World Sequence Day 2024

Symposium held at the University of Connecticut on May 24, 2024
convened by Matthew Mandelkern (NYU) and Stefan Kaufmann (UConn)
Heritage Room (4th Floor, Rm. 4118), Homer Babbidge Library
369 Fairfield Way, Storrs, CT

The relationship between the probability of a conditional ‘if A, C’ and the conditional probability of C given A has long been one of the most hotly debated topics in epistemology and philosophy of language, as well as more recently in psychology and linguistics. The 1970’s saw groundbreaking work in this area, including Stalnaker’s (1970) proposal to identify the two probabilities, sometimes known as “Stalnaker’s Thesis” or simply “The Thesis”; Lewis’s (1976) argument that The Thesis is seriously at odds with certain deeply entrenched assumptions about truth conditions and the semantics of conditionals; and van Fraassen’s (1976) ingenious proposal to resolve the tension by adopting a new kind of model theory. In van Fraassen’s models, possible worlds are replaced with sequences of possible worlds. This move solves a surprising number of problems. But it took several more decades of arguments and counterarguments, scrutinizing the topic from every conceivable angle, before researchers began in earnest to explore such world sequence models as an alternative to conventional possible-worlds models. Since the aughts of the new millenium there has been a slew of new proposals and results in this arena, enough to warrant a moment of reflection to take stock and exchange some ideas. Our symposium is meant to provide a forum for this discussion. It brings together two of the original pioneers – Bas van Fraassen and Robert Stalnaker – and a group of younger scholars who have been drivers of the recent surge of interest in the topic.
 

