"Part" implies some but not all of. How do you propose that we can have some but not all of, any particular whole, or supposed continuum, without a separation? "Some but not all of" implies necessarily, separation, that's what "some but not all of" means, separation.

Out of curiosity, I checked my dictionary to see how it defines "continuous." Here is what it says: "Having continuity of parts; without cessation or interruption; continued." Once again, you got it backwards - having parts is necessary for something to be continuous; otherwise, it would be "indivisible," which is a completely different concept.

I've never seen a definition of continuous, which refers to parts, but I'm sure you can find one, even if you just make it up yourself. My OED defines continuous as unbroken, uninterrupted, connected throughout space and time. Any philosophical definition I've seen describes continuous as unbroken, uninterrupted. And that's exactly what division does, it breaks, or interrupts. It is necessary therefore that the continuous is indivisible, because if it is divided it is not continuous. To divide the continuous would make it no loner continuous, so to describe it as consisting of parts is to describe it as non-continuous. It is a well known metaphysical principle, that the continuous is indivisible.

You want to describe the continuous as consisting of contiguous parts. But then you are describing a contiguity rather than a continuity. Do you recognize the difference between contiguous and continuous?

I've never seen a definition of continuous, which refers to parts ... — Metaphysician Undercover

Yes, you have - I just quoted one to you, verbatim, from Webster's Collegiate Dictionary, Fifth Edition (1936), which is what I happen to have on the shelf here at home. See below for a philosophical definition that explicitly refers to parts.

It is a well known metaphysical principle, that the continuous is indivisible. — Metaphysician Undercover

Sources, please? On the contrary, here is what the SEP article on "Continuity and Infinitesimals" has to say (italics in original, bold mine).

While it is the fundamental nature of a continuum to be undivided, it is nevertheless generally (although not invariably) held that any continuum admits of repeated or successive division without limit. This means that the process of dividing it into ever smaller parts will never terminate in an indivisible or an atom - that is, a part which, lacking proper parts itself, cannot be further divided. In a word, continua are divisible without limit or infinitely divisible. The unity of a continuum thus conceals a potentially infinite plurality.

In other words, being continuous is generally (although not invariably) the exact opposite of being indivisible.

Consider this example aletheist. Let's assume a continuity denoted by A to Z. Everything between A and Z is continuous. This continuity is not absolute by any means because it begins at A and it ends at Z. So it is a limited continuity. Now if we assume a point in between A and Z, say B, such that we have A to B, and B to Z then we no longer have a continuity of A to Z, we have two distinct continuities, A to B, and B to Z. So if we assume that A to Z consists of such parts, we are not assuming that A to Z is a continuity.

On the contrary, here is what the SEP article on "Continuity and Infinitesimals" has to say (italics in original, bold mine). — aletheist

Your SEP article appears to have a very shallow and unmetaphysical explanation of continuity. Suppose we assume that a continuum is in principle divisible, how do you avoid the problem of my prior post? It is necessary that the continuum does not actually consist of the parts which it will be divided into, or else it is not, at that time a continuum.

You already acknowledged that this is not a true continuum, because it has points at the ends, which are discontinuities. When you add a third point, you indeed break the continuity yet again; in fact, that is precisely the nature of all points on a line - they are discontinuities that we introduce by the very act of marking them. Before you posit point B, it does not actually exist; if anything, it is merely potential. Furthermore, the "two distinct continuities" that you get by assuming the point B are not "parts" of the original continuity in the relevant sense, since the point B itself is not part of the original continuity at all. Remember, the parts of a continuous line are not points - they are shorter lines.

By the way, according to your view, which "part" contains B - the one from A to B, or the one from B to Z?

"My" SEP article? I certainly did not write it, I just referenced it. I asked you for sources to justify your claim, "It is a well known metaphysical principle, that the continuous is indivisible"; but you provided none, which is telling. See above for my response to your example.

Before you posit point B, it does not actually exist; if anything, it is merely potential. — aletheist

I agree.

Furthermore, the "two distinct continuities" that you get by assuming the point B are not "parts" of the original continuity in the relevant sense, since the point B itself is not part of the original continuity at all. — aletheist

Right, the two distinct continuities are not parts of the original continuity, they are produced by division.

