Logically Negative Thoughts without Negaters

Is (1) a constituent of (2)? Is the negation in (2) sentential, as in (2a) or (2b) or (2c)? (1) Aristotle was dumb. (2) Aristotle wasn’t dumb. (2a) ~Dumb(Aristotle) (2b) ~$x[Aristotle(x) & Dumb(x)] (2c) $x[Aristotle(x) & ~Dumb(x)] Is the thought expressed with (2) a constituent of the thought expressed with (1)? Is the negation in (3) sentential? (3) Pegasus doesn’t exist. Like many others, including Aristotle and Larry Horn, I think the answers are negative—pace standard textbooks in semantics and a lot of analytic philosophy. But what’s the alternative? In first part of the talk, I’ll describe a possible language of thought—a computational system that generates endlessly many complex concepts from a finite stock of atomic concepts—that has no sentential negation (or variables), but is powerful enough to reconstruct propositional logic and syllogistic logic, in a way that easily captures the pattern of valid inference illustrated with (4-7). (4) A spy poked a soldier with a pencil in a library (5) A spy poked a soldier with a pencil (6) A spy poked a soldier in a library (7) A spy poked a soldier I sketched this system in Conjoining Meanings (OUP, 2018) and showed how it can be used to reconstruct a lot of elementary semantics. Icard and Moss (2023) formalized the system as a logic and proved some interesting results that I’ll review, focusing on the absence of a negation operator and corresponding kinds of computational simplicity. Some of the material I’ll present is from Pietroski and Icard (forthcoming). In the second part of the talk, as time permits, I’ll review some collaborative experimental work (with Jeff Lidz, Justin Halberda, and others) that bolsters the following idea: sentential negation is foreign to the cognitive systems that humans use to understand the “logical vocabulary” of the languages we naturally acquire. This all coheres with a conjecture, urged by Bill Idsardi, according to which semantics (like phonology) is computationally simpler than syntax