Changes

==Logic as sign transformation==

==Logic as sign transformation==

We have been looking at various ways of transforming propositional expressions, expressed in the parallel formats of character strings and graphical structures, all the while preserving certain aspects of their "meaning" — and here I risk using that vaguest of all possible words, but only as a promissory note, hopefully to be cached out in a more meaningful species of currency as the discussion develops.

We have been looking at various ways of transforming propositional expressions, expressed in the parallel formats of character strings and graphical structures, all the while preserving certain aspects of their "meaning" — and here I risk using that vaguest of all possible words, but only as a promissory note, hopefully to be cached out in a more meaningful species of currency as the discussion develops.

I cannot pretend to be acquainted with or to comprehend every form of intension that others might find of interest in a given form of expression, nor can I speak for every form of meaning that another might find in a given form of syntax.  The best that I can hope to do is to specify what my object is in using these expressions, and to say what aspects of their syntax are meant to serve this object, lending these properties the interest I have in preserving them as I put the expressions through the paces of their transformations.

I cannot pretend to be acquainted with or to comprehend every form of intension that others might find of interest in a given form of expression, nor can I speak for every form of meaning that another might find in a given form of syntax.  The best that I can hope to do is to specify what my object is in using these expressions, and to say what aspects of their syntax are meant to serve this object, lending these properties the interest I have in preserving them as I put the expressions through the paces of their transformations.

|}

|}

The first way of transforming the expression that appears on the left hand side of the equation can be described as ''proof-theoretic'' in character.  This appeared in Note 35.

 

| [[Directory:Jon_Awbrey/Papers/Futures_Of_Logical_Graphs#Praeclarum_theorema|The first way of transforming the expression]] that appears on the left hand side of the equation can be described as ''proof-theoretic'' in character.

:* [http://stderr.org/pipermail/inquiry/2005-November/003214.html FOLG 35]

 

| [[Directory:Jon_Awbrey/Papers/Futures_Of_Logical_Graphs#Example|The second way of transforming the expression]] that appears on the left hand side of the equation can be described as ''model-theoretic'' in character.

The other way of transforming the expression that appears on the left hand side of the equation can be described as ''model-theoretic'' in character.  This appeared in Note 50.

 

What we have here amounts to a couple of different styles of communicational conduct, or conductive communication, if you prefer, that is to say, two sequences of signs of the form ''e''₁, ''e''₂, …, ''e''_''n'', each one beginning with a problematic expression and eventually ending with a clear expression of the appropriate ''logical equivalence class'' (LEC) to which each and every sign or expression in the sequence belongs.

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.