Archive for the ‘Mind-Body Dualism’ Category

The Stone Gamut

May 17, 2013

stone_gamut

Our thesis is that the category Set is the ultimate abstraction of body, and that Set^op, equivalent to the category of complete atomic Boolean algebras (i.e. power sets), which we shall advocate thinking of as antisets, is dually the ultimate abstraction of mind.

— From Chu Spaces: automata with quantum aspects by Vaughn Pratt

Reflecting an era of reduced expectations for the superiority of humans, we have implemented causal interaction not with the pineal gland but with machinery freely available to all classical entities, whether newt, pet rock, electron, or theorem (but not quantum mechanical wavefunction, which is sibling to if not an actual instance of our machinery).

— From Rational Mechanics and Natural Mathematics by Vaughn Pratt

http://en.wikipedia.org/wiki/Boolean_algebra

http://en.wikipedia.org/wiki/Distributive_lattice

http://en.wikipedia.org/wiki/Vector_space

http://en.wikipedia.org/wiki/Partially_ordered_set

http://en.wikipedia.org/wiki/Set_%28mathematics%29

References:

http://boole.stanford.edu/pub/ph94.pdf

http://boole.stanford.edu/pub/ratmech.pdf

http://chu.stanford.edu/

http://en.wikipedia.org/wiki/Chu_space

[*7.140]

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Arthur M. Young’s Fourfold Theory of Process

January 2, 2011

I have recently come across the philosophical work of Arthur M. Young (AMY). This is an initial impression of that work since I have only read what is available from the web links below, and even then there is a great deal to digest. In addition, there is difficulty in presenting a summary of his theory because of similarities to my ideas as well as substantial differences. I am sure I will need to return to AMY’s theory after more consideration.

I have hinted at a correspondence between several double duals presented in this blog, but I have steered away from claiming that they are all linked to each other – that they are essentially equivalently exchangeable. AMY’s theory links the four elements, the four causes, Jung’s functions of the psyche, geometrical elements and transformations, as well as several other fourfolds into a cosmic theory of reality.

Some of these same fourfolds are present in my theory, and I am considering how others may be introduced. Some not mentioned by AMY are only mentioned in earlier entries on this blog, without presentation. However, from many of these same fourfolds I have reached substantially different conclusions from AMY. I believe this is because AMY’s theory of process is essentially dualistic, whereas my theory appears to be physicalistic, although one might also say it is a process and/or relational theory.

Below is a table of some of the correspondences for AMY’s theory of process:

Aristotle’s
Four
Causes
Jung’s
Functions
of the Psyche
Four
Elements of
Empedocles
Geometric
Transform-
ations
Purpose Final Intuition Fire Rotation Spirit
Value Material Emotion Water Scale Soul
Form Formal Intellect Air Inversion Mind
Object Efficient Sensation Earth Translation Body

Below is a table of some of the correspondences for my theory:

Four Elements
of Empedocles
The Here and
the Now
Aristotle’s
Four Causes
Duality of
Time and
Information
Hjelmslev’s
Net
Fire Before Efficient Change time Substance
of content
Water After Final Bear time Form of
content
Air Above Formal Bear
information
Form of
expression
Earth Below Material Change
information
Substance
of expression

References:

Arthur M. Young / The Reflexive Universe

Arthur M. Young / The Geometry of Meaning

http://www.arthuryoung.com/index.html

http://www.arthuryoung.com/barr.html

http://www.arthuryoung.com/4levels.html

http://www.arthuryoung.com/the2exc.html

[*6.84-*6.89, *7.78, *7.79, *8.2, *8.62, *8.63]

<>


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