Please, Sung - try to read a basic course in logic. Your endless attempts to
link things with each other, whether it's Saussure with Peirce, or Bohr with
Bohm or whatever - run into theoretical problems, empirical problems and
logical problems.
Last time, your syllogism was invalid because of the Fallacy of Four terms.
This time, your syllogism is both formally false and logically invalid...the
Fallacy of the Illicit Major.
As a comparison with your format, think about this comparable example.
All logicians are men
All logicians are mean
Therefore all men are mean.
Get it? Your syllogism makes the same error. Your terms of 'mathematics'
and 'Peircean sign' are undistributed in the premises and therefore, can't
be distributed in the conclusion - but you have done just that.
Edwina
----- Original Message -----
From: "Sungchul Ji" <[email protected]>
To: <[email protected]>
Sent: Saturday, July 05, 2014 5:33 PM
Subject: [PEIRCE-L] Burgin's Fundamental Triads as Peirceasn Signs.
(Undistorted figures are attached.)
Stephen R on the Peirce list cited Peirce as saying:
"The undertaking which this volume inaugurates is to (070514-1)
make a philosophy like that of Aristotle, that is to say, to
outline a theory so comprehensive that, for a long time to
come, the entire work of human reason, in philosophy of
every school and kind, in mathematics, in psychology,
in physical science, in history, in sociology, and in
whatever other department there may be, shall appear
as the filling up of its details. The first step toward
this is to find simple concepts applicable to every
subject."
At least one of the potential "simple concepts" that Peirce is referring
to above may turn out to be his concept of "irreducible triadicity"
embedded in the following quote that Jon recently posted and further
explained in Figure 1 and (070514-4):
"Logic will here be defined as formal semiotic. (070514-2)
A definition of a sign will be given which no more
refers to human thought than does the definition of
a line as the place which a particle occupies, part
by part, during a lapse of time. Namely, a sign is
something, A, which brings something, B, its interpretant
sign determined or created by it, into the same sort
of correspondence with something, C, its object, as
that in which itself stands to C. It is from this
definition, together with a definition of "formal",
that I deduce mathematically the principles of logic.
I also make a historical review of all the definitions
and conceptions of logic, and show, not merely that my
definition is no novelty, but that my non-psychological
conception of logic has virtually been quite generally
held, though not generally recognized." (NEM 4, 20-21).
a b
C --------> A --------> B
| ^
| |
|_______________________________|
c
Figure 1. A diagrammatic representation of the principle of irreducible
triadicity as applied to the definition of a sign. A = sign; B =
interpretant; and C = object. a = the sign-object relation (which can be
iconic, indexical or symbolic); b = the sign-interpretant relation (which
can be rheme, dicisign or argument); c = the object-interpretant relation
(which is lacking in Peircean semiotics but may be provided by
microsemiotics [1] or biosemiotics (e.g., [2, 3, 4]).
"A is determined by C and determines B in such away (070514-3)
that C is indirectly determined by B."
The purpose of this email is to suggest the possible connection between
the Peircean sign and Burgin's fundamental triad shown in Figure 2 that is
postulated by Burgin to underlie all mathematical constructions [5, 6].
f
X -------------- > I
Figure 2. The "fundamental triads" (also called "named sets") of Burgin
[5, attached, 6]. X = set of objects called "support"; I = set of objects
called "names", and f = "naming relation".
The key to connecting Burign's triad and Peircean sign is to re-express
the 2-node network in Figure 2 in the form of the 3-node network shown in
Figure 3 which is expressed in words in (070514-4).
a b
X -------- > f --------> I
| ^
| |
|_______________________________|
c
Figure 3. Burign's fundamental triad, Figure 2, re-expressed as an
irreducible triad of Peirce, Figure 1. a = causality (?); b = convention
(?); c = symbol grounding (?).
"X determines f which in turn determines I in such (070514-4)
a way that I is constrained by or correlated with X."
If the Burgin-Peirce connection depicted in Figure 3 turns out to be true,
the following syllogism would result:
Burgin's fundamental triad can unify mathematics. [5, 6] (070514-5)
Burign's fundamental triad is a Peircean sign. [Figure 3] (070514-6)
Therefore Peircean sign (or semiotics) can unify (070514-7)
mathematics. (Prediction}.
With all the best.
Sung
__________________________________________________
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
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