Can mathematics help us reformulate Cartesian Dualism? I have previously tried to diagram some of computer scientist Vaughan Pratt’s notions, such as a Duality of Time and Information and the Stone Gamut. Another recent attempt is the diagram above of four transformations that issue out of his analysis of Chu Spaces. Pratt’s conceptualization of these generalized topological spaces led him to propose a mathematization of mind and body dualism.
The duality of time and information was actually an interplay of several dualities, such as the aforementioned time and information, plus states and events, and changing and bearing (or dynamic and static). The philosophical mathematization in his paper “Rational Mechanics and Natural Mathematics” leads to additional but somewhat different dualities, shown in the following table:
Mind
Body
Mental
Physical
States
Events
Anti-functions
Functions
Anti-sets
Sets
Operational
Denotational
Infers
Impresses
Logical
Causal
Against time
With time
Menu
Object
Contingent
Necessary
Pratt reveals two transformations that are “mental”: delete and copy, and two that are “physical”: adjoin and identify.
These four transformations are functions and their converses which:
Identify when the function is not injective.
Adjoin when the function is not surjective.
Copy when the converse is not injective.
Delete when the converse is not surjective.
Ordinarily we think of mind and body as being radically different in kind, but perhaps they are the same but merely viewed from a different perspective or direction. Recall what Heraclitus says, “the road up and the road down are the same thing”.
The states of a computing system bear information and change time, while its events bear time and change information.
Here we have three duals:
