Sung, list,You're mixing apples and oranges, using the word 'sign' equivocally. Saussure's 'sign' is not Peirce's 'sign' or even Peirce's 'symbol'; Saussure's 'sign' is Peirce's 'linguistic symbol'.
Peirce defines a symbol as a sign that refers to its object by a norm or rule of interpretation. He does not generally characterize such rule or norm as arbitrary. In Peirce's system, individual instances of the words 'dog' and (Spanish) 'perro' are replicas of the general word-symbols 'dog' and 'perro' which specify qualities of appearance of their word-instances and which, in turn, are, 'dog' and 'perro', two general replicas of the _/same symbol/_, a symbol which consists in their shared conception, is not a word in a particular language and does not prescribe qualities of appearance for its instances. See "New Elements of Mathematics" MS 517 (1904), EP 2:300-324, see p. 317 (EP page numbers are added to the MS 517 transcription at Arisbe http://www.cspeirce.com/menu/library/bycsp/stoicheia/stoicheia.htm).
The qualities of appearance prescribed for word-instances by particular languages' words are usually arbitrary with respect to the denoted objects. But when words in different languages are replicas of the same essential symbol, that symbol does not partake of the arbitrariness of linguistic words.
Hence, from the Peircean standpoint, the symbols in mathematics are arbitrary in the sense of Saussurian signs insofar as they specify, for their replica instances, qualities of appearance that are arbitrary with regard to the denoted objects, e.g., the numeral '5' doesn't look like five things, or like the set of all sets of 5 things, or however you conceive of 5.
Best, Ben On 7/3/2014 5:27 PM, Sungchul Ji wrote:
Edwina wrote: "The difference is as I explained in my original post: (6061-1) that between a model and the process of reasoning which are not the SAME empirical reality; . . ." Before I comment on (6061-1), let me repeat what I said about the UAM (Unreasonable Arbitrariness of Mathematics) thesis. Major premise: All signs are arbitrary (Saussure) Minor premise: Mathematics is an argument symbolic legisign (Peirce) Coclusion: Mathemtica is arbitrary (consistent with the experimental evidecen provided), where "mathematics" means "mathemtical equations" such as the Planckian distribution, the double exponetial function of Lu et al (1998), or the ex-Gaussian function of R. D. Luce (1986, p. 100), and NOT "mathematcal reasonig" as you wrongly assumed. Based on this anlaysis, I conclude that "Statement (6061-1) is a red herring desinged to (6061-2) mis-lead readers, away from the true significance of the UAM thesis, whihc is empiricallly substantiated" as evident in the graphs that I pains-takingly provided to help readiers to understand what I mean. With all the best. SungNo, Sung, the difference in meaning between your terms is not similar to 'half-empty' and 'half-full' which uses different terms to describe the SAME empirical reality. The difference is as I explained in my original post: that between a model and the process of reasoning which are not the SAME empirical reality; and the nature of Saussurian semiology. I won't repeat it here. Edwina ----- Original Message ----- From: "Sungchul Ji" <[email protected]> To: <[email protected]> Sent: Thursday, July 03, 2014 3:10 PM Subject: [biosemiotics:6057] Re: "UnreasonableYou can read my syllogism in eithr of two ways -- as a 3-term arguement (as I intended) or as a 4-term argument (as you mis-interpret agaisnt he evidence I presented), just as there are two ways of describing a half-filled galss of water -- "half-empty" as you prefer, or "half-ful" as I see it. With all the best. SungNever mind your endless acronyms, Sung. The fallacy in your syllogism remains. You can divert the issue to the triadic basis of the sign which is not relevant here, but the syllogistic structure itself has to be examined - and your syllogism, though formally correct (Barbara) is invalid because of the ambiguity of its terms. Oh, and by the way, if you want to base your comments on Peirce, then, using the 'data-based' approach, it is normal to provide the exact reference to any quotes or analysis of his that you use. Your equally endless numbers-in-parentheses does not provide the reference sources. Edwina ----- Original Message ----- From: "Sungchul Ji" <[email protected]> To: <[email protected]> Sent: Thursday, July 03, 2014 1:36 PM Subject: [biosemiotics:6051] Re: "Unreasonable(Undistorted Figure 1 is attached.) Edwina wrote: "The error is called 'the fallacy of four terms'. (6030-1) 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." It seems to me that, in her zeal to apply "the fallacy of four terms" to my syllogism, she may have missed or conveniently ignored the EVIDENCE that I provided in my email (see the attached), which unambiguously indicates what is meant by the term "mathematics" appearing in the UAM thesis, i.e., "mathematical equations" - more specifically, the Planckian distribution, a double-exponential function, and the ex-Gaussian distribution. To prove me wrong, she should provide the EVIDECNE to support her own conclusion, just as I have done so to support mine. Her failing to provide any such evidence would indicate to me that she is engaged in doing "data-free philosophy (DFP)", whereas I am interested in doing "data-based philosophy (DBP)". No wonder we do not communicate with each other. It is my humble opinion that "Conflating data-free and data-based philosophies may (6030-2) underlie most, if not all, major unproductive debates in philosophy, semiotics, and natural sciences." To make a long story short, I am of the opinion that data-free philosophies do not deal with genuine triadic signs, since they ignore the third mapping c, in the triadic definition of the Peircean sign: a b Object/Referent -----> Sign/Representamen/Signifer -----> Interpretant | ^ | | |_______________________________________________________| c Figure 1. The triadic definition of the Peircean viewed as a mathematical category. The key to the triadic definition of sign given above is the composition condition, a x b = c, which states that "An object determines/constrains a sign (or representamen) (6030-3) which in turn determines its interpretant in such a way that the interpretant is indirectly determined by (or correspond or is correlated to ) the same object that the sign is referring to." It may be convenient to define two classes of signs - those signs that meet the requirement of a mathematical category as in Figure 1 and those lacking one or more of the three mappings essential for a mathematical category. Such latter signs may be referred to as "Pseudo-signs", "dyadic signs", "degenerate signs", or "incomplete signs." Using these terms, I am tempted to propose the following statement whose validity may be testable:": "All nonproductive debates in science, philosophy, and (6030-4) semiotics result from using pseudo or incomplete signs." A corollary of (6030-4) would be: "All intellectual debates in philosophy, science, semiotics, (6030-5) etc. may be resolved by replacing incomplete signs with complete, triadic signs of Peirce." 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.netSung 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":: EvidenceMalcolm, 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.netThanks. 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?. 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? 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? (062914-2) which we may refer to as the â?oWigner thesisâ?. 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? The reason that the Wigner thesis is incomplete is because of â?oThe Unreasonable Arbitrariness of Mathematics (UAM)â? (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? 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? [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? 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).
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