[Inquiry] Re: Kaina Stoicheia -- Discussion

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

KS.  Discussion Note 5

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

JP = Jim Piat

Re: KS-DIS 4.  http://stderr.org/pipermail/inquiry/2005-December/003297.html
In: KS-DIS.    http://stderr.org/pipermail/inquiry/2005-December/thread.html#3272

Jim, Peirce List,

Replies interspersed.

JP: Would you give me an example of one of Peirce's genuine, necessary and sufficient,
    descriptions of a sign, and perhaps for the purpose of contrast one of his
    non-genuine definitions that fails to meet these criteria.  Also would
    you give me the necessary and sufficient conditions for discerning
    which is which.

I've given what I think is one of Peirce's better definitions of a sign relation.
It is by no means perfect, but it does provide enough of a basis to start up the
business of drawing necessary conclusions.  The nice thing about a good-enough
definition, if you catch my object-relational drift, is that it affords us
the ontological security to begin thinking for ourselves, as we may hope
to do in scientific inquiry, instead of constantly needing to run back
to our primal source for the assurance of some scriptural quotation
that we have not strayed from the path of right-group-thinking and
remain in conformity with the established doctrine, in that most
likely exaggerated caricature of the medieval seminary scholar,
but just as likely a graphic icon with a hint of truth to it.

As I've indicated, some of the descriptions that fall short of this standard
are those that rely on undefined psychological or sociological notions, for
all the possibility of their still being useful in application to specific
subjects, when taken with the due grain of salt.  Other descriptions that
tend to lead us astray are those that are afflicted with the residual
biases of essentialism, in spite of all the work that Peirce did to
make clear that the minimal unit of description is a sign relation,
not the isolated sign in itself, which is a meaningless concept.

With respect to the last part of your question, yes, we can give
a logically necessary and sufficient definition of "definition".
For instance, the following from Peirce will do as well as any:

| A 'definition' is the logical analysis of a predicate in general terms.

He immediately elaborates this definition of definition as follows:

| It has two branches, the one asserting that the definitum is
| applicable to whatever there may be to which the definition is
| applicable;  the other (which ordinarily has several clauses),
| that the definition is applicable to whatever there may be to
| which the definitum is applicable.  'A definition does not
| assert that anything exists.'
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 237
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.

What we cannot provide so easily is a definition of 'good' definition,
because that is more properly an applied, empirical, pragmatic matter,
not just a logical or a mathematical question.  Here we are "reduced"
to "holism", whereby only models as a whole of theories as a whole
can be judged by their empirical fertility and logical integrity.

To be continued ...

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o