Hi Frederik, Gary F., Lists
I've been thinking a bit more about Frederik's account of optimal iconicity.
One point I'd like to note is that Peirce does not appear to use "optimal" when
talking about iconicity, at least not in the CP. He does, however, use
"perfect" as a modifier of iconicity. This shouldn't be surprising, given the
fact that the tradition in logic through the medieval period and up through
philosophers such as Leibniz and Kant think of perfection as a logical
principle that can be applied to any conception. Along these lines, I think
there is only one concept of humanity in Kant's writings on ethics and
aesthetics. There is only one conception even though he shows us how to form
an ideal based on the aesthetic perfection of the conception, the practical
perfection of the conception and the logical perfection of the conception. On
my reading of Peirce's account of iconicity, ideals such as the aesthetic ideal
of humanity are quite good examples of iconic representations that are taken to
perfection. I've collected a small number of quotes where Peirce talks about
perfection applied icons--or to the use of signs more generally. I think the
passages provide a sense of how he is applying the principle of perfection to
the the conception of the icon in mathematics, the existential graphs, and in
other (less formal) areas of inquiry.
Here are three passages:
For the "somethings," being indesignate, cannot be described in general terms.
It is necessary that the signs of them should be connected in fact. No way of
doing this can be more perfectly iconic than that exemplified in Fig. 78 (CP
4.442)
Logic may be defined as the science of the laws of the stable establishment of
beliefs. Then, exact logic will be that doctrine of the conditions of
establishment of stable belief which rests upon perfectly undoubted
observations and upon mathematical, that is, upon diagrammatical, or, iconic,
thought. (CP 3.429)
I may as well, at once, acknowledge that, in Existential Graphs, the
representation of Modality (possibility, necessity, etc.) lacks almost entirely
that pictorial, or Iconic, character which is so striking in the representation
in the same system of every feature of propositions de inesse. Perhaps it is in
the nature of things that it should be so in such wise that for Modality to be
iconically represented in that same "pictorial" way in which the other features
are represented would constitute a falsity in the representation. If so, it is
a perfect vindication of the system, upon whose accusers, I suppose, the burden
of proof lies. Still, I confess I suspect there is in the heraldic
representation of modality as set forth [below] a defect capable of being
remedied. If it be not so, if the lack of "pictorialness" in the representation
of modality cannot be remedied, it is because modality has, in truth, the
nature which I opined it has (which opinion I expressed toward the end of the
footnote [to 552], and if that be the case, Modality is not, properly speaking,
conceivable at all, but the difference, for example, between possibility and
actuality is only recognizable much in the same way as we recognize the
difference between a dream and waking experience, supposing the dream to be
ever so detailed, reasonable, and thoroughly consistent with itself and with
all the rest of the dreamer's experience. Namely, it still would not be so
"vivid" as waking experience. . . -- from "Phaneroscopy, {phan}," c.1906; part
of the manuscript used in 534n. (CP 4.553)
This fourth and last passage is full of really interesting suggestions:
Transuasion in its obsistent aspect, or Mediation, will be shown to be subject
to two degrees of degeneracy. Genuine mediation is the character of a Sign. A
Sign is anything which is related to a Second thing, its Object, in respect to
a Quality, in such a way as to bring a Third thing, its Interpretant, into
relation to the same Object, and that in such a way as to bring a Fourth into
relation to that Object in the same form, ad infinitum. If the series is broken
off, the Sign, in so far, falls short of the perfect significant character. It
is not necessary that the Interpretant should actually exist. A being in futuro
will suffice. Signs have two degrees of Degeneracy. A Sign degenerate in the
lesser degree, is an Obsistent Sign, or Index, which is a Sign whose
significance of its Object is due to its having a genuine Relation to that
Object, irrespective of the Interpretant. Such, for example, is the exclamation
"Hi!" as indicative of present danger, or a rap at the door as indicative of a
visitor. A Sign degenerate in the greater degree is an Originalian Sign, or
Icon, which is a Sign whose significant virtue is due simply to its Quality.
