Space: Kant vs. Reimann
SPACE
and TokenSpace
(very much a work in progress. I think maybe these two ways of taking space* way be the key to unlocking the secret of human's dual relation to reality through sogn-use: by text (Kantian space) and by token (Reimannian space. It might be the case that both are "true" to the whole, self-consistent, while being inconsistent with each other at the level appl;ied S*. What is the case cannot be affirmed without self-contradiction. - Tertullian)
SPACE
Kantian:
Space is the form of outward sensory intuition ("over there...")
(as form....)
-the synthetic apriori sensory manifold (reality given as a totality simultaneously extended in all directions from a given point* -- add.)
The outward manifold of sensory intuition is (the conception of) that which remains in experience as a 'possible field', or 'tabula rosa', after imagining or 'thinking away' awareness of all content -- representations (words, numbers, geometry), qualities, feeling-impulses, etc.. However, as someone interested only in the possibility of knowledge contemporary science embodied, which was the theory of sense perception -- paradigmatically visual, as in Plato's Timaeus. The starry heavens above and the moral law within: these, woven together by sign-use and reason, are the twin pillars of Kantian consciousness.
Riemannian
Space is the receptacle of extended magnitudes: singly, doubly, triply,..ordered. In geometry, these would correspond, respectively, to a point, line/surface, square/solid. All lines experienced in actual space are powers actualized along 'edges': n+1 dimensional geometrical forms penetrating an n-dimensional surface, like the rings a spherical bubble passing though a penetrable membrane would inscribe on its surface. Thus, in the knowing situation, as Kepler discerned, the same powers that move the knower must proceed from the known. "Geometry" in this sense does not need an apriori form of sensible intuition: it IS such a form as active agency expressing itself and bringing into unity knower and known.
These versions of the competing philosophical positions of the two camps, crude and naive as they may be, support a reconciliation attempt that (A) invokes the distinction between consciousness and thought in the psychological metalanguage; and (B) introduces the term TokenSpace for the field-within-the-field of space proper* constituted by humans in the process of using signs to communicate.
wers connecting
and TokenSpace
(very much a work in progress. I think maybe these two ways of taking space* way be the key to unlocking the secret of human's dual relation to reality through sogn-use: by text (Kantian space) and by token (Reimannian space. It might be the case that both are "true" to the whole, self-consistent, while being inconsistent with each other at the level appl;ied S*. What is the case cannot be affirmed without self-contradiction. - Tertullian)
SPACE
Kantian:
Space is the form of outward sensory intuition ("over there...")
(as form....)
-the synthetic apriori sensory manifold (reality given as a totality simultaneously extended in all directions from a given point* -- add.)
The outward manifold of sensory intuition is (the conception of) that which remains in experience as a 'possible field', or 'tabula rosa', after imagining or 'thinking away' awareness of all content -- representations (words, numbers, geometry), qualities, feeling-impulses, etc.. However, as someone interested only in the possibility of knowledge contemporary science embodied, which was the theory of sense perception -- paradigmatically visual, as in Plato's Timaeus. The starry heavens above and the moral law within: these, woven together by sign-use and reason, are the twin pillars of Kantian consciousness.
Riemannian
Space is the receptacle of extended magnitudes: singly, doubly, triply,..ordered. In geometry, these would correspond, respectively, to a point, line/surface, square/solid. All lines experienced in actual space are powers actualized along 'edges': n+1 dimensional geometrical forms penetrating an n-dimensional surface, like the rings a spherical bubble passing though a penetrable membrane would inscribe on its surface. Thus, in the knowing situation, as Kepler discerned, the same powers that move the knower must proceed from the known. "Geometry" in this sense does not need an apriori form of sensible intuition: it IS such a form as active agency expressing itself and bringing into unity knower and known.
These versions of the competing philosophical positions of the two camps, crude and naive as they may be, support a reconciliation attempt that (A) invokes the distinction between consciousness and thought in the psychological metalanguage; and (B) introduces the term TokenSpace for the field-within-the-field of space proper* constituted by humans in the process of using signs to communicate.
wers connecting
posted by Sid Thomas | 11:20 PM
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