Re: Animated Logical Graphs


Cf: Animated Logical Graphs • 66

Re: Richard J. Lipton • The Art Of Math
Re: Animated Logical Graphs


Once we bring the dual interpretations of logical graphs to the
same Table and relate their parleys to the same objects, it is
clear we are dealing with a triadic sign relation of the sort
taken up in C.S. Peirce’s “semiotics” or theory of signs.

A “sign relation” L ⊆ O × S × I, as a set L embedded in a
cartesian product O × S × I, tells how the “signs” in S
and the “interpretant signs” in I correlate with the
“objects” or objective situations in O.

There are many ways of using sign relations to model
various types of sign-theoretic situations and processes.
The following cases are often seen.

• Some sign relations model co‑referring signs or transitions
between signs within a single language or symbol system.
In that event L ⊆ O × S × I has S = I.

• Other sign relations model translations between different
languages or different interpretations of the same language,
in other words, different ways of referring the same set of
signs to a shared object domain.

The next Table extracts the sign relation L ⊆ O × S × I involved
in switching between existential and entitative interpretations
of logical graphs.

Table. Peirce Duality as Sign Relation (also attached)

• Column 1 shows the object domain O as the
set of 16 boolean functions on 2 variables.

• Column 2 shows the sign domain S as a representative set
of logical graphs denoting the objects in O according to
the existential interpretation.

• Column 3 shows the interpretant domain I as the same set
of logical graphs denoting the objects in O according to
the entitative interpretation.


C.S. Peirce • Logic and Signs

C.S. Peirce • Logic as Semiotic

Sign Relation

Triadic Relation



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