Jerry, list - as someone with no background in chemistry, I have a
few questions:
1) I understand your analysis using the 'doctrine of valency' in
chemistry and, as you point out, Peirce was a chemist. Now, in
Robert's, p.115, he shows several figures - and figure 3 'represents
triadic spots'. And he explains that the definition of the rhema or
spot, which is the proposition [subject and predicate] - can be shown
by a line/tail and heavy dot, so to speak. A monad has one dot and an
open/loose end or tail. If you join two monads/spots you get closure,
i.e., no open ends. A dyad has two open ends/tails but if you add
another, you'll get another dyad [which is the problem with
linearity]. But the triad - and the image is the same as that given
in 1.347- obviously, since Roberts is working from that section. [See
also Peirce 3.470]. I hope I've understood you correctly.
2) I still don't see why this isn't an image of the semiosic triad.
The rhema is the proposition, i.e., a semiosic relation made up of a
subject and predicate. In a triadic spot/rhema/proposition which has
three 'loose ends' or blank forms - which means, as I understand it,
that it is open to being filled by some subject. So, the representamen
as a predicate connects to the 'subjects' of the Dynamic Object and to
the Dynamic Interpretant..and even, to its own nature in itself. That,
to me - shows the triad - but the key to this semiosis is the 'loose
ends or blank forms which enable interactions rather than dyadic
closure or monadic/medad closure.
Now- what am I missing in this view?
Edwina
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On Thu 13/04/17 3:59 PM , Jerry LR Chandler
jerry_lr_chand...@icloud.com sent:
List:
(This post is rather technical and the contents may be intractably
perplex for many readers of this list. One purpose of this post is
to crisply separate the fundamental philosophical concept of identity
from the mathematical concept of identity. To differentiate CSP view
of lines of identity from classical views, see McGinn’s, Logical
Properties, 2000, OUP Chapter 1, p.1-14, Identity, for an overview of
one philosopher’s notion of “Identity" )
On Apr 13, 2017, at 8:14 AM, g...@gnusystems.ca [1] wrote:
But even from the fragment published in CP 1.343-9, one can glean
some of Peirce’s key insights on the subject, given some slight
acquaintance with existential graphs. In graphs such as the one at
1.347, the lines (Peirce calls them “tails” here) are lines of
identity each representing that something exists. The relation is
represented in the graph by the labelled spot to which they are all
attached, and the three “tails” are the relata. In propositional
terms, the graph represents a predicate (the spot) with three
subjects, (i.e. with a “valency” of three). To read the lines in
the graph as relations is to misread the graph. The graph is itself a
diagrammatic sign, but there is no attempt to represent its object(s)
or its interpretant on the sheet of assertion. In fact, I have never
seen, anywhere in Peirce’s writings, an attempt to represent the
basic triadic sign relation in a single diagram. I think the reason
is simple: thatkind of triadic relation cannot be represented that
way. But if someone can show me a text where Peirce has done that,
I’ll happily retract that claim. This would explain, by the way,
why it is that Edwina “can't 'imagize' what 'one triadic Relation'
would look like or how it would function.” If you represent
relations as lines (or “spokes”), you can only represent dyadic
relations. Then Peirce’s graph can only appear to you as a triad of
(dyadic) relations.
I think Gary’s conclusion is problematic because of the the way
CSP uses the concept of identity in chemistry as a basis for his
concept of identity in logic and / or mathematics.
First, a bit of historical context for the emergence of CSP’s view
of lines of identity in relation to concrete signs and symbols in
applied mathematics and graph theory.
CSP's early writings (1860’s, 1870’s) were very accurate
representations of the facts of chemistry as they stood in his day.
But, following the Karlsruhe Conference of 1861(?), the
relationships between chemical symbols and chemical signs underwent
rapid development during the remainder of the 19 th Century with
three major changes. With the development the electrical structure of
atom (1913) and Quantum Chemistry (Schodinger, 1926), and Pauling’s
notion of the mechanics of the chemical bond, further profound
changes in the logic of chemistry emerged in the 20 th Century.
The three major changes following the 1860’s were:
1. Acceptance of the concept of atom identities as separate units
conjoined by a chemical bond, forming the relations WITHIN molecules
with clear and distinct IDENTITIES different from atoms.
2. Acceptance of the notion of Kekule’s aromatic compounds,
benzene, etc. forming cyclic compounds, that is, chemical IDENTITIES
with cyclic graphs. The concept of aromatic compounds also modified
Dalton’s notion of valence of whole numbers to include fractional
valences of ratios of numbers.
3. Pasteur’s separation of molecules with IDENTICAL atomic
identities into the optical isomers of D and L tartaric acid with
separate physical IDENTITIES. The tetrahedral carbon atoms of
tartaric acid must be fitted onto a Procrustean bed in order to
maintain a triadic view of chemistry. The fitting process is
logically simple. Simply assert that four relations is a combination
of three relations.
This is his famous reduction hypothesis.
It is critical to observed that:the first of these is change in the
meaning of chemical signs in relation to chemical symbols; the second
of these is a fundamental abstraction about the relationship between
atoms and geometry;the third of these is a deep conundrum that
DISASSOCIATES the symbol system of chemistry from the symbol system
of physics. Thus, these three conceptual scientific break-throughs
all extended the notion of chemical identity to aspects of graph
theory. Were these concepts the origin of CSP’s views on the
supreme importance of identity in the logic of his “chef
d’oeuvre"?
In Robert’s “The Existential Graphs of Charles S Peirce”,
(1973) p. 25, Figures 5 and 6, (3.469 and 4.561) two apodeictic
representations of the forms of triadic relations are presented for
scrutiny and analysis. The linguistic sentence "John gives John to
John” is contrasted with the sentence of a logical graph for
ammonia.
Is this an adroit usage of the procrustian bedding process to seduce
the reader to believe that triadicity has a universal meaning in logic
and science? This line of reasoning is further illustrated in the
grammar of forming a rheme from icons by invoking the chemical notion
of “unsaturated" valences (3.420 and 3.421, Robert’s p. 22).
CSP asserts that “Every proposition has one and only one
predicate” (4.438) and richly illustrates his view of linguistic
theory (Robert’s, p. 114.) Is this another Procrustean bed?
In my mind, I am left with an intractable question: Is a Procrustian
Bed essential to understanding the role of the identity relation in
CSP’s theory of logical graphs of relations? Or, is a semantic
explanation possible?
Gary F: How do you interpret your views of triadic relations in
reference to the citations from Roberts work?
Cheers
Jerry
.
These three historical developments forced CSP to attempt to place
the facts of chemistry into fabric of mathematics.
Links:
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