The way was prepared in Britain by Thomas Reid, who departed from Locke's devotion to the truth-function
of language to give priority to its communicative function, and by Jeremy Bentham, who recognized the performative hermeneutic circle by which "the success of the law-as-command depends on the authority of the law-giver, but the authority of the law-giver depends equally on the pragmatic success of the law-as-command" (44).
(The Minority connective refers to the truth-function
MIN, where MIN ([X.sub.1],[X.sub.2],[X.sub.3])=T iff only a minority of [X.sub.1],[X.sub.2],[X.sub.3] are T; the Majority connective refers to MAJ, where MAJ([X.sub.1],[X.sub.2],[X.sub.3])= T iff a majority of [X.sub.1],[X.sub.2],[X.sub.3] are T.) C * is both truth-functional and unnatural: It is truth-functional since it does not distinguish between arguments with the same truth values (that is, if <v([p.sub.1]),v([p.sub.2]),v([p.sub.3]>=<v([p.sub.4], v([p.sub.5]),v([p.sub.6])>, where v(p) is the truth-value of p, then C * ([p.sub.1],[p.sub.2],[p.sub.3])=C * ([p.sub.4],[p.sub.5],[p.sub.6])).
Crucial to the theme is the notion that art is as legitimate a medium for truth-function
as the rationalistic codifications of the world of the natural sciences.
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.
Frege's two fundamental logical truth-functions
, negation and conditionality, are subjected to scrutiny.
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').
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.
The principle of explicability can be discerned in the weighted charitable treatment of observation sentences and truth-functions
and can easily accommodate attributions of irrationality.