Cf: Mathematical Method • Discussion 3
Here's a revision, hopefully clearer, of a previous comment on
the Peirce List, part of a discussion stemming from John Sowa's
citation of an article by Carolyn Eisele.
Eisele, C. (1982), “Mathematical Methodology in the Thought
of Charles S. Peirce”, Historia Mathematica 9, pp. 333–341.
Auke van Breemen wrote:
AvB: It seems to come down to: never consider the textual production
of a scientist only in itself, but also look at the reality the text
tries to explain.
I took this as an admirably succinct statement of the difference
(1) scriptural hermeneutics — I'd call it “corpus hermeneutics”
except for the risk of confusion with Corpus Hermeneticum — and
(2) scientific interpretation, that is, any development of
interpretant texts in relation to an independent object domain
with the aim of forming true descriptions or gaining knowledge
of that domain.
What I wrote in response to Auke was this:
We interpret texts
in relation to
the object in view.
All I did there was mention the three roles in a sign relation.
We take in texts or whole bodies of work as signs of an object
domain and we form interpretive texts as signs of the same domain.
For my part, I interpret Peirce's work as signs of an object world,
one with respect to which other writers, artists, signifactors of
all sorts have generated signs worthy of our interpretation.
I wouldn't take the words “in view” too literally. I just as
easily could have said “at hand” or “in mind” but I went with
“object in view” on account of the fondness one of my old
teachers had for Dewey's signature “end in view”. As far as
indicial signs are concerned, we're all embroiled in concernful
situations all the time, making our selves the initial signs of
those pragmata, from which we derive all the remainder.
Peirce's distinction between theorematic and corollarial reasoning
has come up before. From what I recall of previous discussions, we
should not read the word “theorematic” in too reductive or purely
deductive a sense. Years ago it was something of a commonplace,
even outside Peircean circles, to call attention to the etymology
of “theorem” as having an observational, even “visionary” sense,
cognate with “theatre”, and some would even point to the sacred
origins of theatre, though maybe that's a bridge too far ...
As far as the iconic aspects of mathematics go, or even our knowledge
representations in general, they are nice when we can get them, but I'm
careful not to stress them too far — it's too easy to “fall victim to a
picture”, in Wittgenstein’s phrase, or succumb to the short-sightedness
of Russell's isomorphism theory of knowledge. Icons are specializations
of symbols and thus fall short of symbols' full potential. There is more
to science than serving as a mirror of nature.