Schedule

Friday, May 24
 8:45- 9:00 Opening
9:00-10:00
In van Fraassen’s, Probability and conditional”, he responds to David Lewis’s triviality result by identifying and rejecting an implicit premise that was crucial to Lewis’s proof, a premise concerning the independence of the truth-conditions for conditionals from the probability judgments about those conditionals. This premise, he wrote, must have been motivated by Lewis’s metaphysical realism, “according to which one should always be able to say: let the possible worlds in my model structure be those which there actually are.” In my response at the time, I acknowledged that Lewis’s proof depended on this premise, but argued that one can get the same triviality result without it, so long as one made an assumption about that the logic of conditionals that I, at least, was prepared to make. In this talk, I want to explore the relationship between general philosophical theses about metaphysical realism and specific theses (such as Lewis’s implicit premise) about connection between truth-conditions (in a model) for conditionals and probability values. Van Fraassen’s own view was that “counterfactual conditionals do not have the function of stating facts, and in a strict sense, none deserve to be called true or false,” but a metaphysical realist who rejects this bold anti-realist thesis (as I do) may still allow for conceptual connections between propositions that make factual claims and propositions (such as probability judgments) about the epistemic status of those claims.
 Handout
10:10-11:10
I will defend several theses about the relation between conditionals (on various interpretations of them, including both counterfactual and indicative conditionals) and probability (on various interpretations of it, including both objective chance and ideally rational credence). These theses have several common features:
  1. While it is not obvious that they are consistent with the nontriviality of the relevant form of probability, this consistency can in fact be established using van Fraassen’s (1975) method.
  2. They only require the probabilities of conditionals to be approximately, not exactly, identical to corresponding conditional probabilities. Motivations for this include Humeanism in the case of objective chance and failures of introspectiveness in the case of rational credence.
  3. They avoid Stalnaker's triviality result by only applying to conditionals with what we call “vanilla” antecedents. While one might be tempted to gloss ‘vanilla’ using some heavyweight metaphysical notion of ‘categoricality’, ‘objectivity’, or ‘factuality’, we’ll suggest that it should be instead be conceived of along similar lines to the notion of a “macroscopic” proposition used in the foundations of statistical mechanics. By allowing for context-sensitivity in what counts as vanilla, one can even allow conditionals as interpreted in one context to count as vanilla by the standards of a different context.
  4. They generalize familiar conditional-probability theses by putting conditional probabilities on both sides: so long as A and B are vanilla and A entails B, the probability that if A then C, conditional on B, is (approximately) equal to the probability of C conditional on A. This additional generality makes the equations robust under a wide range of contextual variations in which the values of certain questions (probabilistically independent of the antecedent) are held fixed, such as those suggested in the work of Kaufmann. It also enables explanation of little-discussed patterns involving indicative conditionals embedded under conative attitude verbs, such as the similarity in the truth conditions of ‘x hopes that if A then C’ and ‘x would prefer that A and C than that A and not C’.
 Slides
11:20-12:20
Snow Zhang, UC Berkeley
Probability judgments play a central role in the philosophy of conditionals. However, probabilities are hard, and our intuitions are notoriously unreliable. So, how should we adjudicate between competing intuitions about the probabilities of conditionals? One method, as adopted by McGee (1989), is to “equate the problem about probabilities with a problem about how to settle a bet fairly” (p.503). However, as pointed out by Paris (2009), there are multiple notions of “fair bets”; different notions justify different sets of probability axioms. This talk applies Paris’ insight to the context of conditionals. I develop a general framework for defining fair bets and Dutch books, and prove a general result that entails Dutch-book results for the probability axioms of sequence semantics and trivalent semantics. If time permits, I’ll discuss how to generalize the framework to define dynamic Dutch-books, and how this generalization might shed light on the status of reflection principles with respect to probabilities of conditionals.
 Slides
12:20- 1:20 Lunch break
 1:20- 2:20
Calum McNamara, University of Michigan, Ann Arbor
A prominent challenge for Bayesians is to say how your credences should change when you learn an indicative conditional. A number of cases in the literature seem to show that the standard Bayesian update rules—conditionalization and Jeffrey conditionalization—give implausible results when you learn conditionals of this kind. The most famous of these cases is Bas van Fraassen’s Judy Benjamin problem, where it's shown that if, after learning an indicative conditional, your credences satisfy some intuitive desiderata, then you can't be updating in accordance with standard Bayesianism. In response to this case, some authors have argued against van Fraassen's desiderata, while others have given additional updating rules, intended to supplement standard Bayesianism. In this talk, however, I’ll argue that both kinds of response are mistaken. I'll first draw a connection between the Judy Benjamin problem, on the one hand, and the thesis known as Stalnaker's thesis, on the other. Stalnaker's thesis—which relates your credences in indicative conditionals to your conditional credences—was for a long time thought to be untenable, owing to the famous triviality results of Lewis and others. However, recent work has shown that, given a sophisticated contextualist view about indicative conditionals, this thesis is tenable after all. In the talk, I’ll show that, given the same contextualist view of indicative conditionals, the standard Bayesian update rules can satisfy all of the intuitive desiderata in van Fraassen’s case. I’ll then show that certain alternatives to the Bayesian rules actually turn out to be equivalent to those rules in particular contexts. Thus, what we end up with is a nice, unified account of rational learning—one which fits well with recent work on the semantics of conditionals, and on Stalnaker's thesis more specifically.
 Handout
 2:30- 3:30
Melissa Fusco, Columbia
I present a hybrid decision theory, coinciding sometimes with (traditional) EDT, but usually with (traditional) CDT, which is inspired by recent work on the probabilities of indicative and subjunctive conditionals. The hybrid theory features a few other loci of interest: the partitionality of options fails in an important way, and close attention is paid to how one might (dis)confirm chance hypotheses under the umbrella of the Principal Principle. On this theory, the credences it is epistemically rational to assign to these conditionals can guide updating on one’s own acts. This implies some departures from Conditionalization—departures I defend on epistemological grounds. This has important ramifications for cases of diachronic instability.
 Handout
 3:40- 4:40
I will argue for three claims. First, that lack of closure under conditionalization is ubiquitous and not a fault. Second, that the CCCP (Stalnaker’s Thesis) has consequences for our basic concept of the relation of logical consequence. Third, that Alan Hajek’s view, that conditionals are true only if the corresponding conditional probability equals 1, can receive a tenable formulation by relinquishing possible world semantics.

Logistics:

For those who will be driving and don't have a UConn parking permit, the best parking option is the Downtown Storrs Parking Garage at 33 Royce Circle. It's about a 15-20min walk from there to the venue. Parking is also available (slightly closer to the venue) in two public garages on Storrs Campus.

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