I have to agree with Edwina. In addition, I think Sung is misrepresenting Wigner, whose comments are foundational, iow, the "unreasonable effectiveness" relates to a uniformity of effective structure in mathematics.
Steven On Wednesday, July 2, 2014, Edwina Taborsky <[email protected]> wrote: > Sung wrote: > > "Mathematics is a species of the sign according to Peirce. (070114-1) > >> All signs are arbitrary according to Saussure. Therefore, >> mathematics is arbitrary." >> > > This is invalid for two reasons: > > First, it is logically invalid. The error is called 'the fallacy of four > terms'. A valid syllogism must have exactly three unambiguous categorical > terms. But the term 'mathematics' as outlined above is ambiguous. > Mathematics is both a process and a producer of models. The specific model > chosen may be 'arbitrary' in the sense that it is symbolic, but the process > used within that mathematical reasoning is not arbitrary. There are two > meanings of mathematics in the syllogism above. > > Second, it is only symbolic signs that are arbitrary, in the sense that > their models are assigned by an external agent; iconic and indexical > semiosic relations are not arbitrary. Saussure's semiology applies only to > symbols, therefore, there are also TWO meanings of the term 'sign' in the > above syllogism. > > Edwina > > > ----- Original Message ----- From: "Sungchul Ji" <[email protected]> > To: "Malcolm Dean" <[email protected]> > Sent: Tuesday, July 01, 2014 7:37 PM > Subject: [PEIRCE-L] Re: "Unreasonable Arbitrariness of Mathematics":: > Evidence > > > Malcolm, >> >> Did I attach the evidence for UAM (unreasonable aribtrariness of >> mathematics) to this email ? If not, it is now attached below. >> >> As you can see in the table attached, each of the two sets of experimental >> data, i.e., the single-molecule enzyme kinetic data and the decision-time >> histogram, can be fit into two very different mathematical equations -- >> the Planck distribution and a double-exponential function for the former >> and the Planck distribution and the ex-Gaussian distribution for the >> latter. These recent findings of mine suggested to me that mathematical >> models may be arbitrary. In fact you do not need any experimental data to >> come to such a conclusion, since the same conclusion can be reached at by >> simply combining the definition of the sign given by Peirce and the >> linguistic principle of the arbitrariness of signs apparently first >> articulated by Ferdinand de Saussure: >> >> "Mathematics is a species of the sign according to Peirce. (070114-1) >> All signs are arbitrary according to Saussure. Therefore, >> mathematics is arbitrary." >> >> Let me refer to Statement (070114-1) as the UAM (Unreasonable >> Arbitrariness of Mathematics) thesis. If we apply the UAM thesis to >> quantum mechanics (as a body of experimental data on the microscopic >> world), it may be predicted that >> >> "There should exist at least two mathematical models of (070114-2) >> quantum phenomena that are compatible with all known >> experimental data." >> >> I suggest that Prediction (070114-2) based on the UAM thesis has been >> validated by the fact that physicists, after over one century of quantum >> mechanical research, are still passionately debating as to which of the >> two theories are true - i) the non-deterministic, probability-wave theory >> of Bohr, Bon, Heisenberg, etc, or ii) the deterministic, pilot-wave theory >> of de Broglie, Schroedinger, Einstein, Bohm, and their more recent >> followers, including my fellow professor at Rutgers, S. Goldstein, and his >> research group. >> >> Since Statement (071014-2) seems to be well supported by the modern >> history of physics, it may be further asserted that >> >> "The century-old debate between Einstein and Bohr on (070114-3) >> the mathematical nature of quantum mechanics may be >> ascribed to the principle of the arbitrariness of >> mathematics specifically and the principle of the >> arbitrariness of signs more generally. There may be >> neither winner nor loser on this debate, since both >> schools of thought can be judged valid within their >> own theoretical framework." >> >> If the above argument proves to be valid, the century-old debate in >> physics may end up being finally solved by the knowledge gained outside of >> physics, namely in biology, linguyistics and semiotics. It is possible >> that the problem under debate is/was too complex to be resoved within >> physics, just as some of the current probelms fased in biology may turn >> oout to be too difficult to be solved within biology or even within >> natural sciences assisted by mathemtics and high-power computer science. >> >> 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 >> >> >> Thanks. >>> >>> I think the enthusiasm with which mathematicians present their "accuracy" >>> is produced by very narrow observations of the phenomena which