## Thursday, February 27, 2014

### A Proof of Self-Proof; 4 of 15

Four Logical Quanta

Four quanta are of particular interest to logicians. Here I nickname them the quanta of Self-Doubt, Self-Shame, Self-Pride and Self-Trust.
The quantum of Self-Doubt says
“ ‘Is unprovable when quined’, is unprovable when quined.”
Or in other words: “This sentence is not provable.”
Or in other words: “Doubt me.”
It is the mathematical quantum of uncertainty. Its equation is:
D       =        not prv D

The quantum of Self-Shame says
“ ‘Is refutable when quined’, is refutable when quined.”
Or in other words: “This sentence is provably false.”
Or in other words: “Refute me.”
It is the mathematical quantum of error. Its equation is:
S        =        prv not S

The quantum of Self-Pride says
“ ‘Is irrefutable when quined’, is irrefutable when quined.”
Or in other words: “This sentence is possible.”
Or in other words: “Tolerate me.”
It is the mathematical quantum of power. Its equation is:
P        =        not prv not P

The quantum of Self-Trust says
“ ‘Is provable when quined’, is provable when quined.”
Or in other words: “This sentence is provable.”
Or in other words: “Trust me.”
It is the mathematical quantum of certainty. Its equation is:
T        =        prv T

The quantum of self-doubt is also known as a Gödelian sentence. It is literally a paradox, for it calls itself beyond belief. The quantum of self-trust is also known as a Henkin sentence (after the man who asked if it is true) or a Löbian sentence (after the man who proved that it is). The quanta of self-shame and self-pride are unclaimed, for good reason.