Jon Awbrey
Registered: Feb 2004
Posts: 557 
Sign Relations  Commentary
SR. Commentary Note 2
I record here my analysis of one of Peirce's
definitions of a sign relation that I gave
a few years back.
Here are two versions of the definition,
given in the context of defining logic:
 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 nonpsychological conception of logic has
 'virtually' been quite generally held, though not
 generally recognized. (CSP, NEM 4, 2021).

 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,
 Carolyn Eisele (ed.), Mouton, The Hague, 1976.

 Also available at the Arisbe website:
 http://members.door.net/arisbe/menu...csp/l75/l75.htm
Here is an extract of the second version:
 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'.
It is important to note that the "correspondence" referred to here is
a "triple correspondence", what might be called a "3place transaction"
in database terms. Let us refer to this 3place relation as L. To say
that "A brings B to correspond with C in the same way that A corresponds
with C" is simply to say that A brings B into the same 3place relation L
with something else B' and C, in that order, as A occupies in the 3place
relation L with B and C, in that order.
To make this clearer, I will draw out the inference over several steps:
Using the acronym "SOC" for "sort of correspondence",
I form the following paraphrase of the main condition:
 A brings something into the same SOC with C
as the SOC in which A stands to C.
In order to expand the expression correctly, one has to ask:
 What is the SOC in which A stands to C?
The SOC in which A stands to C is given by Formula 1.
1. A brings something into some SOC with C,
 namely, the SOC in which A stands to C.
If B enters into the same SOC with C as A stands in, that is to say,
if B takes up the same role that A had in Formula 1, then we obtain:
2. B brings something into some SOC with C,
 namely, the SOC in which A stands to C.
Let us suppose that B' is the something in Formula 2.
Now, B' can either be something old or something new.
If B' is something old, then it belongs to {A, B, C}.
If B' is something new, we leave it with the name B'.
In any case, we have:
3. B brings a thing B' into some SOC with C,
 namely, the SOC in which A stands to C.
In sum, the bringing of a new, possibly old, thing
into the relation is part of being in the relation.
Jon Awbrey

Last edited by Jon Awbrey on 01062005 at 09:08 PM
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