Tue Dec 6, 2022–Wed Dec 7, 2022
234 Moses or Howison Library
Workshop on Probability and Meaning
This is the second part of a two-part workshop sponsored by the France-Berkeley Fund, with additional support from Paul Egré, Benjamin Spector, John MacFarlane, the Townsend Center for Humanities, and Berkeley’s Meaning Sciences Club. The first workshop took place in Paris in June 2022. The workshop is open to anyone interested in the topic.
Linguistic meaning since the 1970s has been modelled successfully within the framework of formal semantics, building on model theory and logic in the wake of pioneering work by Carnap, Montague, and Lewis (based on ideas introduced earlier by Frege and Church). This approach fundamentally equates the meaning of an expression with its contribution to the truth conditions of sentences containing it. Communicative interactions and contextual effects, originally outside the scope of logic, have also been successfully regimented in the field of formal pragmatics, itself based on the work of Grice about the importance of communicative intentions and cooperative principles in discourse. Formal semantics and pragmatics have given rise to predictive and empirically fine-grained characterization of many phenomena, and to a rich and principled typology of semantic and pragmatic inferences. However, in part due to the roots of this tradition in the methodology of deductive logic, the probabilistic dimension of pragmatic inferences has been mostly ignored, and the field has few contact points with other theoretical branches of cognitive science.
Probabilistic approaches, on the other hand, are able to ground accounts of linguistic inferences in independently motivated approaches to inductive reasoning (Bayesian reasoning in particular), and can model the probabilistic nature of these inferences, in line with other developments in cognitive science and in AI. However, they tend to be less concerned with uncovering fine-grained generalizations than formal semantics/pragmatics approaches.
Taking into consideration the relative gap between these two traditions, this collaborative project is guided by the following underlying question: what is the role of probabilities in natural language semantics and pragmatics? In particular, how does probabilistic knowledge influence interpretation and production?
Tuesday Dec. 6
Department of Linguistics, Stanford
On the role of gradient referential utility and incrementality in cross-linguistic referring expression production
Reference is one of the most basic and prevalent functions of language use. A long-standing puzzle for theories of language production is that speakers routinely include redundant modifiers – i.e., modifiers that aren’t strictly speaking necessary for the purpose of uniquely establishing reference – in referring expressions. This redundancy has been argued to violate the tenets of rational language use, thus posing a challenge for standard pragmatic and psycholinguistic theories that treat language production as an efficient tradeoff between maximizing utterance informativeness and minimizing utterance cost.
I show that maintaining the standard theory (as formalized within the Rational Speech Act framework), but relaxing the semantics of words from Boolean to continuous values, yields a number of well-documented patterns in English whereby redundancy is modulated by linguistic (e.g., adjective type) and extra-linguistic (e.g., visual scene complexity) contextual factors. However, this model does not capture a key result: that redundancy appears to be less likely in languages with post-nominal modifiers, like Spanish. I describe the cross-linguistic predictions of an incrementalized version of the model and present data from production studies on a small but diverse set of languages that calls into question the relative importance of language-specific incremental pressures over the inherent contextual utility of mentioning certain properties. This work highlights the need for more explicit formalizations of notions of efficiency in language production; and for further cross-linguistic investigations of reference.
Institut Jean Nicod
Certain and Uncertain Inference with Trivalent Conditionals
In this paper we provide a (non-classical) account of the probability of conditionals, and two logics of conditional reasoning: (i) a logic C of inference from certain premises that generalizes deductive reasoning; and (ii) a logic U of inference from uncertain premises that generalizes defeasible reasoning. Both logics rest on the Cooper conditional (Cooper 1968), a variant of the De Finetti conditional also considered by Belnap, Olkhovikov, and Cantwell. The two logics preserve Import-Export and are connexive, handling the interaction of conditional and negation in a way that departs from classical logic. But whereas C is monotonic for the conditional, U is not, and whereas C obeys Modus Ponens, U does not without restrictions. We use the distinction between the two systems to cast light, in particular, on McGee’s puzzle about Modus Ponens, and draw connections with recent approaches with which our approach converges (Santorio 2022, Neth 2019). (Joint work with Lorenzo Rossi and Jan Sprenger)
Institut Jean Nicod
Relevance, rationality, and confirmation
Despite, or perhaps because of, the hubristic title, this talk will be very much work in progress. In the past 15 years or, psychologists, sometimes in partnership with philosophers and logicians, have produced powerful accounts of (apparent) failures of reasoning in terms of confirmation-theoretic notions (chiefly work by Tentori, Crupi, Fitelson, Tenenbaum, Griffiths). The sharpest empirical phenomena of interest here are from the realm of reasoning by representativeness, as first characterized by Tversky and Kahneman, and as exemplified by the somewhat tiresome but still puzzling conjunction fallacy. More recently, my collaborators and I have argued that the same puzzles from the psychology of reasoning can be described and understood in terms of question-answer dynamics. In published work (with Sablé-Meyer, 2021) and work in progress (with Spector et al., in prep.), we show that these two lines of research can be combined by cashing out the notion of relevance in question-answer dynamics in terms of evidential support, whether directly or by means of suitably Bayesian theory of pragmatics like the RSA. However, recent work by Dorst and Mandelkern gives an account of some of the same puzzles by means of a question-answer dynamic that eschews confirmation theory and predicts a much larger role for “static” posterior probabilities, tempered mainly by a notion of informativeness of an answer A that cares about the proportion of cells from the question partition that are eliminated by A. Each of these proposals has merits and failings, so that the connection between relevance, confirmation, and rationality, at least within the test bed provided by puzzles of reasoning with representativeness, is far from settled. In this talk, I will give a critical review of the state of the art as I see it, and present work in progress on these and related questions.
