|Bivalence: the division in the evaluation of statements on two possible values. These can be interpreted as "true" and "false", but also can be interpreted differently. In multivalued logic there are three to infinitely many values. See also probabilities.|
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|Bivalence||EMD II 103
Principle of Bivalence/Truth/Dummett: PoB already presumes the concept of truth - and that is transcendental in the case of undecidable sentences - it goes beyond our ability to recognize what a manifestation would be.
EMD II 103f
Undecidability/anti-realism/Dummett: (without bivalence) the meaning theory will then no longer be purely descriptive in relation to our actual practice.
- - -
Dum III 17
Sense/Frege: explanation of sense by truth conditions - Tractatus: dito: "Under which circumstances"
- DummettVsFrege/DummettVsWittgenstein: for that one must already know what the statement that P is true means - Vs: if they then say P is true means the same as asserting P. - VsVs: then you must already know what sense it makes to assert P! But that is exactly what should be explained. - VsRedundancy theory: we must either supplement it (not merely explain the meaning by assertion and vice versa) or abandon the bivalence
Sense/Reference/Bivalence/Dummett: bivalence: Problem: not every sentence has such a sense that in principle we can recognize it as true if it is true (e.g. unicorn, Goldbach’s conjecture) - but Frege’s argument does not depend at all on bivalence.
Bivalence, however, works for elementary clauses: if here the semantic value is the extension, it is not necessary to be possible to decide whether the predicate is true or not - perhaps application cannot be effectively decided, but the (undefined) predicate can be understood without allocating the semantic value (truth value) - therefore distinction between sense and semantic value.
Ursprünge der analytischen Philosophie Frankfurt 1992
Wahrheit Stuttgart 1982
G. Evans/J. McDowell
Truth and Meaning Oxford 1977
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989