Remember, the parts of a continuous line are not points - they are shorter lines. — aletheist

Now why do you go and contradict yourself? There are no such shorter lines until you posit some points of division. If there were such shorter lines, there would not be a continuity, because the shorter lines would be already separated out. There would be a series of shorter lines in contiguity. Do you understand the difference between continuity and contiguity? I really don't think that you do because you keep describing a contiguity, and claiming that it is a continuity. They are not the same. If the long line consists of shorter lines, then it is necessary that there is a boundary between the shorter lines, so that it actually consists of shorter lines. But these boundaries contradict "continuity", you have only a contiguity.

By the way, according to your view, which "part" contains B - the one from A to B, or the one from B to Z? — aletheist

This is not my view, I was offering you a compromise, to allow for your insistence that a continuity can consist of parts. Parts imply separation, so I offered points in the continuity as separations. You seem insistent that the continuity consists of such parts, without any separations, but this is purely contradictory. Without the separations there are no parts.

"It is a well known metaphysical principle, that the continuous is indivisible"; but you provided none, which is telling. — aletheist

It's simple Aristotelian logic. Anything divisible necessarily consists of parts. Every part is individuated, or separate from every other part. A continuity has no such separations. Therefore a continuity is indivisible.

You seem to take exception to the opening premise, assuming that something which does not consist of parts (continuum) is divisible. But then you contradict yourself by describing that thing as consisting of parts.

There are no such shorter lines until you posit some points of division. — Metaphysician Undercover

Why is it so hard for you to understand that there are no points in a continuous line, only shorter lines? Positing points of division makes the line discontinuous.

Do you understand the difference between continuity and contiguity? — Metaphysician Undercover

Yes, contiguity only applies to discrete things; so that is obviously not what I am describing.

If the long line consists of shorter lines, then it is necessary that there is a boundary between the shorter lines, so that it actually consists of shorter lines. — Metaphysician Undercover

NO! There are no intrinsic boundaries between the parts of a continuum; in this case, between the smaller lines within a continuous line.

It's simple Aristotelian logic. Anything divisible necessarily consists of parts. Every part is individuated, or separate from every other part. A continuity has no such separations. Therefore a continuity is indivisible. — Metaphysician Undercover

I asked you for sources, not a rationalization; and in any case, it should be quite clear by now that I reject your unwarranted stipulation that a "part" is necessarily "individuated" or "separate." Besides, what did Aristotle himself have to say about this matter? Warning - you are not going to like it!

Now if the terms 'continuous', 'in contact' [i.e., contiguous], and 'in succession' are understood as defined above - things being 'continuous' if their extremities are one, 'in contact' if their extremities are together, and 'in succession' if there is nothing of their own kind intermediate between them - nothing that is continuous can be composed 'of indivisibles': e.g. a line cannot be composed of points, the line being continuous and the point indivisible ...

Again, if length and time could thus be composed of indivisibles, they could be divided into indivisibles, since each is divisible into the parts of which it is composed. But, as we saw, no continuous thing is divisible into things without parts. Nor can there be anything of any other kind intermediate between the parts or between the moments: for if there could be any such thing it is clear that it must be either indivisible or divisible, and if it is divisible, it must be divisible either into indivisibles or into divisibles that are infinitely divisible, in which case it is continuous.

Moreover, it is plain that everything continuous is divisible into divisibles that are infinitely divisible: for if it were divisible into indivisibles, we should have an indivisible in contact with an indivisible, since the extremities of things that are continuous with one another are one and are in contact. — Physics VI.1

Now a continuum is that which is divisible into parts always capable of subdivision ... — On the Heavens I.1

If you want to stick to your guns and claim that Aristotelian logic somehow contradicts Aristotle's own explicitly stated views ... well, good luck with that.

Why is it so hard for you to understand that there are no points in a continuous line, only shorter lines? Positing points of division makes the line discontinuous. — aletheist

If they are shorter lines, they must end. Where they end, there must be something which signifies the end or else there is no end and therefore no shorter lines. If you don't want to acknowledge that "end" as a point, then call it something else, but the fact is that this "something else" interrupts any supposed continuity.

quote="aletheist;57607"]NO! There are no intrinsic boundaries between the parts of a continuum; in this case, between the smaller lines within a continuous line.[/quote]

Then what ends the short lines, making then short lines? How can you not see the contradiction? How can there be short lines if there is nothing to end these lines, making them short lines.

