Joe, list,
I do want to belatedly comment on this provocative post. The dependency of
the symbol on the interpretant is, it seems to me, rather strictly limited.
While symbols are arbitrary in some sense, Peirce does not contemplate a
free play of semiotic exchange, limited only by, as Rorty might say, what is
rhetorically convincing.
Rather, every symbol refers more or less directly to an icon and every
symbol refers. . . to a real object through an index. Every symbol.
Further, as interpretants, we are able to meaningfully use symbols in
communicating with one another because we are embedded in a ground of shared
reactional experiences.
Interpretation is, therefore, sharply constrained by such referentiality
and by the additional constraints of shared reactional experiences. Further,
symbols are ultimately more dependent on iconicity and indexicality than
upon any whims or vagaries of interpretants.
Creath Thorne
Joseph Ransdell writes:
Considered as an introduction to a book on mathematical reasoning, the New
Elements is probably best regarded as incomplete because Peirce does not in
fact get around to saying anything specifically about that sort of reasoning
except for the definition in Part II of "diagram", which is important but is
not followed up in Part III although some groundwork is laid for doing do.
If the introduction were complete I would expect Peirce to have gone ahead
to a Part IV in which the distinction between corollarial and theorematic
deduction is drawn, and the differing role of the diagram in the two kinds
of deduction is explained, and if not there then in still another new part
there would be other things to be explained, too, at least briefly, as, for
example, the peculiarly hypothetical status of distinctively mathematical
reasoning. But since, as it stands, there is actually very little in the
New Elements which seems to be designed specifically to explain or provide
the logical basis for understanding the nature of mathematical reasoning in
particular, I conclude that it is simply incomplete and therefore best
understood in respect to what Peirce actually does accomplish, or at least
attempt to accomplish as far as he got with it.
Looking at it that way, it seems to me, then, that the question is, what is
Part III about? What is it mainly attempting designed to accomplish? And I
would say that Peirce is mainly attempting there to make clear to the reader
what is implicit in understanding a symbol as essentially dependent on its
interpretant for its identity as the particular symbol it is. The
peculiarity of the symbol is that no conclusion can be drawn as to what it
is, as a symbol, on the basis either of an intrinsic characteristic of it,
or on the basis of it as something in existential relationship with other
entities. It is essentially dependent on its interpretant for its identity
as a symbol, which supplies what is missing in the symbol itself considered
as replicated in something which has no properties of its own, qualitative
or existential, that account for its meaning.
This is what makes semiosis essentially dialogical: the actually occurring
sign is "hostage to the future" in the sense that, apart from what its
interpretant can do for it, it is meaningless and is not really a symbol at
all. (See Thomas Riese's recent message on this in the interchange with
Gary Richmond.) Contrary to what some interpreters of Peirce think, there
is no implication in this that it is hostage to some infinitely remote
interpretant: any authentic interpretant of it will do, provided it is an
interpretation of it as significant in the sense of being connotative or
having sense or logical intension (i.e.. signifying a quality or character).
If it is an interpretation of it as denotative or referential (having
logical extension) it must, as a matter of logical priority, already be
significative connotationally. And this is true of it a fortiori if it is
an interpretation of it as propositional since that presupposes referential
interpretation. So if we suppose that a given symbol actually has been
replicated in a sinsign occurrence, we are supposing that an authentic
interpretant of it either has occurred or will occur.
Nevertheless, Peirce also wants to make clear, before going into the special
considerations involved in understanding mathematical representation and the
way symbolism works in that respect, that the critically reflective symbol
user should understand that there is indeed the promise of an infinitude of
prospective future interpretation to be taken duly into account, the
practical import of which is that the critical interpreter will understand
that there is indeed a potentially infinitely interpretational future
implicit in the symbol which precludes the possibility of absolute certainty
that interpretation of it at any given time is not mistaken. And he seems
especially concerned to convey the understanding that the relation of the
symbol to its interpretant is driven by the symbol itself, which cannot be
itself other than in its transference of its own identity to the sign that
interprets it, which must therefore also be a symbol with the same absolute
need to reproduce itself in its offspring in order to be what it is.
Now all of this is paradoxical -- seemingly incoherent, in fact -- since it
seems to say at once that the symbol is essentially at the mercy of the
interpretant and that it is itself responsible for what the interpretant is.
The conception which he relies upon here for explicating this idea in such a
way as to show that it may be paradoxical but is not really incoherent --
for Peirce certainly is not aiming at being perceived as the sort of
romantic nihilist who celebrates incoherence as a good higher than reason
(much less as a higher form of reason) -- is the concept of determination,
which is why it seems to me to be an unusually important paper in spite of
its often puzzling character. It is the only account I know of in which the
concept of determination is discussed so closely in connection with the
notion of causation, and the only place I know of where he relates his view
to the Aristotelian four-fold causal analysis. (I am especially interested
in it myself for just this reason since I put in quite a lot of time, a good
many years back, in some unpublished stuff, in trying to see if I could
accommodate the Aristotelian fourfold analysis within Peirce;s account of
semiosis, as I had reconstructed that. I distributed some of that on
PEIRCE-L a few years ago but I had not read the New Elements at that point
and could make no comparison then. I'll have to dig back into that as soon
as I get the time to see if it agrees with Peirce's own account or not, but
I haven't tried that yet.)
Part III ends, then, after some exploration of the apparent paradoxes which
this being in futuro of the symbol harbors within it, and it would perhaps
be in a missing Part IV that the account of the role of iconicity implicit
in the conception of symbolism would be explained in such a way as to throw
light on the nature of mathematical reasoning in particular. It is, I
think, made clear enough that the conception of the symbol cannot be
understood without understanding the role of the icon in its functioning in
semiosis, but precisely how it functions therein is only sketched out
minimally in this paper as it stands.
So it seems to me that the best bet interpretationally is to proceed as if
Part III of the New Elements is all there is to it and see what it adds up
to on that assumption. I am not, of course, dictating how anybody else is
to interpret it but just describing my own view.
Joe Ransdell
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