SUO: Not Of Necessity (NON)
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A recent inquiry about my gloss on the functional particle "non",
as used by Peirce in his remark on the "non-psychological" nature
of his theory of signs, leads me to believe that some further bit
of clarification may be necessary. It is, above all, important to
distinguish Peirce's view from any sort of "anti-psychologism" with
which it might otherwise be confused. Indeed, it is from Peirce that
I came to acquire my own brands of "anti-anti-ism" and "anti-ism-ism".
Just for accuracy, I restate Peirce's original definitions and remarks:
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| 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.
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Just for context, I recite my earlier remarks:
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A "sign" is -- surprise! surprise! -- anything
at all that satifies a/the definition of a sign.
For pragmaticians, Peircean style, there are any
one of a number (76 to 88 the last time somebody
took the trouble to count) putative "definitions"
of a sign, but most sensible folks believe that
they all boil down to pretty much the same idea.
The most important feature of Peirce's concept
is that being a sign is not an absolute or an
essential property, but a relational property.
I have been working on the extensional side
of understanding sign relations, mostly just
because less careful work has been done from
that standpoint so far. Here, one views the
category or the variety of "sign relations"
much as one might view "groups", namely, as
a highly diverse family of 3-place relations,
satisfying an extremely simple definition or
a highly "non-categorical" axiom set, but
by no means being anywhere near as simple
as the definition might deceive one into
believing at the outset.
My personal best explanation so far is here:
| Second, Peirce's claim that his definition of a sign involves
| no reference to human thought means no necessary reference.
| The adjective "non-psychological" that he often attaches to
| this conception of signs and logic is not intended to be
| exclusive of human thought but to expand the scope of the
| concepts beyond it (Peirce, NEM 4, 21). The prefix "non"
| is better read as an acronym for "not of necessity," and
| is commonly used in mathematical discourse in just this way.
| It extends the use of a concept into wider domains than the
| paradigm cases upon which our original intuitions were formed.
|
| A definition of signs and their processes which is not limited
| by prior restriction to human psychology can be used to investigate
| human thought as a species of natural process. There is considerable
| power in this naturalistic viewpoint. It allows us to put human thought
| in a context of other sign processes, to ask what might be the specific
| differences that distinguish it, and to consider its evolution through
| different orders of complexity.
Full paper at:
http://www.chss.montclair.edu/inquiry/fall95/awbrey.html
I began to introduce these ideas to the SUO List here:
http://suo.ieee.org/email/msg00815.html
http://suo.ieee.org/email/msg00829.html
http://suo.ieee.org/email/msg00894.html
http://suo.ieee.org/email/msg01111.html
http://suo.ieee.org/email/msg01112.html
http://suo.ieee.org/email/msg01113.html
Just to extract the core from my personal
favorite one of Peirce's definitions:
| 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'.
|
| CSP, NEM 4, pages 20-21, & cf. page 54, also available at:
| http://www.door.net/arisbe/menu/library/bycsp/L75/L75.htm
A punctuation mark, space, character, sentence, paragraph, book,
rock, painting, sculpture, building, person, whole person's life,
the entire cosmos, and so on, can all be signs, of some "object",
that is, "objective" or "pragma", to some interpreter. Or not.
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Since the time that I adduced this material, initially
in response to one reader's feigned or real puzzlement
as to how we thinkers of a Peircean persuasion use the
term "sign", I have observed that some readers, well,
actually, the same reader, appear just as curiously
oblivious to the sense of the modal context that I
introduced through the use of the auxiliary "can",
the relational context that is marked throughout,
and the optative context that was qualified by
the closing comment "Or not", but I have come
to appreciate the fact that attentions waver,
and reading skills vary. It caint be helped.
Anyway, finally, here is my appended clarification:
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My remark was limited to a particular and, yes, slightly peculiar usage,
one that tends to come up more in describing collections of mathematical
systems that are subject to a variable set of axioms than in describing
the elements of a fixed domain. For example, a very common situation
occurs when folks have been discussing, say, the sort of structure
that is officially called an "algebra", say, X, which somewhere in
the list of its axioms contains an associative law -- in other words,
"for all x, y, z in X, x(yz) = (xy)z" -- and then they get bored with
that and decide to generalize the family of structures under review by
removing that axiom from the list. The new subject will then typically
be called "non-associative algebras". But note that all of the original
algebras fall under the heading of "non-associative algebras". This is
a longstanding usage that Peirce would have known quite well -- some of
the few theorems in math that still bear the Peirce's name are in the
field of non-associative algebras. Moreso in the 19th Century, they
used the word "mock" as a similar sort of analogizing or generalizing
functor, as memorialized in Lewis Carroll's (C.L. Dodgson's) Mock Turtle --
CLD is alluding to the issue of associativity here, as part of the joke
is over whether a Mock (Turtle Soup) is a (Mock Turtle) Soup. Ergot,
to summit up, mathematicians are some really strangely chirping birds.
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Many Reargards,
Jon Awbrey
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