We should not take logic to be essentially about the mind, or language, or exclusively about an abstract realm, or about reasoning, truth, truth-tables, truth-functions
, topic-neutrality, or form.
She then describes alternative semantics for truth-values and truth-functions
(with numeric truth-values and abstract algebras), then covers the semantics of three-valued propositional logics, derivation systems for three-valued propositional logic, three-valued first-order logic semantics, derivation systems for three-valued first-order logic, alternative semantics for three-valued logic, fuzzy propositional logics, fuzzy algebras, semantics of fuzzy first-order logics, derivation systems for fuzzy first-order logic, extensions of fuzziness and fuzzy membership functions.
He also identifies for a post-modern age the siren voice which lay at the heart of logical positivism, namely the radical distinction between the truth-functions
of grammar and science and the "make-believe" words of poetry, or myth and metaphor.
This is the subject of chapter 2, where the notion of "operation" in the Tractatus is seen as pivotal to the theory of truth-functions
and to a non-extensional theory of arithmetic (where numbers are conceived of as the "exponent of an operation').
Since Wittgenstein's Tractatus, in the view of the Circle, correctly held that all meaningful statements are truth-functions
of simple observation statements, they concluded that all those statements that were not so reducible were meaningless, for instance those of metaphysics.
Frege's two fundamental logical truth-functions
, negation and conditionality, are subjected to scrutiny.
147); and from there by gradual steps to the notions of contradiction and entailment, the truth-functions
, logical truth, first-order quantification, and so forth.
Peter Hylton, in "Functions, Operations and Sense in Wittgenstein's Tractatus," provides an account of how Wittgenstein sought to use the notion of an operation to account for nonelementary propositions without having to introduce truth-functions
as additional items in his ontology.