I asked you for sources, not a rationalization; and in any case, it should be quite clear by now that I reject your unwarranted stipulation that a "part" is necessarily "individuated" or "separate." — aletheist

If it's not individuated, or separated from the whole, how can you say that there's a part? All you have is a whole.

The problem with your metaphysics, is as I described earlier in this thread. You have some idea of the way things should be described, an ideal, then you define your terms according to this ideal. But this ideal is just a fantasy, a fiction, and you have no respect for reality, for the way that things actually are, according to empirical observation. So you continue your metaphysics based in some fictional ideal, rather than in solid principles of how things actually are.

If you want to stick to your guns and claim that Aristotelian logic somehow contradicts Aristotle's own explicitly stated views ... well, good luck with that. — aletheist

Aristotle says many different things in many different places, often contradicting himself. That's not odd, he has a lot of material. Pretty much the entirety of "On the Heavens" has been discredited, proven wrong.

Your obstinate dogmatism would be quite impressive if it were an admirable trait. You simply refuse to accept the established definitions - as quoted from a standard dictionary, an online philosophy encyclopedia, and the writings of Aristotle - of what it means for something to be continuous. Once again, engaging with you has been a waste of my time. Cheers.

Just answer a couple quick questions for me, if you really believe that you have a tenable position. How can you have short lines unless they have ends? And how can you have a continuity which has ends inherent within it?

I explained this already, multiple times and in various ways. A continuous line has no ends, so by definition its parts also have no ends. You cannot actually divide a continuous line without introducing a discontinuity (point), but it is potentially divisible without limit, as the SEP article explains. Mathematically, infinitesimals likewise have no ends; they are indistinct, such that the principle of excluded middle does not apply to them. In Aristotle's words, "the extremities of things [i.e., parts] that are continuous with one another are one [i.e., not two or more] and are in contact [i.e., not separate]."

Based on our past encounters, I expect you to respond by insisting that a line is "divisible" only if someone can actually divide it. I see no use in going back down that road, so again, cheers.

You cannot actually divide a continuous line without introducing a discontinuity (point), but it is potentially divisible without limit, as the SEP article explains. — aletheist

This is where you stray from observed empirical reality. Empirically proven principles demonstrate that anything which is divisible is such because it consists of parts. The points which provide for division are already existent within the divisible thing, or else it could not be divided. You are assuming that a continuous thing, a thing which exists without such points for potential division, can still be divided. This is an unsupported fantasy.

Mathematically, infinitesimals likewise have no ends; they are indistinct, such that the principle of excluded middle does not apply to them. — aletheist

And this is nonsense. Such entities have no individual identity.

This is where you stray from observed empirical reality. Empirically proven principles demonstrate that anything which is divisible is such because it consists of parts. — Metaphysician Undercover

Explain any empirical evidence that anything is truly divisible, that is stands completely separate from all that surrounds it. It must be shown at the finest granularity that has been empirically explored.

Things are separable from their surroundings because each one is a part of the overall whole. If it were not a part, it would not be separable from the whole. Any individual object, like a rock, is divisible itself because it consists of parts, molecules. A molecule is divisible because it consists of atoms, etc.. If a whole did not consist of parts it would not be divisible. And because it consists of parts, the whole is not continuous.

We could assume the existence of a continuous whole, but it would be false to say that this continuity consists of parts. It is equally false to say that it is divisible.

Is you saying this is your belief or are you saying there is empirical evidence? As far as I understand there is no evidence one way or the other, but there is evidence of persistent entanglement and fields that extend forever. I know of no evidence for separation of waves into distinct particles. Models should not be confused with nature and there is no splitting of atoms. Energy is merely being re-formed from less to more substantial and vice-versa. One way to picture this would be the shaping and reshaping of waves in an ocean. There is never separation. The "parts" we carve out (waves) are simply different shapes within the whole. Wheeler's quantum foam or Bohm's Implicate Universe might be two ways to visualize the fabric of the universe.

