Theme:
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14286
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14290
GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/14313
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14350
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14351
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14352
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14359
GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/14383
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/14388
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14394
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14409
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14422
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14433
JBD:http://permalink.gmane.org/gmane.science.philosophy.peirce/14434
BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/14435
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14436
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/14437
FS:http://permalink.gmane.org/gmane.science.philosophy.peirce/14444
Dear Frederik,
That accords with my understanding. In this usage, "generic" and "genuine" are
near synonyms, so a generic sign is a genuine sign, and that is simply a symbol.
A symbol is that which satisfies the bare definition of sign in a sign
relation, with no adornments or added axioms, or if it has additional properties
they are not relevant to its role as a symbol pure and simple.
Not too coincidentally, this bears on the caution that mathematicians are taught
to exercise with regard to diagrams, meaning initially the concrete pictures of
mathematical objects that we construct in various media but extending also to
any orders of representation that are more concrete than the intended object.
When we set out to prove theorems that are true of all triangles, for example,
we need to show what follows logically from the relevant axioms and definitions.
We naturally tend to reason by way of examples and so we draw an illustrative
figure that is "representative", and that in a double sense, being an icon of a
particular mathematical object that is "elected" or selected to represent its
"constituency", the general population of all triangles at large. Elections
have consequences, or so they say. If our representative, for all its obvious
charisma, is too beholden to special interests, then we find ourselves at risk
for much deception and self-deception in the consequences of our choice.
The point of the New Elements is that all the same considerations and cautions
apply to the prospective theory of signs as applied to the established theories
of geometries.
Regards,
Jon
Frederik Stjernfelt wrote:
> Dear Jon, lists, Peirce use the concept "degenerate" in his sign theory in
> analogy to the geometric sense of the term. Referring to conic sections,
> certain sections are generic (hyperbolas, ellipses) while other sections are
> degenerate because corresponding to non-generic cases where one or more
> variables vanish (parabolas, circles, crossing lines, point). Thus,
> degenerate cases only exist as limit cases of generic ones - (but there is
> nothing "impure" in being a circle …). Thus, isolated icons and indices
> exist, but only as limit cases of symbols - of which full, general
> propositions constitute the center category (this is paraphrasing
> the Kaina Stoikheia from memory). Best F
>
> Den 27/09/2014 kl. 06.00 skrev Jon Awbrey:
>
> Pure Icon and Pure Index. What in the world could those be?
> And how could a "degenerate" something be a "pure" anything?
> And while we're at it, must there also be pure symbols, too?
>
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