**Speaker: ** Benjamin Spector (Institut Jean Nicod (CNRS-ENS-EHESS))

**Title: **Reasoning with Quantifiers, Lewisian Imaging and the Confirmation Paradox

**Time: **Friday, December 8th, 3:30pm – 5pm

**Location: **32-141

**Abstract: **From a normative point of view, the conclusions we can draw from a sentence of the form No A is B are the same as the ones we can draw from No B is A, because No is a symmetric determiner, and therefore these two sentence types are logically equivalent. I will present experimental evidence (based on joint work with Vincent Mouly) showing that people do not in fact reason in the same way with No A is B and with No B is A. In particular, people’s estimate of the number of As after processing No A is B is higher than after processing No B is A (and vice-versa for B). I will argue that this instantiates a more general property of restrictors: we tend not to revise our beliefs about the size of the restrictor set even when receiving information that would in fact warrant such a revision. I will argue that this effect can be explained if we make the following hypotheses:

– Belief update does not (always) correspond to probabilistic conditionalization, but can also proceed by Imaging, as defined by David Lewis (1976). In a nutshell, when revising our beliefs with a proposition S, our posterior degree of confidence in a certain proposition T corresponds to our prior degree of confidence in the conditional ‘If S, T’ (using Stalnaker’s semantics for conditionals), rather than to the conditional probability P(T|S).

– Restrictors tend to serve as anchors when we engage in conditional reasoning: when considering the different ways in which a quantified sentence could be true, we mentally keep constant the restrictor set. I will relate this both to the possibility of de re readings for restrictors and to recent experimental results about verification strategies for quantified statements (Knowlton, Pietroski, Williams et al. 2023).

I will show that how these findings and the proposed theory can shed light on the confirmation paradox (see also Rinard 2014): given a statement S of the form ‘All As are Bs’, people are more prone to think that an observation of an object that has both properties A and B ‘confirms’ S than they are to think that observing an object that is both not-B and not-A confirms S, and I will discuss, time permitting, further experimental results (based on joint work with Nicolas Poisson) pertaining to the confirmation paradox.

Selected References:

– Knowlton, T., Pietroski, P, Williams, A., Halberda, J & Lidz, J. (2023), Psycholinguistic evidence for restricted quantification. Nat Lang Semantics 31, 219–251. https://doi.org/10.1007/s11050-023-09209-w

– Lewis, D., (1976), Probabilities of Conditionals and Conditional Probabilities, Philosophical Review, 85(3): 297–315. doi:10.2307/2184045

– Rinard, S. (2014), A New Bayesian Solution to the Paradox of the Ravens, Philosophy of Science 81 (1):81-100 (2014)