Visiting Student Researcher, UC Berkeley
Frequencies of Conditionals and Conditional Frequencies
There is an extensive list of analogies between an epistemic reading of indicative conditionals, seem- ingly talking about epistemic possibilities, and an iterative reading, seemingly talking about events or situations. For the epistemic reading, there is a long-standing problem stemming from the observation that probabilities of conditionals seem to be conditional probabilities. A parallel observation can be made for the iterative reading: frequencies of conditionals seem to be conditional frequencies. This leads to a hitherto unrecognized version of the problem. We present several triviality results involving frequencies of conditionals, and argue that a unified solution for probabilities and frequencies should be sought. We investigate which approaches facilitate such a unified solution, and argue that this desideratum favors views that do not identify probabilities of conditionals with probabilities of conditional propositions. (Joint work with Ivano Ciardelli.)
Department of Philosophy, Northeastern University
Probability & Logic/Meaning: Two Approaches
In this talk, I will compare and contrast two approaches to the relation between probability and logic/meaning. First, I will examine the Traditional (“Kolmogorovian”) Approach of setting up probability calculi, which presupposes semantic/logical notions and defines conditional probability in terms of unconditional probability. Then, I will discuss the Popperian Approach, which does not presuppose semantic/logical notions, and which takes conditional probability as primitive. Along the way, I will also discuss the prospects (and pitfalls) of adding an Adams-style conditional to various probability calculi.
Wednesday Dec. 7
Department of Philosophy, UC Berkeley
Nonclassical Probability for Epistemic Modals
In this talk, based on joint work with Matthew Mandelkern (NYU), I will give an overview of our proposed nonclassical semantics and logic for epistemic modals (https://arxiv.org/abs/2203.02872) with special attention to the treatment of probability operators.
Department of Linguistics, UC Berkeley
Semantic categories in computational perspective
I will review recent and ongoing computational work that addresses two related questions at the intersection of language and cognition: (1) Why do languages have the semantic categories they do, and (2) Do semantic categories shape non-linguistic cognition? Specific issues to be addressed include efficient communication, the evolution of semantic systems, and the existence or non-existence of a universal cognitive foundation for linguistic meaning. A general theme will be that approaching these contested questions in probabilistic terms has the potential to resolve some of the tension that surrounds them.
Institut Jean Nicod
The confirmation paradox, Lewisian Imaging and the de re reading of restrictors
This talk is about the psychological side of the confirmation paradox.
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, even in a context where, from a normative point of view, these two types of observations should have the same confirmatory value (where confirmation is construed in Bayesian terms: o confirms S if P(o|S) > P(o)).
I will provide a theory that explains this bias, which is based on the following assumptions:
- Restrictors of determiners are preferably interpreted de re
- Belief update proceeds by Lewisian Imaging rather than by Conditionalization (at least when assessing confirmatory value, cf. next point)
- o is perceived to confirm S given a certain belief state modeled by a probability distribution P if the probability distribution P_S that results from revising P with S by Lewisian Imaging is such that P_S(o) > P(o)
I will present preliminary results from an experimental study which support this theory, as well as additional thought-experiments (essentially experiments yet to be run) for which my introspective judgments also go in favor of the proposed theory.
(Based on joint work with Vincent Mouly)