Is you saying this is your belief or are you saying there is empirical evidence? — Rich

You don't think that there is evidence that the area of your field of vision is made up of separate objects, separate parts? Isn't the fact that I can pick up a chair and move it to the other side of the room, or move the dishes from the cupboard and use them, then wash them, evidence that they are individual parts, able to move independently of the others? Isn't the fact that water boils and evapourates evidence that it is made of separate parts, molecules? Aren't chemical reactions evidence that the molecules are made of parts, atoms? What more evidence do you need.

As far as I understand there is no evidence one way or the other, but there is evidence of persistent entanglement and fields that extend forever. — Rich

Fields are mathematical formulae. You are just entering a fictional fantasy like aletheist, referring to some ideal, a fiction of how you think reality should be, then you will describe things to match this ideal, instead of shaping your ideal to the way thins really are..

I know of no evidence for separation of waves into distinct particles. — Rich

Waves are something distinct from particles, but they clearly are a pattern of movement of particles, like sound waves and water waves.

Models should not be confused with nature and there is no splitting of atoms. — Rich

I believe the atom has been split, in the nuclear reaction. And electrons are commonly separated from atoms in electrical practises.

One way to picture this would be the shaping and reshaping of waves in an ocean. There is never separation. The "parts" we carve out (waves) are simply different shapes within the whole. — Rich

A wave can only exist within an assembly of parts, it is a particular type of activity of particles.

You don't think that there is evidence that the area of your field of vision is made up of separate objects, separate parts? — Metaphysician Undercover

I am saying that as far as empirical evidence exists at this time, there is no evidence of full and total separation. There seems to be more evidence to the contrary. You are speaking of separation (the concept of isolated particles) for which there is no empirical evidence and never was. The idea of somehow separate particles is a belief system, which one is free to embrace, but then one must explain what is in-between. It is rather simple, on the other hand, to have a continuous fabric of waves from which substantive matter is formed (and collapses into).

There is certainly empirical evidence for fields which are continuous and stretch forever. Much more evidence for this than separate and distinct particles. Particles are probably nothing more than perturbations (spikes) in the fields that appear and disappear in the field, but there is no empirical evidence one way or another. They would be real but they would also be part of and inseparable from the field since the field would be the fabric.

Actually, the splitting is a metaphor. Energy was release as the "droplet" (as Bohr described it) was reformed. One can analog this as one massive wave being reformed into two smaller ones and in the process releasing energy, as a wave hitting a beach might.

The wave in the above description is not part of anything, it would be the fabric of the universe. Consciousness, movement (energy) and memory are all sewn into this fabric and are everywhere just as an image is sewn into every part of a hologram. It is waves that make this all happen.

I am saying that as far as empirical evidence exists at this time, there is no evidence of full and total separation. — Rich

I apprehend "full and total separation" as a rather useless concept. Things always exist in relation to other things. To not have a relation to something else (full and total separation) is to not exist. Unless you conceive of a whole which consists of all existing things (the universe), and this whole, by definition would not have a relation to anything else, because it is everything, full and total separation is impossible. But what kind of separation is that? It's just the logical separation between what is, and what is not. So is this the "full and total separation" you refer to, the separation of logic, between being and not being?

There seems to be more evidence to the contrary. You are speaking of separation (the concept of isolated particles) for which there is no empirical evidence and never was. The idea of somehow separate particles is a belief system, which one is free to embrace, but then one must explain what is in-between. — Rich

As I said, we move objects around, in different directions relative to each other. Does this not indicate a separation between them to you? It's nonsense to insist that this separation must be absolute, such that there is not even any relationship between the two, because then one object would have to be existing and the other not-existing. So you requirement for "separation" is to completely annihilate the object. You will not admit that one object is separable from another unless it can be completely annihilated, removed from any relationship to the other. Why do you not allow that moving one object in all sorts of different directions relative to another, constitutes a real separation between them? What we assume as "in-between", which allows for such movement, is "space". Why do you hold such a strong propensity to reject this idea?

