Gary,
Can you combine elements of both heuristic efficiency and strong iconicity
through parenthesis and dotted lines?
v(........F.........)
The parenthesis place a limitation on the thought of the operation. The dotted
line suggests the identity of the operation throughout that limitation. I
realize that math notation desires substitution and the power of generality
over analytical detail.
Yet the thought is filled in by imagination. I have some trouble understanding
why the question of "extreme realism" must ride with strong iconicity.
Jim W
Date: Wed, 14 Jan 2015 16:32:20 -0500
From: gary.richm...@gmail.com
To: biosemiot...@lists.ut.ee
CC: Peirce-L@list.iupui.edu
Subject: [PEIRCE-L] Re: [biosemiotics:7869] Re: Natural Propositions: Chapter 8
Lists,
I'd like to continue this reflection on Frederik's discussion of iconicity in
existential graphs by considering a passage quoted by him, one which succinctly
states the purpose of EGs (NP, 271-18):
. . [The] purpose of the System of Existential Graphs, as it is stated in the
Prolegomena [4.533], [is] to afford a method (1) as simple as possible (that is
to say, with as small a number of arbitrary conventions as possible), for
representing propositions (2) as iconically, or diagrammatically and (3) as
analytically as possible. . .These three essential aims of the system are,
every one of them, missed by Selectives. ("The Bedrock beneath Pragmaticism"
[2], 1906, 4.561, note 1)
So, in a word, Peirce wants to make his graph system "as simple as possible" in
having a minimum of arbitrary conventions, and to represent propositions as
iconically and analytically as possible. This involves, firstly, preferring the
line of identity to selectives. But in consideration of his Beta graphs Peirce
finds that it not always possible or, rather, it is not always desirable to do
so in very complex graphs (for essentially visual and psychological reasons).
So, somewhat reluctantly, he substitutes selectives for identity lines in such
complex graphs. Frederik gives the reason for this reluctance:
The substitution of selectives for the line of identity is less iconic because
it requires the symbolic convention of identifying different line segments by
means of attached identical symbols. The line of identity, on the other hand,
is immediately an icon of identity because it makes use of the continuity of
the line. . . [and is also] a natural iconical representation of a general
concept [NP, 218].
Yet Peirce introduces selectives because in such complicated graphs "involving
many variables taking many predicates," the complex network of lines of
identity becomes visibly hard for the vision system of a human to handle
(Frederik considers the possibility of a kind of mind which could comfortably
observe such a complicated network, and such a mind may perhaps be suggested by
the machine reading of even exceedingly complex conceptual graphs as has been
made possible with Sowa's CGs). Frederik concludes:
[T]he important issue here is Peirce's very motivation for preferring identity
lines to Selectives in the first place: they are more iconical, because they
represent in one icon entity what is also, in the object, one entity. This thus
forms an additional, stronger iconicity criterion in addition to the
operational iconicity criterion (NP, 218-19, emphasis added).
Here Frederik reminds us that Peirce's arguments against the use of selectives
is in particular directed towards his own, earlier algebraic formalization
which, it should be noted, is the very first version of modern symbolic logic.
Thus, while in some cases Beta graphs with selectives are deemed heuristically
superior to graphs without selectives, and while the two versions are logically
equivalent, Peirce yet clearly preferred the more iconical version all things
being equal.
So we arrive at the second important reason to prefer "more iconic" graph
representations, an ontological one, that "Beta graphs more appropriately
depict logical relations like they really are, thus adding to the pragmatic
operational criterion of iconicity an ontologically motivated extra criterion"
(NP, 219). This connects the optimal iconicity notion to Peirce's realism,
which, while realism is there from the get go (as Max Fisch and, later, Robert
Lane have convincingly argued), his realism became more and more extreme over
the course of his philosophical career (Frederik rehearses the famous diamond
example contrasting Peirce's earlier "more nominalistic" version of 1878 in
"How To Make Our Ideas Clear" with the "extreme realism" of 1905 in "Issues of
Pragmatism," which essay allows for "real possibles" such that were the diamond
to be tested, say at some future time, that it would be found to be hard).
Frederik holds that Peirce's admitting would-bes into his philosophy,
"considerably changes and enriches" not only his conception of Thirdness, but
also the pragmatic maxim, it finally allowing for real possibilities.
Perhaps this is a good place to stop for now since at this point in the chapter
Frederik quotes the important long passage I mentioned in my first post in this
thread and analyzes it in terms of how Peirce "relativized" material
implication to go beyond it in revising parts of his Beta and Gamma graphs.
However, that is a somewhat technical discussion and I'm am not sure that there
is enough interest here in EGs to continue it.
At this point I would like to ask the following questions: Do list members find
Frederik's notion of two kinds of iconicity of interest and value? If so, what
is that value? 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? And
finally, is there any interest in discussing the long passage on EGs on how
Peirce relativizes and goes beyond material implication?
Best,
Gary R
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