ABSTRACT
Philosophy.—Syntax is the study of word combinations in sentences and of derivation relations between propositions (→LANGUAGE). Complete-ness (in the broad sense) warrants the equivalence between syntax and semantics (→SEMANTICS), to the extent that any formula in a coherent formal system (propositional logic or predicate logic; →LOGIC) has a model, that is, an interpretation (→INTERPRETATION, MODEL). On the other hand, Kurt Gödel demonstrated the incompleteness of formal arithmetic: its syntactic and semantic properties are no longer equivalent.
