we cut up an object. In such an instance, we are destroying a particular state of the world. When we cut a carrot, we don't target the whole. The knife doesn't split a whole into two halves, such there is a division of the whole.

If I try and say: "Here is half the whole carrot," my statement is incohrent. Since the whole is indivisible, I can't split it such that I have half the whole here and the other half of the whole over there.

In a sense we could say I destroy the whole. In cutting, I take a state expressing an infinite of continuity out of the world. Where one the whole was expressed in the world in front of me, now it is only done so in logic. There's never a split in the whole though, such that we end up with seperate parts of it. We are only destroying an object which expesses the whole.

Following on, this also means particular continuities don't have a beginning or end. Yes, any given object has a start and end, but this is not the unity expressed by it. Whether we are talking about a rock, a person or bacteria, it doesn't take existence for them to be whole-- imagined objects are no less whole than existing ones. In the birth and death of states, there only presence in time, as divided moments. It is only those divided moments, expressing a whole, which are lost and formed. Wholes themsleves are neither created or destroyed.