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What we have here amounts to a couple of different styles of communicative conduct, that is, two sequences of signs of the form <math>e_1, e_2, \ldots, e_n,\!</math> each one beginning with a problematic expression and eventually ending with a clear expression of the ''logical equivalence class'' to which every sign or expression in the sequence belongs.  Ordinarily, any orbit through a locus of signs can be taken to reflect an underlying sign-process, a case of ''semiosis''.  So what we have here are two very special cases of semiosis, and what we may find it useful to contemplate is how to characterize them as two species of a very general class.

What we have here amounts to a couple of different styles of communicative conduct, that is, two sequences of signs of the form <math>e_1, e_2, \ldots, e_n,\!</math> each one beginning with a problematic expression and eventually ending with a clear expression of the ''logical equivalence class'' to which every sign or expression in the sequence belongs.  Ordinarily, any orbit through a locus of signs can be taken to reflect an underlying sign-process, a case of ''semiosis''.  So what we have here are two very special cases of semiosis, and what we may find it useful to contemplate is how to characterize them as two species of a very general class. Ordinarily, any orbit through a locus of signs can be taken to reflect an underlying sign-process, a case of ''semiosis''.  So what we have here are two very special cases of semiosis, and what we might just find it useful to contemplate is how to characterize them as two species of a very general class.

 

Ordinarily, any orbit through a locus of signs can be taken to reflect an underlying sign-process, a case of ''semiosis''.  So what we have here are two very special cases of semiosis, and what we might just find it useful to contemplate is how to characterize them as two species of a very general class.

We are starting to delve into some fairly picayune details of a particular sign system, non-trivial enough in its own right but still rather simple compared to the types of our ultimate interest, and though I believe that this exercise will be worth the effort in prospect of understanding more complicated sign systems, I feel that I ought to say a few words about the larger reasons for going through this work.

We are starting to delve into some fairly picayune details of a particular sign system, non-trivial enough in its own right but still rather simple compared to the types of our ultimate interest, and though I believe that this exercise will be worth the effort in prospect of understanding more complicated sign systems, I feel that I ought to say a few words about the larger reasons for going through this work.

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This can be read as "not <math>p\!</math> without <math>q\!</math> and not <math>q\!</math> without <math>p\!</math>", or what's the same thing, <math>(p \Rightarrow q) ~\operatorname{and}~ (q \Rightarrow p).</math>

This can be read as <math>{}^{\backprime\backprime} \operatorname{not}~ p ~\operatorname{without}~ q ~\operatorname{and~not}~ q ~\operatorname{without}~ p {}^{\prime\prime},</math> in symbols, <math>(p \Rightarrow q) \land (q \Rightarrow p).</math>

Graphing the topological dual form, one obtains this rooted tree:

Graphing the topological dual form, one obtains the following rooted tree:

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