Clark, Kirsti, List: > On Apr 20, 2016, at 4:09 PM, Clark Goble <[email protected]> wrote: > >> >> The issue of concern to me is the interpretation given to the meta-languages >> that use mathematical symbols. >> >> Tarski’s insistence of the role of meta-languages in logical and >> mathematical communication seems to be one of the roots of the >> “purification” of mathematical proofs - and in logic itself. (See 13 >> Questions Universal Logic paper) > > I think the more interesting question is whether there is a master > meta-language or whether there’s a certain endless semiosis of translation > (or dis-quotation). I believe that grammar and linguistics play an extremely important in CSP thought and logic, but this root of his thinking is seldom explored. Predicate logic dominates the modern scientific logic perspectives (perhaps as they should, given the utility for physical thought.)
But, let’s explore the your meaning of your thought a bit, OK? What might you mean by the term “master” meta-language? How would such an innovative concept relate to semiosis? At present, each discipline develops its own set of terms by asserting propositions judged relevant to its subject matter. The later integration of the disciplines, which eventually follows in time, accommodates the various meanings by selection. This is a very slow process but it keeps the common language lively from generation to generation. Have you thought about Beziau 13 Questions About Universal Logic from this perspective? Bulletin of the Section of Logic Volume 35:2/3 (2006), pp. 133–150Bulletin of the Section of Logic Volume 35:2/3 (2006), pp. 133–150 One of the conundrums that arises in the conceptualization of meta-languages is the meaning of number with respect to semiosis. Imagine the meta-languages of mathematics, physics, chemistry, biology, and the clinical sciences. What would the number 13 mean in each meta-language? What would the number 47 mean in each meta-language? In each meta-language, when is the product of 13 x 47 meaningful? Or, under what contexts and constraints, that is, which set of propositional terms and propositional functions does the number (13 x 47 = ) 611 have meaning? For example, atomic number 13 multiplied by atomic number 47 has no meaning within the meta-language of the physical sciences. (I select this example from thoughts about Leibniz’s desire to calculate with linguistic terms.) More generally, what would be the roles of the logic of connotation and denotation between meta-languages? What is the difference in semiosis between a term which has an exact meaning in one meta-language and no meaning in another meta-language? Is this “difference that makes a difference” an essential element of the role of natural kinds (sinsigns) in the logic of CSP’s triadic triads? Is the form of the index a consequence of the legisigns selected as representamen? Cheers Jerry
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