Conditionals and testimony

Abstract

Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much-perhaps most-of what we believe through the testimony of others, the simple matter of acquiring conditionals via others' assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning -a challenge which no account presently fully meets. IntroductionEach day we encounter conditional sentences: sentences, most typically, of the form "If P, (then) Q". Conditionals can make assertions: "If people smoke, they have a higher risk of lung cancer." They can give advice or warnings: "If you stand here (there), you'll have a better (worse) view." They can express promises-"If I'm free, I promise I'll come to your party"-and bets-"If Liverpool and Tottenham make the final, I bet you £50 Liverpool will win." They can make claims about worlds that turned out differently from our own-"If Oswald hadn't killed Kennedy, someone else would have"-or that may yet come to pass-"If a sane candidate were to win, we might not be doomed." In short, conditionals are a flexible way to communicate information, or perform speech acts, under uncertainty.When we receive such conditionals, we must interpret them and we may change our beliefs. These sentences seem natural: we seem to understand them effortlessly and, where appropriate, assimilate their content seamlessly. And yet it remains somewhat mysterious how we change our beliefs when we encounter a conditional. This paper pursues the question of how we change our beliefs in response to conditional assertions. It will focus on indicative conditionals: conditional sentences in the indicative mood or, roughly, in which tense has the usual temporal meaning: present means present; past means past; and so on (Declerck & Reed, 2001). Another key type of conditional is the subjunctive or counterfactual conditional. To see the difference, compare these examples from

Inference from explanation.

“…For example, research on conditional reasoning has shown that people’s assumptions about the causal structure (Bonnefond et al, 2014; Byrne, 1989; Byrne et al, 1999; Espino & Byrne, 2020) and their normative expectations about the frequency of events (Oaksford & Chater, 1994, 2003) affect what inferences people draw. Precisely what people infer from conditional statements is still very much under investigation (Barrouillet et al, 2008; Collins et al 2020; Khemlani & Johnson-Laird, 2013; Sebben & Ullrich, 2021; Skovgaard-Olsen et al, 2021). Given the tight relationship between conditionals and causality (e.g., Goldvarg & Johnson-Laird, 2001; Over et al, 2007), we suspect that inferences from conditional statements, just like inferences from explanations, may be illuminated by considering what role these statements play in communication (see also Evans, 2005; Johnson-Laird & Byrne, 2002; Sebben & Ullrich, 2021).…”

Bayesians Still Don’t Learn from Conditionals

“…Conflict of Interest The authors declare no competing interests. 17 Collins et al (2020) show that no present Bayesian approach accounts satisfactorily for the behavioral data, including a precursor of Eva et al's updating strategy based on distance minimization to be found in Eva and Hartmann (2018). Vandenburgh (2021Vandenburgh ( , p. 2428) puts forth a promising account, where the first step of learning a conditional is to learn a causal model, or a set of structural equations, that expresses "the right dependence" between the conditional's antecedent and consequent.…”

On logical inference over brains, behaviour, and artificial neural networks

“…(emphasis added, Rogers et al, 2004, p. 229) The use of "may" makes the syllogism probabilistic modus ponens in a clear way, which might not leave the door open to accidentally affirming the consequent. Importantly, however, this is only true in a fully formal setting and natural language can still lead to affirming the consequent Collins, Krzyanowska, Hartmann, Wheeler, & Hahn, 2020). Avoiding affirming the consequent can also be subserved by the clarification that ANNs "may simply rely on brute-force memorization and interpolation to learn how to generate the appropriate linguistic outputs in light of prior contexts" (Goldstein et al, 2021) -something which does appear to be true in certain contexts (Zhang, Bengio, Hardt, Recht, & Vinyals, 2016).…”