Conditionals and inferential connections: A hypothetical inferential theory

Abstract

Intuition suggests that for a conditional to be evaluated as true, there must be some kind of connection between its component clauses. In this paper, we formulate and test a new psychological theory to account for this intuition. We combined previous semantic and psychological theorizing to propose that the key to the intuition is a relevance-driven, satisficing-bounded inferential connection between antecedent and consequent. To test our theory, we created a novel experimental paradigm in which participants were presented with a soritical series of objects, notably colored patches (Experiments 1 and 4) and spheres (Experiment 2), or both (Experiment 3), and were asked to evaluate related conditionals embodying non-causal inferential connections (such as "If patch number 5 is blue, then so is patch number 4"). All four experiments displayed a unique response pattern, in which (largely determinate) responses were sensitive to parameters determining inference strength, as well as to consequent position in the series, in a way analogous to belief bias. Experiment 3 showed that this guaranteed relevance can be suppressed, with participants reverting to the defective conditional. Experiment 4 showed that this pattern can be partly explained by a measure of inference strength. This pattern supports our theory's "principle of relevant inference" and "principle of bounded inference," highlighting the dual processing characteristics of the inferential connection.

The Psychology of Uncertainty and Three-Valued Truth Tables

“…We certainly acknowledge that there is a need for additional experiments using other languages and, more importantly, that vary the source of uncertainty. There are perhaps other types of visual uncertainty, e.g., arising from soritical series (see Douven et al, 2018 ), and we should move beyond the visual modality, e.g., to sound or haptic modalities, and then beyond the sensory modalities, e.g., to logical or semantic uncertainty (as can be found in the paradoxes of self-reference; see Elqayam, 2006 ). The choices are unlimited, for uncertainty is everywhere in natural language, a point de Finetti himself would have emphasized.…”

What is wrong with false-link conditionals?

“…One way to account for the oddity of false-link conditionals is to demand the presence of, e.g., an inferential or causal relation between antecedents and consequents for conditionals to be true or acceptable (e.g., Douven 2008;Krzyżanowska et al 2014;Skovgaard-Olsen 2016;Douven et al 2018;van Rooij and Schulz 2018). The connection is then understood as a part of what is said -a conventional, or even truth-conditional content of a conditional, hence sentences such as (1) come out as unacceptable or false.…”

A Conciliatory Answer to the Paradox of the Ravens

“…Although predictive confirmation is a novel idea, at least as I have defined it, and it does not seem to presuppose any particularly controversial theses in the philosophy of language, there are affinities between my notion and some recent work on conditionals. According to the inferentialist theory of conditionals, an utterance of 'If P, then Q' is true if and only if (1) P is evidentially relevant to Q given the utterer's background knowledge 15 and (2) P is consistent with those background knowledge or else is evidence for Q in the absence of relevant background beliefs (Krzyżanowska et al 2013;2014;Douven 2017;Douven et al 2018). This idea is not much younger than Western philosophy (something like it was apparently proposed by Chrysippus) but unlike some earlier versions of the same idea, the inferential connection does not have to be deductive.…”