Following on, this also means particular continuities don't have a beginning or end. Yes, any given object has a start and end — TheWillowOfDarkness
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. — Rich
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. — aletheist
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. — aletheist
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. — aletheist
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. — TheWillowOfDarkness
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. — TheWillowOfDarkness
I'm not talking about energy here, I'm talking about the physical things in the room. — Metaphysician Undercover
They are one and the same. It is a continuum. The is no discontinuity between that which physical and that which creates it. I am bewildered at how you are able to separate the two. If we aren't energy, then what are we? The energetic form is simply moving within an energy field as a wave moves in water. There is no separation. — Rich
To describe a thing, and to describe the activity of a thing, is two distinct description. — Metaphysician Undercover
An individual is a physical object and it is divisible (the name "individual" is misleading) ... To begin with, we could recognize that what you have described is a physical object, and it is highly unlikely that any physical object has all parts of the same kind. — Metaphysician Undercover
There is probably more than one contradiction in this description, but I'll try to sort it out ... We have already determined that it is impossible that there is something real which satisfies your definition of "continuous", because it is contradictory ... You want to take "continuous", and give it an ideal definition which has already been shown to be contradictory. — Metaphysician Undercover
This is a collection of discrete individuals. Being described as consisting of parts indicates that it is discrete. — Metaphysician Undercover
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." — aletheist
As I have repeatedly made clear, I am discussing mathematics here, which has to do with ideal states of affairs; I am not saying anything whatsoever about physical objects. — aletheist
There has to be a way to distinguish a continuum (such as a line) from an indivisible (such as a point). — aletheist
There is nothing contradictory about my/Peirce's definition, and if you are going to keep insisting that there is, we might as well call yet another impasse and go our separate ways. — aletheist
But by my definition, it cannot be so divided; therefore, not only is it not discrete, it is not even potentially discrete. A true continuum cannot be composed of discrete elements, and it also cannot be decomposed into discrete elements. We can only introduce indivisible points along a continuous line, and those points are not parts of the continuous line itself. — aletheist
We can only introduce indivisible points along a continuous line, and those points are not parts of the continuous line itself. — aletheist
Therefore, the principle of excluded middle does not apply to that which is continuous; and this is all that it means to say that a continuum has only indefinite or potential parts. — aletheist
But we've already determined that mathematics refers to discrete units. — Metaphysician Undercover
So as soon as you describe something as a continuum we are not dealing with mathematics, and therefore I cannot assume that we are dealing with ideal states of affairs. — Metaphysician Undercover
You want an ideal continuum, so that perhaps you can establish a compatibility with mathematics, but this requires that you can define "continuity" in a way which is not contradictory. — Metaphysician Undercover
To be divisible, it requires this spatial extension, and this means that to be divided it requires extension outside the mind ... The truly ideal line cannot be divided. — Metaphysician Undercover
If it cannot be "so divided", then how is it divided? — Metaphysician Undercover
Why are the ideal points not part of the ideal line? — Metaphysician Undercover
As I said, I do not agree with the way that Peirce dismisses logical principles. — Metaphysician Undercover
Unless it can actually be divided, it is false to say that it is divisible. — Metaphysician Undercover
So while I do think that mathematics in accordance with the arithmetic/Dedekind-Cantor/set-theoretic paradigm is intrinsically discrete, I deny that all mathematics is constrained to refer only to discrete units. We certainly have not determined otherwise in this thread. — aletheist
One more time: I have always and only been dealing with mathematics and ideal states of affairs throughout this thread. Your unwillingness or inability to think of a continuum in mathematical/ideal terms is your own limitation, not mine. — aletheist
Which is exactly what I have done. You have not demonstrated otherwise; you just keep asserting it over and over, apparently expecting a different result. Where have I claimed that both P and not-P are true at the same time and in the same respect? — aletheist
What I stated is that a continuum cannot be divided into parts that are themselves indivisible; so it can be divided into parts that are themselves divisible, although once that happens it is no longer a continuum. — aletheist
Because points are indivisible, and a continuous line cannot be divided into parts that are themselves indivisible. Try to keep up. — aletheist
As I said, you are locked into the standard rules of classical logic, which are very useful for most purposes, but not for understanding the nature of true continuity. Failure of excluded middle is not a contradiction in all viable forms of logic. — aletheist
Any object has a start and end... but these can only be finite states. They are never a whole in the first place. — TheWillowOfDarkness
Niether of these objects are a whole, either of the plan or the object. — TheWillowOfDarkness
My plan doesn't suddenly become "not whole" because it began and ended. Nor does the created object. The point is starts and ends do not amount to a breaking of a contiuum. — TheWillowOfDarkness
If one could break a contiuum, it not indivisible. The infinite nature of a contiuum means it must be unaffected by beginnings and ends. — TheWillowOfDarkness
There is no such thing as a mathematical continuity, you are making that up. — Metaphysician Undercover
You have claimed that a continuum is both divisible and not divisible. — Metaphysician Undercover
If it is necessary that the continuum is undivided, then it is not possible to divide it. — Metaphysician Undercover
But this, acting on the continuum, is not "dividing it" in the mathematical sense of division, it is a change, which constitutes going from continuum to not-continuum. — Metaphysician Undercover
... you come up with the idea that the two parts produced are mathematically equivalent to the continuum. — Metaphysician Undercover
The ideal line is defined as consisting of a succession points, and is therefore not continuous, it is discrete. — Metaphysician Undercover
