Languages, grammars, etc.
CM20019—Computation III: Formal Logic and Semantics
Semantics – the study of Meaning. Hofstadter argues that meaning is a Morphism (often an Isomorphism) between a language (produced by a Formal system) and another space. The mapping itself is known as an interpretation.
Meaningfull interpretations are those where there is an identifications between the theorems and non-theorems of the Formal system, and a pair of sets that correspond to some aspects of Reality, for instance a set of true and false statements. See page 51 of GEB. An interpretation is otherwise known as meaningless.
symbols of a formal system, though initally without meaning, cannot avoid taking on "meaning" of sorts, at least if an isomorphism is found. However, unlike Natural language and other non-Formal systems, we can't add new rules or axioms because the meaning we have found; by definition of formality, the rules are fixed. To distinguish these we call these active and passive Meanings