Theory of Meaning

Meaning, that most illusive of philosophical concepts, is without doubt a ternary relation M(A,B,C): A means B relative to/in/according to C. To us "meaning" is simply a finitary algorithmic transformation that takes finite structured data of sort 1 into finite structured data of sort 2 (which can be the same sort 1, for instance in normalization of types). The canonical example is a compiler.  The Tarskian "meaning" used in model theory is, as usually conceived, misleading. In reality it is nothing more than a finitary recursive transformation of the expressions of a formal system into expressions in some version of formal set theory.  This transformation is interpretation. And interpretations can themselves be interpreted or transformed. 

Our natural term logic NTL gives three examples of meaning, of finitary recursive transformation or interpretations. The normalization of NTL terms to reveal the canonical term which conveys core logical "meaning", the tranformation of NTL terms into terms in the more coarse-grained Bealer Logic and the transformation of Bealer Logic terms into normal NTL terms. 

Another interpretation is the one that follows from a priori meta-theoretic postulates whereby deductive data in one system is taken as sufficient grounds for meta-theorems about another systems (meta-theoretic mirroring).

Feedback for queries of data bases, for questions or commands, are also interpretations.  

Theories of "meaning-as-use" are false and circular and do not explain "meaning" and cannot count as a theory of meaning (this is explored elsewhere). 

We can think of interpretations as functors. Natural transformations are themselves particular cases of functors.

The human mind is equipped with a finite series of interpretations which are successively or concurrently applied to symbolic data.  But this process has to stop, it has to have a fixed point. Thus there are finite, bounded, combinatoric, recursive-algorithmic, rule-constituting, self-reflecting  "semantic primes" or "intuitive primes" which have no interpretation beyond themselves (up to isomorphism?). The task of semantics and the philosophy of language is to find these generators and in particular universal components which must be assumed for any adequate possible logic or programing language. It may be the ultrafinitism may shed light on these problems.