92) The argument is that classical logic, by assuming the principle of bivalence, assumes one too many logical truths.
Both under classical logic with a probability overlay and under fuzzy logic, the MIN rule will reduce to the product rule--if one assumes bivalence and then adds an assumption of random independence.
When a problem calls for rejecting bivalence, you should expect that sometimes the answer will be similarly nonobvious.
We saw above, with respect to 44 (a), that he thinks that the "uncovering" cannot accommodate the crucial bivalence
of true and false, which is essential for statements.
That is, Braver tries to unpack the position of a particular continental philosopher in terms of his stand on the realism theses, resulting in the eventual emergence of the antirealism theses (Al Mind-Dependence, A2 Rejection of Correspondence Truth, A3 Ontological Pluralism, A4 Rejection of Bivalence
, A5 Active Knower, A6 Plural Subject) (10.
This, however, doesn't hold for all undecidable propositions, for Dummett here endorses the view that the past-tense counterparts of decidable present-tense statements do sustain bivalence
, even though they are not themselves decidable.
Logical considerations might narrow it down to some extent, for example, by discounting conflictual hypotheses or theories entailing some clear violation of bivalence
or excluded middle.
FIGUEROA, "Debating the Paradigm's of Justice: The Bivalence
of Environmental Justice.
While developing in greater detail his own version of antirealism that respects those two constraints, Tennant combines the knowability requirement with the claim that truth need not be bivalent, which in turn leads him to replace classical logic based on bivalence
by a nonclassical constructive logic, namely, intuitionistic relevant logic.
competence, or about the nature of truth, or about bivalence
, or about the
Dummett runs aground on counterexamples to his construal of antirealism (failures of bivalence
based on vagueness or truth value gaps) and himself slides between incompatible interpretations of "realism.
Indeed, he thinks that his most singular philosophical achievement has been showing that different realisms (about universals, mental states, physical objects, numbers) have a common characteristic: each involves the claim that the principle of bivalence
holds for the relevant class of statements.