Hi Mark,
I just ran into this old email where you asked:
"For instance, when an individual speaks or e-mails to another individual,
it is a fundamental triad
but I don't know how to interpret this system as a Peircean sign."
I do not remember answering this question. In any case, here is my current
answer:
The communication between two individuals, A and B, involves the Peircean
triad (also called the Peircean sign):
f g
A ------------> Message -----------> B
(Utterer) (Sign) (Hearer)
| ^
| |
|_____________________________|
h
Figure 1. Communication between two individuals involves the Peircean
triad, also called the Peircean sign.
Figure 1 is a commutative triangle, or a mathematical category, since f x g
= h, i.e., f followed by g leads to the same result as h. f = encoding; g
= decoding; h = information transfer.
So we may conclude that your fundamental triad and the Peircean sign are
two different names (or representamens) for the same object, i.e., *the
basic unit of communication.*
All the best.
Sung
On Tue, Jul 15, 2014 at 8:59 PM, Burgin, Mark <mbur...@math.ucla.edu> wrote:
> Dear Sung,
> I was out of town and only now read your interesting e-mail. You found a
> challenging connection between a Peircean sign and a fundamental triad. You
> are a very creative person. What you suggest is a possible interpretation.
> However, in general, a Peircean sign consists of three fundamental triads.
> Besides, fundamental triad has more interpretations than a Peircean sign .
> For instance, when an individual speaks or e-mails to another individual,
> it is a fundamental triad but I don't know how to interpret this system as
> a Peircean sign.
>
> Sincerely,
> Mark
>
> On 7/5/2014 2:37 PM, Sungchul Ji wrote:
>
>> Dear Mark,
>>
>> I just sent off this email to semioticians. Please let me know if you
>> have any comments or corrections.
>>
>> With all the best.
>>
>> Sung
>>
>> ---------------------------- Original Message ----------------------------
>> Subject: Burgin’s Fundamental Triads as Peirceasn Signs.
>> From: "Sungchul Ji" <s...@rci.rutgers.edu>
>> Date: Sat, July 5, 2014 5:33 pm
>> To: biosemiot...@lists.ut.ee
>> --------------------------------------------------------------------------
>>
>> (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
>>
>>
>
--
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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