Such, for example, are imaginations of how I would act under certain
circumstances, as showing me how another man would be likely to act. We say
that the portrait of a person we have not seen is convincing. So far as, on the
ground merely of what I see in it, I am led to form an idea of the person it
represents, it is an Icon. But, in fact, it is not a pure Icon, because I am
greatly influenced by knowing that it is an effect, through the artist, caused
by the original's appearance, and is thus in a genuine Obsistent relation to
that original. Besides, I know that portraits have but the slightest
resemblance to their originals, except in certain conventional respects, and
after a conventional scale of values, etc. A Genuine Sign is a Transuasional
Sign, or Symbol, which is a sign which owes its significant virtue to a
character which can only be realized by the aid of its Interpretant. Any
utterance of speech is an example. If the sounds were originally in part
iconic, in part indexical, those characters have long since lost their
importance. The words only stand for the objects they do, and signify the
qualities they do, because they will determine, in the mind of the auditor,
corresponding signs. The importance of the above divisions, although they are
new, has been acknowledged by all logicians who have seriously considered them.
. . . (CP 2.92)
--Jeff
Dear Jeff, lists
>
> You've asked a series of questions.
>
> 1. Do list members find Frederik's notion of two kinds of iconicity of
> interest and value? If so, what is that value? It isn't clear to me what the
> value is of suggesting that Peirce is working with two notions of
> iconicity--despite Peirce's own efforts to develop a unified conception.
> I'll agree that there are a number of aspects that are involved in Peirce's
> conception of iconicity, and that we can draw on the EGs as a tool for
> clarifying some of the aspects that might be hard to articulate using other
> means. What is more, I accept that Peirce was motivated by the aim of
> developing an optimally iconic graphical logic. Frederik is clear that he
> takes himself to be refining Peirce's conception of the icon because he
> believes there are lingering confusions and vagueness in his conception.
> Having said that, I don't think that the separation between the two notions
> clarifies matters in the way I was hoping it might.
Which clarification did you hope for?
I do not speak about lingering confusions and vagueness. I think there are two
pretty precise, different conceptions. But no-one needs despair, as they need
not contradict one another. Peirce just does not make explicit the difference
between them - which I think it would be a service to Peirce scholarship to do.
One conception is what i call operational. It compares iconic representations
after which inferences may be made from them/ theorems may be proved from them.
Measured on this criterion, Peirce's Beta Graphs are equivalent to his Algebra
of Logic system of predicate logic ("logic of relations") of 1885. Optimality
comes into the question when Peirce compares the two representations and judge
Beta Graphs superior, not because they can prove more theorems, but because of
their higher degree of iconic representation of logic relations.
These are obviously two different conceptions. Operational iconicity seems
basic; optimality is an extra criterion introduced in order to distinguish
competing representations of the same content.
> 2. Also, what does one make of Frederik's notion that the introduction of
> would-bes greatly modifies Peirce's conception of Thirdness and that it
> enriches the pragmatic maxim in now involving real possibilities? I don't
> think that Peirce introduced a new concept of would-be's.
> This seems to imply that he didn't have a conception, and that he later saw
> there was something he had missed. Rather, he had an account of how we might
> interpret conditionals, and he later sees that his logical theory leads him
> to treats some arguments as bad that are really good (and vice versa). As
> such, he is modifying his semiotic theory and then revising his metaphysical
> account of real possibilities in light of revisions that he made in his
> theory of logic. I do agree that the revisions in his logical theory involve
> a developing sense of how we might understand the role of triadic
> relationships in semiotics.
>
It is generally assumed that Peirce only introduced "real possibilities" around
1896-97 - Max Fisch famously charted this as yet another step in the
development of Peirce's realism and even calls it the "most decisive single
step" in that development. "Would-bes" is another term for "real
possibilities". Later P himself made the famous self-criticism of his 1878
conception of pragmatism, now deemed too nominalist, the argument centered on
different interpretations of the hardness-of-the-untested-diamond example.
Best
F
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