That seems fair enough. Do you know what Field had to say about the “truth teller” (“This sentence is true”)? While the liar sentence can (classically) be neither true nor false, the problem with the truth teller is that it can be either true or false, with no fact of the matter deciding which. This does seem to be a closely related problem, even it it isn’t always considered a serious paradox. I’m not aware fuzzy truth values can help here. This is on contrast to Kripke’s proposed solution to the liar paradox: On his account, both the liar and the truth teller are “ungrounded” rather than true or false, because they use the truth predicate in a way that can’t be eliminated. Though I think one can construct some revenge paradoxes with his solution as well.
Anyway, I still think the main argument for fuzzy logic (or at least fuzzy truth values, without considering how logical connectives should behave) is still that concepts seem to be inherently vague. E.g. when I believe that Bob is bald, I don’t expect him to have an exact degree of baldness. So the extension of the concept expressed by the predicate “is bald” must be a fuzzy set. So Bob is partially contained in that set, and the degree to which he is, is the fuzzy truth value of the proposition that Bob is bald. This is independent of how paradoxes are handled.
(And of course the next problem is then how fuzzy truth values could be combined with probability theory, since the classical axiomatization of probability theory assumes that truth is binary. Are beliefs perhaps about an “expected” degree of truth? How would that be formalized? I don’t know.)
That seems fair enough. Do you know what Field had to say about the “truth teller” (“This sentence is true”)? While the liar sentence can (classically) be neither true nor false, the problem with the truth teller is that it can be either true or false, with no fact of the matter deciding which. This does seem to be a closely related problem, even it it isn’t always considered a serious paradox. I’m not aware fuzzy truth values can help here. This is on contrast to Kripke’s proposed solution to the liar paradox: On his account, both the liar and the truth teller are “ungrounded” rather than true or false, because they use the truth predicate in a way that can’t be eliminated. Though I think one can construct some revenge paradoxes with his solution as well.
Anyway, I still think the main argument for fuzzy logic (or at least fuzzy truth values, without considering how logical connectives should behave) is still that concepts seem to be inherently vague. E.g. when I believe that Bob is bald, I don’t expect him to have an exact degree of baldness. So the extension of the concept expressed by the predicate “is bald” must be a fuzzy set. So Bob is partially contained in that set, and the degree to which he is, is the fuzzy truth value of the proposition that Bob is bald. This is independent of how paradoxes are handled.
(And of course the next problem is then how fuzzy truth values could be combined with probability theory, since the classical axiomatization of probability theory assumes that truth is binary. Are beliefs perhaps about an “expected” degree of truth? How would that be formalized? I don’t know.)