Animated Logical Graphs • 68

Re: Animated Logical Graphs • (14)(15)(16)(17)(18)(19)(20)(21)
Re: Ontolog ForumMauro Bertani

Dear Mauro,

Let’s take a another look at the Table we reached at the end of Episode 21.

Formal Operation Table (a,b)

I call it a Formal Operation Table — rather than, say, a Truth Table — because it describes the operation of mathematical forms preceding the stage of logical interpretation.  I know the word formal tends to get overworked past the point of semantic fatigue but I can still hope to revive it a little.  We’ll use other labels for Table entries at other times but I tried this time to mitigate interpretive bias by choosing a mix of senses from both Peirce and Spencer Brown. 

Entering the stage of logical interpretation, we arrive at the following two options.

  • The entitative interpretation of \texttt{(} a \texttt{,} b \texttt{)} produces the truth table for logical equality.

En (a,b)

  • The existential interpretation of \texttt{(} a \texttt{,} b \texttt{)} produces the truth table for logical inequality, also known as exclusive disjunction.

Ex (a,b)

Resource

cc: Cybernetics (1) (2) • Peirce (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
cc: Ontolog Forum (1) (2) • Structural Modeling (1) (2) • Systems Science (1) (2)
cc: FB | Logical GraphsLaws of Form

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Animated Logical Graphs • 68

  1. Poor Richard says:

    I’m still thinking of which comes first, logic or math.  Isn’t it like the chicken and egg?

  2. Jon Awbrey says:

    I see them as more like Yggdrasill (math) and Ratatoskr (logic).

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.