Edwina, I think you have been mis-interpreting my syllogism with all sorts of irrelevant examples.
For instance, the following syllogism is a wrong syllogism to compare with my syllogism (or the Burgin-Peirce syllogism) shown in (6089-4), (6089-5) and (6089-6): All logicians are men. (6089-1) All logicians are mean. (6089-2) Therefore all men are mean. (6089-3) which is obviously wrong. My syllogism below does not contain any quantifiers: Burign's fundamental triad is a Peircean sign. (6089-4) Burgin's fundamental triad can unify mathematics. (6089-5) Therefore Peircean sign can unify mathematics. (6089-6) If you wish to add them for the purpose of increasing clarity, the correct way of doing it would be as follows: All Burgin's triads are a subset of Peircean signs. (6089-7) All Burgins triads can unify mathematics. (6089-8) Therefore a subset of Peircean signs can unify mathematics. (6089-9) which has the same logical form as the following: All logicians are a subset of men. (6089-10) All logicians are mean. (6089-11) Therefore some men are mean. (6089-12) This syllogism is obviously true, as is the Burgin-Peirce syllogism shown above. This recent flurry of debates on syllogism indicate to me that, many, if not all, syllogisms may be arbitrary (not surprisingly becvause they are signs !) in the sense that they can be interpreted in three ways -- positive, negative, and neutral. 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 > 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 >> >> > > > -------------------------------------------------------------------------- > > >> >> ----------------------------- >> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> PEIRCE-L to this message. PEIRCE-L posts should go to >> [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L >> but to [email protected] with the line "UNSubscribe PEIRCE-L" in the >> BODY of the message. More at >> http://www.cspeirce.com/peirce-l/peirce-l.htm >> . >> >> >> >> >> > > >
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