I've never seen a definition of continuous, which refers to parts ... — Metaphysician Undercover
It is a well known metaphysical principle, that the continuous is indivisible. — Metaphysician Undercover
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.
On the contrary, here is what the SEP article on "Continuity and Infinitesimals" has to say (italics in original, bold mine). — aletheist
Before you posit point B, it does not actually exist; if anything, it is merely potential. — aletheist
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
Remember, the parts of a continuous line are not points - they are shorter lines. — aletheist
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
"It is a well known metaphysical principle, that the continuous is indivisible"; but you provided none, which is telling. — aletheist
There are no such shorter lines until you posit some points of division. — Metaphysician Undercover
Do you understand the difference between continuity and contiguity? — Metaphysician Undercover
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
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
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
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
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 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
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
Mathematically, infinitesimals likewise have no ends; they are indistinct, such that the principle of excluded middle does not apply to them. — 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. — Metaphysician Undercover
Is you saying this is your belief or are you saying there is empirical evidence? — Rich
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
I know of no evidence for separation of waves into distinct particles. — Rich
Models should not be confused with nature and there is no splitting of atoms. — Rich
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
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. — Rich
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
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
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
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. — Metaphysician Undercover
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