Changes

This section extracts the graph-theoretic content of the previous series of Tables, using it to illustrate the logical description, or ''intensional representation'' (IR), of graphs and digraphs.  Where the points of graphs and digraphs are described by conjunctions of logical features, the edges and arcs are described by differential features, possibly in conjunction with the ordinary features that depict their points of origin and destination.

This section extracts the graph-theoretic content of the previous series of Tables, using it to illustrate the logical description, or ''intensional representation'' (IR), of graphs and digraphs.  Where the points of graphs and digraphs are described by conjunctions of logical features, the edges and arcs are described by differential features, possibly in conjunction with the ordinary features that depict their points of origin and destination.

Because of the formal confound that I mentioned earlier, anchored in the essentially accidential circumstance that <math>\text{A}\!</math> and <math>\text{B}\!</math> and I all use the same proper names for <math>\text{A}\!</math> and <math>\text{B},\!</math> I cannot analyze the denotative aspects of the sign relations <math>L(\text{A})\!</math> and <math>L(\text{B})\!</math> without analyzing the corresponding parts of my own denotative conduct, namely, those actions of mine that involve parallel uses of the signs <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math> and <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}.\!</math> However, it will soon become obvious that I have not prepared the discussion at this point with the technical means it needs to carry out this task in any meaningful way.  In order to do this, it would be necessary to consider the common world <math>W =\!</math> <math>\{ \text{A}, \text{B}, {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \},\!</math> of the two sign relations as an initially homogeneous set and then to provide explicit logical features that mark the distinction between objects and signs.  For the sake of simplicity, I am putting these considerations off to a subsequent round of analysis.  On this pass, the denotative sections of each analytic scheme are filled in with what amount to inert proxies for the actual analyses to be carried out later.

Because of the formal confound that I mentioned earlier, anchored in the essentially accidential circumstance that A and B and I all use the same proper names for A and B, I cannot analyze the denotative aspects of the sign relations A and B without analyzing the corresponding parts of my own denotative conduct, namely, those actions of mine that involve parallel uses of the signs "A" and "B".  However, it will soon become obvious that I have not prepared the discussion at this point with the technical means it needs to carry out this task in any meaningful way.  In order to do this, it would be necessary to consider the common world W = {A, B, "A", "B", "i", "u"} of the two sign relations as an initially homogeneous set and then to provide explicit logical features that mark the distinction between objects and signs.  For the sake of simplicity, I am putting these considerations off to a subsequent round of analysis.  On this pass, the denotative sections of each analytic scheme are filled in with what amount to inert proxies for the actual analyses to be carried out later.

===6.27. Differential Logic and Group Operations===

===6.27. Differential Logic and Group Operations===