On 8/10/2017 3:23 PM, Jerry LR Chandler wrote:

Is Tarski’s approach to the formal logics of metalanguages essentialto give coherence to communication with the broad array of modernsynthetic symbol systems?

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By itself, Tarski's version of model theory and metalanguage is not sufficient. But something like it is a necessary part of any theory that relates any language or symbol system to the world. The basic foundation is as old as Aristotle. In fact, Tarski quotes Aristotle in the introduction of his famous paper (1933): "To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, or of what is not that it is not, is true." Aristotle used that principle to determine which patterns of syllogisms are or are not valid. John Venn developed his famous diagrams as a systematic way of testing the validity of syllogisms. The Stoics used the same principle to test the validity of their rules of inference for propositional logic. A combination of the Aristotelian and Stoic logics was developed in detail by the Scholastics. Ockham developed a model-theoretic foundation for that subset of Latin that expressed the Aristotelian- Stoic combination. Peirce lectured on Ockham at Harvard, he knew Venn's work, and he developed his endoporeutic (outside-in evaluation) for determining the truth values of existential graphs. Nobody understood how endoporeutic worked until Risto Hilpinen (1982) showed that it is equivalent to a version of Hintikka's game theoretic semantics (GTS), which is an extension (improvement) of Tarski's method. For a summary of GTS, see http://www.jfsowa.com/logic/math.htm#Model As for metalanguage, the Scholastics called it second-intentional language, and Peirce developed it further. I discuss those issues in http://jfsowa.com/pubs/rolelog.pdf The role of logic and ontology in language http://jfsowa.com/pubs/eg2cg.pdf From existential graphs to conceptual graphs http://jfsowa.com/pubs/fuzzy.pdf What is the source of fuzziness? Summary: As I said, Tarski's methods (or the many equivalent versions) are necessary. But they're not sufficient. Peirce, as usual, went beyond the limitations of 20th-century philosophy. John

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