Page 282 - Encyclopedia of Philosophy of Language

Language and Logic
have been at fault in giving vagueness the go-by' he had in mind primarily indefiniteness in the sense in which an existential quantification ('a man', 'some animal') is indefinite, construing predicate vagueness as implicit quantification ('is bald in some sense of the term').
Those contemporary logicians who urge the merits of a nonstandard logic of vagueness are apt to have specifically in mind that in the presence of vagueness there will be borderline cases, cases where it is inde- terminate whether or not a vague predicate such as 'short,' 'red,' 'bald,' 'pretty,' applies. When vague predicates are applied to borderline cases, the thought is, the result is a sentence which is neither true nor false, and this constitutes a challenge to classical, bivalent, logic.
The simple proposal that vague sentences be accom- modated by a 3-valued system in which they take the third value, however, faces the difficulty that, though it no longer requires a sharp line to be drawn between cases in which a vague sentence is straightforwardly true and cases in which it is straightforwardly false, it still requires a sharp line to be drawn between cases in which the application of a vague predicate is bor- derline, and cases in which it is not. And this seems not so much to solve as to shift the problem.
With fuzzy logic the situation is much more complex, but not much more encouraging. The assumption here is that the meta-linguistic predicates 'true' and 'false' are themselves vague. Zadeh's linguis- tic evidence for this claim is questionable at best: 'very true,' surely, means 'true and important,' rather than 'true to a high degree'; and 'not very true' and 'rather true' are arguably not proper locutions at all. And in any case, despite Zadeh's suggestion that fuzzy logic is itself vague, in fact his approach requires an artificial imposition of precision more striking even than a 3- valued approach. Consider, for example, Zadeh's definition of 'true':
true=d(. 0.3/0.6+0.5/0.7+0.7/0.8+0.9/0.9+1/1
i.e., as the fuzzy set to which degree of truth 0.6
belongstodegree0.3,0.7todegree0.5,...,0.9to
red and orange at once. The suggestion is, roughly, that a vague sentence is to count as true if it would be true for all ways of making it precise. The 'supertruth' approach (which has an obvious affinity with the method of supervaluations) conceives of the truth- conditions of vague predicates as quasi-classical; and though it proposes a non-classical semantics it calls for no revision of the theorems or inferences of classi- cal logic, since the principle that a vague sentence count as true if it would be true no matter how it was made precise preserves the classical tautologies even in instances involving vague predicates, such as 'Either Harry is bald or he isn't,' or 'If this patch is red, it is red.'
See: Vagueness.
3.3 Reference Failure,FictionalDiscourse,etc.
Another challenge to classical logic derives from the phenomenon of reference failure, i.e., of sentences containing proper names (such as 'Mr Pickwick' or 'Odysseus') or definite descriptions (such as 'the pre- sent king of France' or 'the greatest prime number') which have no referent. Indeed, an argument to the effect that sentences containing proper names or defi- nite descriptions presupposes that those names or descriptions refer, and thus, if there is failure of refer- ence, are neither true nor false, is to be found in Frege.
Frege himself, however, regarded the phenomenon of reference failure much as he regarded ambiguity or vagueness, as a defect of natural languages to be extirpated from any acceptable formal language. His proposal was that a referent simply be arbitrarily sup- plied for any well-formed expression that would other- wise lack reference, and thus to preserve a bivalent logic.
It is now more usual for reference failure to be accommodated classically by means of Russell's The- ory of Descriptions. 'The F exists' (e.g., 'the greatest prime number exists') is contextually defined as 'there is exactly one thing which is F' (e.g., 'there is exactly one thing which is prime and greater than any other prime'); 'the F is G' (e.g., 'the greatest prime number isodd')isdefinedas'thereisexactlyonethingwhich is F, and whatever is F is G ' (e.g., 'there is exactly one thing which is prime and greater than any other prime, and whatever is prime and greater than any other prime is odd'). 'The F is G,' on this account, does not presuppose, but entails, that the F exists, and is not truth-valueless, but false, if there is no, or no unique, F. Since Russell, like Frege, takes an ordinary proper name to be equivalent to a co-referential definite description, this also accommodates all cases of ref- erence failure within a bivalent framework.
Skeptical, in any case, of the distinction between sense and reference ('Sinn' versus 'Bedeutung') in the context of which Frege's account was set, Russell regarded Frege's approach as unacceptably artificial. The other foil to his theory of descriptions was Mei-
degree 0.9, and 1 to degree 1; or his definition of 'very 2
true' as 'true .'
Since ruling vague sentences beyond the scope of
logic may seem a little high-handed, and proposing that all vague discourse be 'precisified' before for- malization may seem a little optimistic, there is some- thing to recommend the 'super-truth' approach (Meehlberg, Przdecki, D. K. Lewis, Fine), which accommodates the phenomenon of vagueness within a classical framework, and arguably with less artificial precision than deviant logics of vagueness. This approach is motivated partly by the phenomenon of 'penumbral connection,' i.e., the fact that, despite their indefiniteness, there are logical relations among vague predicates: such as, that nothing can be both
260