Inference strength predicts the probability of conditionals better than conditional probability does

Abstract

According to the philosophical theory of inferentialism and its psychological counterpart, Hypothetical Inferential Theory (HIT), the meaning of an indicative conditional centrally involves the strength of the inferential connection between its antecedent and its consequent. This paper states, for the first time, the implications of HIT for the probabilities of conditionals. We report two experiments comparing these implications with those of the suppositional account of conditionals, according to which the probability of a conditional equals the corresponding conditional probability. A total of 358 participants were presented with everyday conditionals across three different tasks: judging the probability of the conditionals; judging the corresponding conditional probabilities; and judging the strength of the inference from antecedent to consequent. In both experiments, we found inference strength to be a much stronger predictor of the probability of conditionals than conditional probability, thus supporting HIT.

Towards a theory of abduction based on conditionals

“…However, the ambiguous results can be explained by a variety of factors (Skovgaard-Olsen et al, 2016; and studies specifically comparing the two conditional theories provide support for inferentialism (Mirabile & Douven, 2020, p. 26;Skovgaard-Olsen et al, 2019;Krzyżanowska et al, 2021;Nickerson et al, 2019, pp. 61f;Krzyżanowska & Douven, 2018;Douven, Elqayam and Mirabile 2022b).…”

Williamson’s Abductive Case for the Material Conditional Account

“…As seen in Section 1.1, Skovgaard-Olsen et al [77] showed that people do not in general evaluate the probabilities of conditionals in accordance with (EQ), not even approximately. Further support for this finding comes from two experiments reported in Douven et al [21]. The materials of these experiments consisted of conditionals with differing inferential connections between their antecedent and consequent.…”

“…For further evidence, see Krzyżanowska et al [40], Vidal and Baratgin [91], Krzyżanowska and Douven [41], Stewart et al ( 2021), Douven et al [18], and Rostworowski et al [68]. 21 What does inferentialism entail for (EQ) and for the triviality result that threatens it? To start with the latter, we recall that it crucially hinges on both Pr(A ⇒ C C) = 1 and Pr(A ⇒ C ¬C) = 0.…”

Coherence, not conditional meaning, accounts for the relevance effect

“…The call by Oaksford and Chater ( 2001 , 2007 ) for a paradigm shift in the psychological study of reasoning to take into account the probabilistic nature of reasoning has undergone major development in recent years and has provided many explanations for the inferences and representations of logical arguments implemented in everyday life (for comments: Over, 2009 , 2020 , 2021 ; Evans, 2012 ; Elqayam and Over, 2013 ; Oaksford and Chater, 2013 ; Baratgin et al, 2015 ; Johnson-Laird et al, 2015 ; Baratgin and Politzer, 2016 ; Elqayam, 2017 ; Knauff et al, 2021 ; Oaksford, 2021 ; Cruz, 2022 ; Douven, 2022 ; Johnson-Laird and Khemlani, 2022 ). This new paradigm gathers two families of theories that make use of Bayesian concepts in somewhat different ways (Elqayam and Evans, 2013 ; Douven et al, 2022 ). “Strict Bayesians” tend to lean closer toward classical Bayesian precepts, explaining deviations from these norms in terms of interactions with other systems—for example, conversational pragmatics and details of natural language semantics (Baratgin, 2002 ; Baratgin and Politzer, 2006 ; Cruz et al, 2016 ; Lassiter and Baratgin, 2021 ; Cruz and Over, 2023 ; Over and Cruz, 2023 ).…”

“…"Strict Bayesians" tend to lean closer toward classical Bayesian precepts, explaining deviations from these norms in terms of interactions with other systems-for example, conversational pragmatics and details of natural language semantics (Baratgin, 2002;Baratgin and Politzer, 2006;Cruz et al, 2016;Lassiter and Baratgin, 2021;Cruz and Over, 2023;Over and Cruz, 2023). "Soft Bayesians", for instance proponents of the Hypothetical Inferential Theory (HIT) agree on the importance of uncertainty and subjective degrees of belief in reasoning but reject some aspects of Bayesian orthodoxy (Douven and Verbrugge, 2012;Douven, 2015Douven, , 2017Douven, , 2022Krzyżanowska et al, 2017Krzyżanowska et al, , 2021Douven et al, 2018Douven et al, , 2022Krzyżanowska and Douven, 2018;Mirabile and Douven, 2020).…”