Punch Card Principles

A logical proposition is a logical formula that has a truth value. Allow P and Q to be propositions, then the tables listed below show the resulting compound formulae truth values as a function of their components.

The circle represents true and the black dot represents false.

Switch It Up

Both prefix and postfix notation are more efficient than infix notation because parenthesis need not be used.

Infix To Prefix

∀X{[¬ (P)] ⇒ (X = X)}

¬ ( P )

¬P

X = X

=XX

[¬P]⇒(=XX)

⇒[¬P](=XX)

⇒[¬P](=XX)

⇒¬P=XX

∀X{⇒¬P=XX}

∀X⇒¬P=XX

∀X⇒¬P=XX

Infix To Postfix

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}

W ∈ Z

WZ∈

W = X

WX=

W = Y

WY=

(WX=) ∨ (WY=)

 (WX=)(WY=)∨

 (WX=)(WY=)∨

WX=WY=∨

(WZ∈) ⇔ [WX=WY=∨]

 (WZ∈)(WX=WY=∨)⇔

 (WZ∈)( WX=WY=∨) ⇔

WZ∈WX=WY=∨⇔

∀W{WZ∈WX=WY=∨⇔}

{WZ∈WX=WY=∨⇔}∀W

{WZ∈WX=WY=∨⇔}∀W

WZ∈WX=WY=∨⇔∀W

∃X(WZ∈WX=WY=∨⇔∀W)

∃XWZ∈WX=WY=∨⇔∀W

∃XWZ∈WX=WY=∨⇔∀W

WZ∈WX=WY=∨⇔∀W∃X

∀Y[WZ∈WX=WY=∨⇔∀W∃X]

∀YWZ∈WX=WY=∨⇔∀W∃X

∀YWZ∈WX=WY=∨⇔∀W∃X

WZ∈WX=WY=∨⇔∀W∃X∀Y

∀X{WZ∈WX=WY=∨⇔∀W∃X∀Y}

∀XWZ∈WX=WY=∨⇔∀W∃X∀Y

∀XWZ∈WX=WY=∨⇔∀W∃X∀Y

WZ∈WX=WY=∨⇔∀W∃X∀Y∀X

WZ∈WX=WY=∨⇔∀W∃X∀Y∀X

Thought Mechanics

Can "Moonlight Sonata" be played on piano or organ, or both? Regardless of the instrument, is the composition not the same? Or at the very least, does the composition not hold the same essence from instrument to instrument? If your answer is yes, then you must concede there is something to be abstracted. Do ideas not dance on the strings of the brain? Why then can the music of the mind not play on a different instrument?

"An idea can be in more than one place at a time." David R Andrews 2010

Symbols 101: How To Build A Fire

∀X{[¬ (P)] ⇒ (X = X)}   Given

∀X{[¬ (P)] ⇒ (X = X)}   A4
∀X{[¬ (P)] ⇒ (X = X)}   F1
∀X{[¬ (P)] ⇒ (X = X)}   F2
∀X{[¬ (P)] ⇒ (X = X)}   F6

∀X{[¬ (P)] ⇒ (X = X)}

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}    Given

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     A4
∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     A4
∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     F3

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     A8

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     F5
∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     F6
∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     F7
∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     F6
∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}     F6

∀X{∀Y[∃X(∀W{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]}         

∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      Given

∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      A8
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      A4
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      A4
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      F3
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      F5
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      F7
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      F6
∀X[∀Y(∃Z{(W ∈ Z) ⇔ [(W = X) ∨ (W = Y)]})]      F6