Theory Of Signs

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TOS.  Note 1

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Robert Marty and his "Semiotique et Communication" group at Perpignan
have put together this collection of 76 + 12 "definitions of the sign":

http://members.door.net/arisbe/menu/library/rsources/76defs/76defs.htm

It is customary in informal discussions to call things definitions
that are really more like partial glosses on the use of a term or
even just illustrations of its application in particular domains.
This is fine as long as everybody knows the difference, but not
everybody does, a circumstance that leads to a lot of needless
wrangling, mostly heedless of anything like a real definition.

For my part I can remember wondering for many long years why
I'd not seen anything like a real definition of anything so
important as a sign in Peirce's work -- it had simply never
crossed my mind to regard his various and sundry exemplary
illustrations as definitions in the formal sense -- until
I happened across the following couple of variants in his
'New Elements of Mathematics':

| 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'.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54, also available here:
|
| http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm
| http://members.door.net/arisbe/menu/library/bycsp/l75/ver1/01.htm
| http://members.door.net/arisbe/menu/library/bycsp/l75/ver2/l75main.htm
| http://members.door.net/arisbe/menu/library/bycsp/l75/ver2/l75frame.htm

More details on how the definition of a sign relation bears on
the definition of logic are given in the contexts of this text:

| 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 it
| 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.  (CSP, 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.  (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.

Jon Awbrey

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