Jeff,
I have merely varied the phrase, the point is the same. Icons are in the "I" of the Interpreter.
Any two things in the universe of discourse X are alike in some way or another, if only in the most
trivial way of belonging to the same universe of discourse X. So anything s is potentially an icon
of anything o. All it takes is for s to determine its interpretant i by virtue if a quality that s
shares with o.
"Anything whatever, be it quality, existent individual, or law, is an Icon of anything, in so far as
it is like that thing and used as a sign of it." (CP 2.247)
The critical question, the one that requires us to leave the realm of
trivialities is this:
By virtue of what likeness exactly between s and o does s determine the i it does in a given moment
of interpretation that constitutes the elementary sign-relation (o, s, i).
Those are the generalities. Our more specific question at the moment has to do with the respect in
which a string of syntax like "x is a giver to y of z" resembles either of these two formal objects:
1. The single ordered triple (Paris, Aphrodite, The Golden Apple).
2. The set of ordered triples (x, y, z) over a given universe X for which x is
a giver to y of z.
The quality of iconicity is notably strained as the case falls from 1 to 2.
Regards,
Jon
Jeffrey Brian Downard wrote:
Jon, List,
In your response, I take you to be clarifying your earlier statement: "Some people like to think of these as "icons" of triadic sign relations, but they are less icons
than mnemonic devices that just barely serve to jog our collateral knowledge of their referents, only if we do indeed have that knowledge, and only if we know the key, the stylistic conventions
that were used to create them." I was trying to resist some implications that might follow from saying that they are just "mnemonic devices."
If my reading of the general tenor of what you are saying is on track, then I agree with
what you say in the clarification (or, I think I do). Having said that, I do want to
emphasize the distinction between the account of the categories as it is used in the
semiotic theory, and the account of the categories as it is developed in the context of
the phenomenological theory. I take Peirce at his word when he says in "The Logic
of Mathematics: an Attempt to Develop my Categories from Within," that he is asking
what is required in the way of an account of the categories for the purposes of refining
his logical theory. My assumption is that Peirce is drawing on the logical theory to
constrain the hypotheses he is formulating about the character of the formal categories
as they are being articulated in the context of a phenomenological theory. He is asking:
what assumptions must I make for the sake of the explanations I've already given in my
theory of logic?
As far as I can tell, the distinction between reference to a ground, reference
to an object and reference to an interpretant supplies the core of the ideas
needed for his account of the formal elements in all experience. At this
point, I'm not able to make out how the phenomenological account of the
categories fits into your reconstruction of the argument of the 1870 Logic of
Relatives. At this point, I haven't yet seen all of the story you're wanting
to tell.
I made a comment in an earlier post on the interpretation of a largely unintelligible fragment of
handwriting in one of Peirce's MS to the effect that he might mean something quite specific when he
uses the term Appearance with a capital "A." My guess is that he is referring quite
directly to Kant's claim that the formal character of the manifold of intuition is that it is a
homogeneous manifold. At some point in the future, I'd like to take up some questions with you
about the possible implications of this idea for our understanding of what Peirce means when he
talks about the categories as being introduced for the sake of unifying the "manifold of
experience."
For now, I'll just wait until I see more of your reconstruction and explanation of the 1870 Logic of relatives before trying to dig further into these questions.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
________________________________________
From: Jon Awbrey [[email protected]]
Sent: Monday, April 07, 2014 2:02 PM
To: Jeffrey Brian Downard
Cc: Sungchul Ji; Peirce List
Subject: Re: de Waal Seminar : Chapter 5. Semeiotics, or the Doctrine of Signs
Jeff,
There's a rather long history of people borrowing Peirce's terminology while
leaving his definitions
and methods behind. I see that fine old tradition has now been extended to
category theory, graph
theory, and who knows what else.
The full title of Peirce's 1870 Logic of relatives is “Description of a
Notation for the Logic of
Relatives, Resulting from an Amplification of the Conceptions of Boole's
Calculus of Logic”. From
the very beginning Peirce is clear about the distinction in semiotic roles
between what plays the
role of a "notation" (a calculus, a language, or any brand of syntactic system)
and what plays the
role of the object domain that is thereby denoted. Relative terms (rhemes or
rhemata) are pieces of
notation in the sign domain. As are logical graphs (entitative or
existential). The structure of a
syntactic expression does convey information about the structure of the
relation it denotes, and
maybe its okay to call the formula "iconic" on that account, so long as you
don't forget the great
differences between a single string of syntax and a whole collection of tuples
that constitutes the
extension of the relation in question.
A good notation is a very handy thing, but only so long as you remember that it
is notation.
Otherwise nothing but confusion reigns ...
Regards,
Jon
Jeffrey Brian Downard wrote:
Sung, Jerry, List,
I understand that we are using somewhat different language and graph systems as bases for
understanding Peirce's arguments in his phenomenology and semiotics. Jon has suggested
that Peirce's different ways of diagramming these relations are hardly more than hints of
ideas, so we should be careful about how much we derive from one or another manner of
representing these things graphically. I want to resist Jon's suggestion. As such, let
me try to restate the question. Given your way of putting things, let me ask the
following question: is there anything that is obscured if you assume that there is an
"internal node" at the heart of every elementary relation? I am suggesting
that any graphical system, including the one that you have formulated or a bipartite
system of graphs that allows nodes to be connected to several lines (i.e. edges,
relations, etc.) will run the risk of obscuring things that Peirce wanted to analyze
further.
I recognize that you and Jerry seem to have different dispositions towards the
way Peirce is using graph theory to analyze these things. You are saying that
your system is equivalent to Peirce's and that it expresses the heart of what
he is really trying to say. Jerry, on the other hand, seems to suggest that
Peirce is hamstrung by limitations that have their source in outmoded 19th
century ways of thinking about and graphing chemical relations.
So, let me try to state the question I've been trying to push as a challenge.
For those who think that the most elemental relations can be understood as a
node with one, two or three relations jutting out from it (such as you have
characterized them in your diagrams, and as the nodes and edges are
characterized in the example of the bipartite graph on the WikiPedia site I
referred to earlier), are you able to articulate the basic points Peirce is
making against Kempe's analysis of mathematical form in your terms? My hunch
is that Peirce's arguments are valid, that they can be used against alternate
analyses of the reasonings--and that these alternate analyses fail because they
tend to obscure points about the elemental character of a triadic relation that
Peirce wanted to make as clear as possible.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
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