deperplex
logic, epistemic modality, trivalence, Gödel, Aymara, paradox

  Originally published on Language and Philosophy, March 21, 2016 Do scientists from differing disciplines have the same goals in addressing the same facts? Linguists attempt to accommodate all the natural language intuitions in their theoretical frameworks. That may lead them to extralogical means. Logicians have often taken on one or another natural language intuition and attempt to augment the logic to accommodate that intuition. In both cases there’s a question of purview: why not accommodate all the intuitions through the logical system, or how much of logic should accommodate the intuitions? This became the battle at a workshop on imperatives at NYU today. Craige Roberts incorporated pragmatics into her analysis of imperatives to include a wide variety of natural language intuitions, while Kit Fine and Peter Vranas developed new logics to deal with some, but not all, intuitions. They both seemed to ignore that traditional logics are not just inadequate for linguistic intuitio...

  Originally published on Language and Philosophy, June 20, 2013 It’s easy to mistake paradoxical sentences for liar paradoxes. “If this sentence is true, then it is false,” is a liar paradox. If the sentence is true, then the antecedent is true. If the antecedent is true, then the consequent must be false, the implication as a whole is false, so the sentence must be false. So if the sentence is true, then it is a contradiction and a falsehood. So the antecedent must not be true. If the sentence is false, antecedent is false, and the implication as a whole is true. “If this sentence is false, then it is true,” however, is not a liar paradox. If it is false, then the antecedent is true and the implication fails, and the whole is false. If the sentence is true, then the antecedent is false, the implication holds, and the sentence is true. That’s not a paradox, it’s just a sentence the truth of which cannot be determined. It’s like the sentence, “This sentence is true.” Is it true or ...

  Originally published on Language and Philosophy, June 16, 2013 “I’m very witty!” someone wrote in a comment box in response to the criticism “You have no wit.” “I’m very witty” might seem at first a witless and therefore unpersuasive response, unless it is sarcastic, in which case it is actually witty. If it’s sarcastic, the meaning intended to convey is that author isn’t witty, and therefore it implies that the comment itself also is not witty. The joke is, the author knows it’s not witty; yet that’s what makes it witty. So if it’s witty, it’s a lie; if it’s a lie, it’s not witty: a liar paradox. But if the comment is merely false, then there’s no paradox — just a reply by someone who thinks he’s witty but is too dull to know he’s not witty, and hasn’t enough wit to say so wittily. So if it’s a lie, then it is a meta-witty paradox; if an honest falsehood, it’s just stupid. What’s interesting is that the intention or speaker’s attitude or character of mind induces the paradox, no...

  Originally published on Language and Philosophy, May 31, 2012 The peculiarity of classical notion of possibility is that it has a relation to the actual world as well as a relation to the irreal world of conditions counter to the actual and the epistemic world of certainty and uncertainty. Lukasiewicz’ notion of possibility seems to apply only to uncertainty — it seems essentially epistemic. So here’s the lay of the land, as I see these two modal programs: Classical actual=>possible (simpliciter) [because the actual is one instance (though merely one)] necessary=>possible (simpliciter) contingent (possible & possible-not)=>not necessary contingent (possible & possible-not)<=>not necessary & not necessarily not actual & not necessary=>contingent [possible-not in some plausible world beyond the actual world] The actual and its entailments are non epistemic; contingency and necessity are epistemic. Non classical actual=>necessary=>not continge...

  Originally published on Language and Philosophy, May 30, 2012 [This post has been updated for clarity.] Łukasiewicz supposed that the actual is necessary (if I have no coins in my pocket, then it is not possible that I do have a coin there) and that possible implies possibly not . I want to contest both of these. There is good reason to distinguish the actual from the necessary — the earth revolves around the sun is an actual fact, but that the sun is the center of the solar system is necessary (on the grounds that “solar” means “sun”). But if the earth does revolve around the sun, and it’s not possible therefore that it doesn’t revolve around the sun, then isn’t the earth’s revolution around the sun necessary (Łukasiewicz’ not-possibly-not)? So hasn’t he leveled a useful distinction? Consider actuality from the perspective of possible worlds. “The earth revolves around the sun” is actually true now. But at another time, maybe not. So to identify the world in which it is actual,...

  Originally published on Language and Philosophy, May 13, 2012 Is there a place for a third truth value? There are two uses for a third truth value: one is the ontological trash bin; the other uncertainty. They are worlds apart. The trashbin is filled with sentences like “The present king of France is bald” (Russell’s example), “Colorless green ideas sleep furiously ” (Chomsky’s), “The a book left,”  “Did you stop beating your wife?” asked of someone who never beat his wife or doesn’t have a wife. Generally, these sentences fail in some presupposition: there is no king of France, nothing can be both green and not, a thing can’t be designated as the particular and not particular,  you can’t spot beating your wife if you never did. Dumping these sentences into a third category of neither true nor false seems harmless to me. It doesn’t have any adverse consequences for logic and has the advantage of dealing simply with presupposition failures. If such a sentence is neither ...