happen to >>> match their expectations. The world is fuzzy and messy, except in rare >>> cases. The mathematics students I have observed have little >>> self-reflection. They do not see that their mathematical experiences are >>> special mental abilities, similar to religious states, in that >>> mathematics >>> is a form of generalization. I once asked Sean Carroll about the ontology >>> of his particle physics. "They are just numbers, statistics," he replied. >>> >>> My departed friends, Michel and Francoise Gauquelin, once set out to >>> finally disprove Astrology. They gathered large statistical databases >>> (30k) >>> and compared planetary positions at birth with adult professions. And lo! >>> Given a complicated statistical method, they were able to demonstrate a >>> significant correlation. American skeptics decided that since this was >>> the >>> most promising evidence for planetary effects in human affairs, a simple >>> replication would provide a knock-out blow to the superstition. And lo! >>> With a U.S. sample size of 15k, they replicated the findings of the >>> Gauquelins. Did they honestly report the results? Of course not. The >>> statistical method was now "problematic" and "unclear." The results were >>> "dubious." >>> >>> Personally, I no longer care whether planetary effects are acknowledged, >>> or >>> whether psi is shown to exist. I'm satisfied that a bunch of skeptics >>> proved that mathematicians can lie just like the rest of us. >>> >>> M. >>> >>> On Sun, Jun 29, 2014 at 4:20 AM, Sungchul Ji <[email protected]> >>> wrote: >>> >>> Hi, >>>> >>>> In 1960, Eugene Wigner made the following statement in a paper with the >>>> now-iconic title, â?oUnreasonable Effectiveness of Mathematicsâ?ť. In >>>> it, he >>>> cites a question presumably raised by one of his students at Princeton >>>> (hence I will refer to it as the â?oWerner questionâ?ť for convenience): >>>> >>>> ". . . someone came to me and expressed his bewilderment [The >>>> remark to be quoted was made by F. Werner when he was a student in >>>> Princeton.] . . . with the fact that we make a rather narrow selection >>>> when choosing the data on which we test our theories. >>>> >>>> â?~How do we know that, if we made a theory which (062914-1) >>>> focuses its attention on phenomena we disregard >>>> and disregards some of the phenomena now commanding >>>> our attention, that we could not build another theory >>>> which has little in common with the present one but >>>> which, nevertheless, explains just as many phenomena >>>> as the present theory?â?T >>>> >>>> It has to be admitted that we have no definite evidence >>>> that there is no such theory." >>>> >>>> Reading between the lines, it seems reasonable to infer that Wigner was >>>> fully aware of the incompleteness of his famous thesis that >>>> >>>> â?oMathematics is unreasonably effective.â?ť (062914-2) >>>> which we may refer to as the â?oWigner thesisâ?ť. >>>> >>>> In other words, >>>> >>>> â?oThe Wigner thesis cannot provide any definitive (062914-3) >>>> answer to the Werner question, neither positive >>>> nor negative, and hence is incomplete.â?ť >>>> >>>> The reason that the Wigner thesis is incomplete is because of >>>> >>>> â?oThe Unreasonable Arbitrariness of Mathematics (UAM)â?ť >>>> (062914-4) >>>> >>>> The purpose of this email is to bring to your attention some recent >>>> developments in theoretical biology (see Table 1 attached) that support >>>> the UAM thesis: i.e., >>>> >>>> â?oTwo or more mathematical models can simulate a given (062914-5) >>>> set of experimental data, just as two or more signs >>>> can represent a given object in semiotics.â?ť >>>> >>>> I think Statement (062914-5) is consistent with the facts (i) that >>>> mathematical models are examples of Peircean signs (or, more >>>> specifically, >>>> the â?~argument-symbolic-legisignâ?T) and (ii) that all signs are >>>> arbitrary , >>>> according to Saussureâ?Ts thesis of the â?oArbitrariness of Signsâ?ť >>>> [2]. I am >>>> assuming here that >>>> >>>> â?oSaussureâ?Ts dyadic theory of signs can be viewed as (062914-6) >>>> a reduced version of Peirceâ?Ts triadic theory of signs >>>> -- reduced in the sense that the role of the semiotic >>>> agent was not EXPLICITLY taken into account.â?ť >>>> >>>> >>>> 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 >>>> >>>> [1] Wigner, E. (1960). The Unreasonable Effectiveness of Mathematics >>>> in the Natural Sciences. Communications in Pure and Applied >>>> Mathematics 13 (I). Available at >>>> https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html. >>>> [2] See, for example, >>>> http://en.wikipedia.org/wiki/Sign_(linguistics). >>>> >>>> >>>> >>>> >>>> >>>> >>> >> > > ------------------------------------------------------------ > -------------------- > > > >> ----------------------------- >> 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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