*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.

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