On 8/10/2017 3:23 PM, Jerry LR Chandler wrote:
Is Tarski’s approach to the formal logics of metalanguages essential to give coherence to communication with the broad array of modern synthetic symbol systems?


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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