Why would you say that an object is not a whole? Sure it is not a whole in the perfect sense, like in the sense of a unity of everything is a the perfect whole, but by its own right as an individual unity, can't we say that it's a whole? — Metaphysician Undercover
How would you define "whole" then? To be a whole, doesn't it suffice just to be a unity? A unity doesn't need to be a perfect unity in order to be a whole. So numeral such as 5, 8, 12, signify wholes, but since they are each not the complete whole of all the numbers, nor the primary unity, 1, they are not perfect in their wholeness. — Metaphysician Undercover
Do you agree that a continuum is a whole? And do you agree that there are wholes, continua which are less than perfect in their nature? If an object which is a unity, a whole, ceases to exist, isn't that the end of that particular continuum? But if that object is described as part of a larger, more perfect whole, then that larger, more perfect continuity would persist, and the annihilation of that smaller whole, which was really just a part of the more perfect whole, would just be a slight change to that more perfect continuum. — Metaphysician Undercover
The discrete can only express a contiuum by reference to its connection to that pantheistic layer of reality. The greeks termed it, "Han Kai Pan", the one that is all. — Wolf
That would be news to mathematicians. — aletheist
Not at the same time and in the same respect, hence no contradiction. — aletheist
An ideal is a timeless truth. And that a continuum cannot be divided is such an ideal. So are you arguing that there will be a time after the ideal continuity is divided and then there would no longer be such an ideal? But since an ideal is a timeless truth, if there will be a time when there is no longer an ideal continuity, then there must not be an ideal continuity even now.It is not possible to divide it and still have a continuum. — aletheist
Dividing it is precisely what causes it to change from a continuum to a non-continuum. — aletheist
You are clearly not paying attention at all. — aletheist
I didn't. — TheWillowOfDarkness
Since this is the case, the problem you present is nothing more than a red-herring — TheWillowOfDarkness
What you suggest as a problem is just a category error, a mistaken assumption that unity is given by other things. — TheWillowOfDarkness
No, the unity of an object does not exist in the first place and has no end, so there is no end to the particular continuum-- hence the dead and fictional are still whole, despite being broken apart or never existing. — TheWillowOfDarkness
Claimed numerical continuum must be an illusions because this, the electromagnetically regulated reality we perceive, is almost always the world of zero. Meaning no matter what we find via the senses and our sensory based instruments we find only +1 & -1 of discrete objects. — Wolf
Descriptions are descriptions and in all situations must be taken as some attempt but in no way or manner so they ever come close to the actual experience. — Rich
Labeling with descriptions are useless. What is useful, is watch the ocean and the waves and observe closely what is actually happening as forms come and go in seamless never ending pattern of becoming and going. No states, no division, no difference between the whole and the parts, no way to divide, no b way to say this is where it begins and this is where it ends, yet it is all there. — Rich
But mathematicians specialize in mathematics, not ontology. — Metaphysician Undercover
Ideals are timeless truths. — Metaphysician Undercover
Oh I'm paying attention, you're just not listening to reason, continually making the same unreasonable assertions over and over again. — Metaphysician Undercover
I am only talking about mathematics in this thread, not ontology; maybe you should start your own thread on "Continuity and Ontology." — aletheist
Are you saying that descriptions are absolutely false? If not, then there must be some truth to a description. Just because it doesn't describe every aspect of the scene which it is describing, doesn't mean that it is false. So if a description describes some things which are unchanging during a period of time, then don't you think that there are some aspects of reality which are unchanging during that period of time, corresponding to the description? — Metaphysician Undercover
ignoring the things which are passive, or unchanging — Metaphysician Undercover
Descriptions are necessarily limited, inaccurate, imprecise, and provide no avenue to understand the nature of nature in themselves. They are simply a tool for communication which may or may not help two explorers to better understand. To this end, I have always felt metaphors to be far more helpful. — Rich
Have you ever tried describing duration in words or mathematics? — Rich
Stop duration, create a state, and describe it while still observing your efforts to describeit in the same duration. with such an attempt you should witness the impossibility of what you are suggesting as should anyone who believes that mathematics, words, logic, or any symbol is adequate to describe the nature of experience in duration. — Rich
A single example? — Rich
I don't understand how a metaphor is a better means for understanding the nature of nature than a description is. — Metaphysician Undercover
OK, this is how I describe duration. I recognize a difference between past and future by means of memory and anticipation. This gives me a sense of being present. As I am aware of being present, I notice that things are changing while I am present, and I can refer to duration through describing these changes which occur. — Metaphysician Undercover
So at the same time that I am noticing changes, which enable me to describe duration, I also notice things which are not changing. I can describe these things as not changing, for the entire duration of the change which I am describing. — Metaphysician Undercover
So for example, I have the blueprint for the layout of my kitchen, and this is a description of the things which are not changing in my kitchen. — Metaphysician Undercover
This provides an actual observation of your own duration and the impossibility for you to describe it. I am asking for a more direct experience. — Rich
However, if I was to be put in the same kitchen, I would observe everything changing on the macroscopic level (the dust in the air, the deterioration in the wood, your life itself, the ink on the paper), and at the microscopic level (the energy of all quanta). — Rich
This is why I say, philosophers need to be constantly exercising their observation skills via the arts. I first learned of the skill in the art of observation when I studied photography many years ago. A philosopher must always be exercising and refining the art of observation. — Rich
I believe that the earth is moving, but that fact is irrelevant to the fact that the layout of my kitchen remains the same. That's the point, we have to have respect for what is staying the same, as well as what is changing. — Metaphysician Undercover
It is quite clear to me that everything is changing in one manner or another all the time. There is nothing I can say or do to convince you of this. — Rich
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