The wave in the above description is not part of anything, it would be the fabric of the universe. Consciousness, movement (energy) and memory are all sewn into this fabric and are everywhere just as an image is sewn into every part of a hologram. It is waves that make this all happen. — Rich

I do not see why you claim that this idea is "rather simple". Do you not recognize that waves require a medium? So all you are doing is reducing the "substantive matter", and taking for granted a new substance which necessarily underlies the waves. I assume a "space" between substantive objects, you assume "waves", which are necessarily in a substance, then you have to account for the appearance of objects, so one is not more simple than the other. You've replaced my lack of substance, "space", with substance, "waves". Now you still must account for what I call substance, objects. The difference, is that my position allows for the real separation between objects, which we utilize daily, to move objects in different directions relative to each other. You deny this real separation. So how is it that we move objects like this then? How do you account for our capacity to freely move objects this way and that way in relation to each other, if there is not real separation (space) between them?

quote="Rich;57691"]The wave in the above description is not part of anything, it would be the fabric of the universe. Consciousness, movement (energy) and memory are all sewn into this fabric and are everywhere just as an image is sewn into every part of a hologram. It is waves that make this all happen.[/quote]

Don't get me wrong, I am not denying the need to refer to wave activity, it as well as objects, is observable, and waves are empirically verified. The point though is that it doesn't get us any further ahead, to deny the reality of the independent activity of objects, for the assumption that all reality is a "whole" consisting of waves. What is needed is to establish compatibility, not to choose one over the other by excluding the possibility of the other.

There is certainly empirical evidence for fields which are continuous and stretch forever. — Rich

Could you point me towards the empirical evidence for these fields which are continuous and stretch forever?

Quantum entanglement.

Moving an object would be analog to one wave in an ocean moving another. Ocean and waves provide the basic analog of nature (it is a mirrored manifestation). The only thing missing is the impetus behind the movement. This would be Consciousness or Bergson's Elan Vital. With this image (that can only be intuited based upon many manifested patterns) one can begin to understand the nature of nature without paradoxes (any unit derived symbol will muddy the waters :) ). What you refer to as parts are simply wave perturbations.

It is unfortunate, but my whole model and approach really does undermine all of academic philosophy as it is instructed since it denies the use of mathematics and logic as a method for penetrating nature.
As I said earlier, for probing nature, the arts should be the major part of the philosophical academic curriculum.

Quantum entanglement. — Rich

What has entanglement got to do with the existence of continuous fields of infinite extent?

It's a rich line of inquiry. Other key ideas are Bohm' quantum potential and how it might explain the delayed choice experiment.

Moving an object would be analog to one wave in an ocean moving another. Ocean and waves provide the basic analog of nature (it is a mirrored manifestation). The only thing missing is the impetus behind the movement. — Rich

But it is this, the missing impetus which demonstrates that the parts are really separate. The free willing act can move the object any which way, so the wave in the ocean analogy is not really adequate to explain this motion.

This would be Consciousness or Bergson's Elan Vital. With this image (that can only be intuited based upon many manifested patterns) one can begin to understand the nature of nature without paradoxes (any unit derived symbol will muddy the waters :) ). What you refer to as parts are simply wave perturbations. — Rich

So how would the conscious, free will act move one particular object independently of the other objects? It cannot be by means of the wave perturbations which you describe, because these are not independent. It's easy to make the claim that Bergson's Elan Vital solves this problem, but until you explain how one object (a living being) moves itself independently of all the surrounding objects, your description of an ocean with waves remains incompatible with this reality.

It's a rich line of inquiry. Other key ideas are Bohm' quantum potential and how it might explain the delayed choice experiment. — Rich

Sorry to break it to you, but entanglement has nothing to do with continuous fields that extend to infinity.

So how would the conscious, free will act move one particular object independently of the other objects? It cannot be by means of the wave perturbations which you describe, because these are not independent. It's easy to make the claim that Bergson's Elan Vital solves this problem, but until you explain how one object (a living being) moves itself independently of all the surrounding objects, your description of an ocean with waves remains incompatible with this reality. — Metaphysician Undercover

It doesn't move it independently. It is embedded within the wave form and uses Will to attempt to move in a specific direction which would change the wave form within the field. Movement is thus a change in the flux of the waveform which is pretty much what quantum probability wave is describing.

When I push something out is one wave acting upon another within the field. The mind is using a reference wave to observe this movement and creating a corresponding memory wave form that itself is constantly changing. Everything would be waveforms but referenced in different ways and some some more substantial than others. Substantiality can be analogued by observing threads being compressed into strings and strings being compressed into balls.

It is necessary to use the creative mind to form the impressions. In the same way, musical sounds (more substantial)are transformed in impressions within memory (less substantial).