A Thought Is A Thing

Sunday, August 16, 2015

Propositional Calculus 0

RULES:

(Ax) Axiom:

Every axiom is a theorem.

(MP) Modus Ponens:

For all wff's P and Q, if P is a theorem and P ⇒ Q is a theorem, then Q is a theorem.

(Sub) Substitution:

For each K, R , and L, if R is a theorem, K is a component of R, and L is a wff, then the propositional form obtained by replacing in R every occurrence of K by L is a theorem.

DEFINITIONS:

A wff is a theorem iff it is obtained using rules Ax, MP, and Sub.

For all wff's P and Q, F1 through F5 are also wff's. Only strings of symbols built from variables using F1 through F5 can be wff's.

F1: ¬P

F2: P ⇒ Q

F3: P ∧ Q
F4: P ∨ Q
F5: P ⇔ Q

Transmutation

Thursday, August 13, 2015

Thought Mechanics 3

Y = { y | x is an intelligible frequency, y is a character, and x ∈ y} (whether or not x arises from an internal or external source is irrelevant). Also, each y in Y is a set and each x is a Fourier series possessing both timbre and content.

Define t to be a thought, and T to be a theory of Y or any subset of Y. If Yn is the nth subset of Y and Ym the mth subset of Y where m and n are natural numbers, then ( c , r ) forms a relation on Yn cross Ym (The Cartesian product). This means that Yn is the source of call c and Ym the source of response r. For each element ( c , r ), let c , r ∈ { t , T }. So, c is either a thought or a theory and r is either a thought or a theory.

If n = m, then Yn = Ym. In other words, character Yn = Ym = y both calls and responds to itself. If the locus (center/subset) of y is capable of forming a relation ( c , r ) on y cross y such that c is a T of y, then y is self-aware. If a character y cannot form a relation ( c , r ) on y cross y where c is a T of y, then that set is not self-aware.

Finally, the cardinal number of a set K is the number of unique elements in K. If K is a subset of Y and the cardinal number of K is greater than any other subset of Y, then K is called the primary locus of Y. A primary locus need not be self aware.

The body is the instrument upon which the soul is played. Is the frontal lobe, a possible locus of Y or even the primary locus, capable of sending and receiving signals to itself and even theorizing about itself hence a locus of consciousness?