Séminaire de Recherche en Linguistique

Restrictor Constancy and Hempel's paradox: probabilistic reasoning  and conditional reasoning with quantifiers

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 (building 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:

- 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) as well as to a recent proposal about conditional semantics where a notion of 'aboutness' takes central stage (McHugh 2024)

- 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'

I will show how these findings and the proposed theory can shed light on the Hempel's famous confirmation paradox (see also Rinard 2014):

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

- McHugh, D. (2024). Figure and Ground in Counterfactuals, Ms. 

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