Re: Laws of Form

I’m making an effort to present this material in a more gradual and logical order than I’ve ever managed to do before.  There are issues about the relationship between episodic and semantic memory that are giving me trouble as I try to remember how I came to look at things the way I do … but never mind that now.  I’ll eventually get around to explaining the forces that drove me to generalize the forms of logical graphs from trees to cacti, as graph theorists call them, and how that made the transition to differential logic so much easier than it would have been otherwise, but I think it would be better now to begin at the beginning with the common core of forms introduced by CSP and GSB.

Here’s a couple of articles I wrote for that purpose:

• Logical Graphs
• Propositional Equation Reasoning Systems

There are versions of those articles at several other places on the web which may be better formatted or more convenient for discussion:

• Logical Graphs (Wikiversity)
• Logical Graphs (Inquiry Blog) • (1) • (2)

One big issue arising at the beginning is the question of “duality”.  Both C.S. Peirce and Spencer Brown understood they were dealing with a very abstract calculus, one which could be interpreted for the purposes of ordinary propositional logic in two different ways.  Peirce called the two different ways of interpreting the abstract graphs his entitative and existential graphs.  He started out with a system of graphs he opted to interpret in the entitative manner but switched over to the existential choice as he developed his logical graphs beyond the purely propositional level.  Spencer Brown elected to emphasize the entitative reading in his main exposition but he was very clear in the terminology he used that the forms and transformations themselves are independent of their interpretations.

Table 1 at either of the locations linked below has columns for the graph-theoretic forms and the parenthesis-string forms of several basic expressions, reading them under the existential interpretation.

• Table 1. Syntax and Semantics of a Calculus for Propositional Logic • (a) • (b)

The Tables linked below serve to compare the existential and entitative interpretations of logical graphs by providing translations into familiar notations and English paraphrases for a few of the most basic and commonly occurring forms.

• Table A. Existential Interpretation
• Table B. Entitative Interpretation
• Table C. Dualing Interpretations

cc: Cybernetics • Laws of Form • Ontolog • Peirce • Structural Modeling • Systems Science