[Inquiry] Logic As Formal Semiotic

[Jon Awbrey]

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LAFS.  Note 8

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The definition of a "sign" as a thing involved in a
specific kind of triadic relation, a "sign relation",
is one that Peirce gives pursuant to his definition of
logic as "formal semiotic", that is, as a formal theory
of signs.

Further details on how the definition of a sign relation
bears on the conception of logic as formal semiotic can
be found by examining the following two variant texts:

| On the Definition of Logic [Version 1]
|
| Logic will here be defined as ''formal semiotic''.
| A definition of a sign will be given which no more
| refers to human thought than does the definition of
| a line as the place which a particle occupies, part
| by part, during a lapse of time.  Namely, a sign is
| something, ''A'', which brings something, ''B'', its
| ''interpretant'' sign determined or created by it, into
| the same sort of correspondence with something, ''C'',
| its ''object'', as that in which itself stands to ''C''.
| It is from this definition, together with a definition
| of "formal", that I deduce mathematically the principles
| of logic.  I also make a historical review of all the
| definitions and conceptions of logic, and show, not
| merely that my definition is no novelty, but that my
| non-psychological conception of logic has ''virtually''
| been quite generally held, though not generally
| recognized. (C.S. Peirce, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is ''formal semiotic''.  A sign is something, ''A'', which
| brings something, ''B'', its ''interpretant'' sign, determined
| or created by it, into the same sort of correspondence (or
| a lower implied sort) with something, 'C', its 'object',
| as that in which itself stands to 'C'.  This definition
| no more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver,
| will support criticism of Weierstrassian
| severity, and that is perfectly evident.
| The word "formal" in the definition is
| also defined.  (C.S. Peirce, NEM 4, 54).
|
| ''The New Elements of Mathematics'', Volume 4,
| Carolyn Eisele (ed.), Mouton, The Hague, 1976.

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