Possibilities and the parallel meanings of factual and counterfactual conditionals

Reasoning about possibilities: Modal logics, possible worlds, and mental models

Everyone reasons about possibilities. This article explains how they could do so using mental models. The theory makes four major claims: 1. Correct inferences are necessary, referring only to facts or possibilities to which the premises refer and not ruling any of them out, for example: She left or hid; Therefore, it's possible that she left and possible that she hid. 2. A possibility such as that she hid, which is represented in an intuitive model, presupposes the possibility that it did not occur, she did not hide, which, if reasoners deliberate, is represented in the resulting model. 3. Reasoners condense consistent possibilities, such as the earlier pair, into one possibility: it is possible that she left and she hid. 4. Inconsistencies, such as she left or hid, and she neither left nor hid, refer to no possibilities whatsoever - they have an empty model - and so their only effects are local. Hence, any inference can be withdrawn with impunity if there is knowledge to the contrary. Experiments have corroborated each of these principles. They are incompatible with four essentials of standard modal logics, which concern deductions based on "possible" or "necessary". Their formal deductions correspond to valid inferences, which have no counterexamples in which the premises are true but the conclusion is false. And so the article examines the differences between the two approaches, and explores the adaptation of a modal logic to account for correct human reasoning. Its feasibility is an open question.

Human verifications: Computable with truth values outside logic

Cognitive scientists treat verification as a computation in which descriptions that match the relevant situation are true, but otherwise false. The claim is controversial: The logician Gödel and the physicist Penrose have argued that human verifications are not computable. In contrast, the theory of mental models treats verification as computable, but the two truth values of standard logics, true and false, as insufficient. Three online experiments (n = 208) examined participants' verifications of disjunctive assertions about a location of an individual or a journey, such as: 'You arrived at Exeter or Perth'. The results showed that their verifications depended on observation of a match with one of the locations but also on the status of other locations (Experiment 1). Likewise, when they reached one destination and the alternative one was impossible, their use of the truth value: could be true and could be false increased (Experiment 2). And, when they reached one destination and the only alternative one was possible, they used the truth value, true and it couldn't have been false, and when the alternative one was impossible, they used the truth value: true but it could have been false (Experiment 3). These truth values and those for falsity embody counterfactuals. We implemented a computer program that constructs models of disjunctions, represents possible destinations, and verifies the disjunctions using the truth values in our experiments. Whether an awareness of a verification's outcome is computable remains an open question.

Scientific counterfactuals as make-believe

Counterfactuals abound in science, especially when reasoning about and with models. This often requires entertaining counterfactual conditionals with nomologically or metaphysically impossible antecedents, namely, counternomics or counterpossibles. In this paper I defend the make-believe view of scientific counterfactuals, a naturalised fiction-based account of counterfactuals in science which provides a means to evaluate their meanings independently of the possibility of the states of affairs their antecedents describe, and under which they have non-trivial truth-values. Fiction is here understood as imagination (in contrast with its most typical association with falsity), characterised as a propositional attitude of pretense or 'make-believe' (Walton 1990). The application of this theory to scientific counterfactuals makes their evaluation a game of make-believe: a counterfactual is (fictionally) true iff its antecedent and the rules of the game prescribe the imagining of its consequent (Kimpton-Nye 2020). The result is a practice-based account of counterfactuals and counterfactual reasoning in science which incorporates insights from theoretical and experimental analytic philosophy as well as cognitive science. This way, the make-believe view of scientific counterfactuals shows that the evaluation of scientific counterfactuals is none other than a question of scientific representation in disguise.