The number one, or unity.

  1. Philosophy Forum
  2. » Logic
  3. » The number one, or unity.

Get Email Updates Email this Topic Print this Page

Reply Sun 11 Apr, 2010 01:37 am
One seems like the Ur-number. The primal number, from which all other numbers are derived. Zero is one's bride? (But perhaps that's sexist. Sorry, ladies. Smile)

Multiplicative identity. And then in philosophy we have Parmenides, Spinoza, Hegel.... The ideal is generally maximum reduction. Occam's razor. The goal is unity, simplicity, the sewing of everything together.

One is also written, in its simplest form, as a vertical stroke. It's glyph is itself one-dimensional, whereas both 0 and 2, it's neighbors, must be written in 2-dimensions. That's just trivia, but it all adds up to charm me.

So I'm just trying to start a conversation about the concept of oneness as it applies to philosophy and/or math. One is the junction of an infinite plurality? The trunk of a tree with an infinite number of branches?
 
Reconstructo
 
Reply Sun 11 Apr, 2010 04:15 pm
@Reconstructo,
Kant made mistakes, in my opinion, but I'll be damned if he wasn't on the right track. And even if his categories can be reduced to lower terms, the general idea is sublime. To seek out the structure of thought, or, in other words, the structure of structure....(or essence of essence)

Quote:

These categories, then, are the fundamental, primary, or native conceptions of the understanding, which flow from, or constitute the mechanism of, its nature, are inseparable from its activity, and are therefore, for human thought, universal and necessary, or a priori. They are not contingent states or images of sensuous consciousness, and hence not to be thence derived. But they are not known to us independently of such consciousness or of sensible experience. On the one hand, they are exclusively involved in, and hence come to our knowledge exclusively through, the spontaneous activity of the understanding. But, on the other hand, the understanding is never active, until sensible data are furnished as material for it to act upon, and so it may truly be said that they become known to us "only on the occasion of sensible experience." For Kant, in opposition to Wolff and Hobbes, the categories exist only in the mind.[27]
These categories are "pure" conceptions of the understanding, in as much as they are independent of all that is contingent in sense. They are not derived from what is called the matter of sense, or from particular, variable sensations. But they are not independent of the universal and necessary form of sense. Again, Kant, in the "Transcendental Logic," is professedly engaged with the search for an answer to the second main question of the Critique, How is pure physical science, or sensible knowledge, possible? Kant, now, has said, and, with reference to the kind of knowledge mentioned in the foregoing question, has said truly, that thoughts, without the content which perception supplies, are empty. This is not less true of pure thoughts, than of any others. The content which the pure conceptions, as categories of pure physical science or sensible knowledge, cannot derive from the matter of sense, they must and do derive from its pure form. And in this relation between the pure conceptions of the understanding and their pure content there is involved, as we shall see, the most intimate community of nature and origin between sense, on its formal side (space and time), and the understanding itself. For Kant, space and time are a priori intuitions. Out of a total of six arguments in favor of space as a priori intuition, Kant presents four of them in the Metaphysical Exposition of space: two argue for space a priori and two for space as intuition.[28]
 
north
 
Reply Sun 11 Apr, 2010 08:26 pm
@Reconstructo,
the number one has no complexity , it can't sustain , anything
 
Reconstructo
 
Reply Sun 11 Apr, 2010 08:45 pm
@Reconstructo,
Multiplicative identity. In math-world, that's one piece of the magic of one.

In philosophy world, it seems that unity is the core of the real transcendental analytic. How much of Kant's other analytic derivable from operations on this core unity? For instance, causality. Is causality just a complex network of unities?

For instance, a cat is the qualia of the cat tied together with other concepts by its own particular unifying concept, namely "cat." And as to the causality-time relation, we seem to think of time either as sequenced memory involving change or in numerical terms, which are measured according to non-numerical change. Sunrises or half-life, etc. Can we build it all up from unity? Unity would be simultaneously synthetic and negative. The qualia added are no more important, really, than the qualia excluded. Of course concepts also unify and exclude other concepts. But it's the same deal. Inclusive and exclusive seem logically simultaneous. But I have rambled long enough..
 
Reconstructo
 
Reply Mon 19 Apr, 2010 03:19 am
@Reconstructo,
I'm wondering if anyone will agree that one is the root of all ratio. You can write any number in binary. And therefore any ratio. You can even do it in unary. But we cannot have math without a zero dimensional object in a bi-directional dimension. (One dimensional number line.) The number one if written as a vertical stroke just happens to be a perfect representation of the number line it lives on, especially since we privileged one end of the spectrum (the positives) as higher. And of course one doesn't need the negatives. The natural numbers are already bi-directional. Tied off at one end, but essentially enough. The number one (as straight line) is also the only number that is written one-dimensionally. Well, it has the width necessary to manifest its height, but you get the point.
 
Reconstructo
 
Reply Thu 27 May, 2010 02:19 pm
@north,
north;150655 wrote:
the number one has no complexity , it can't sustain , anything


It has no complexity. Right on! Because it's a logical atom. The logical atom. Or the shell of the logical atom.
 
 

 
  1. Philosophy Forum
  2. » Logic
  3. » The number one, or unity.
Copyright © 2021 MadLab, LLC :: Terms of Service :: Privacy Policy :: Page generated in 0.02 seconds on 09/23/2021 at 12:22:13