ABSTRACTTreating conditionals as probabilistic statements has been referred to as a defining feature of the “new paradigm” in cognitive psychology. Doing so is attractive for several reasons, but it complicates the problem of assessing the merits of conditional arguments. We consider several variables that relate to judging the persuasiveness of conditional arguments with uncertain premises. We also explore ways of judging the consistency of people's beliefs as represented by components of conditional arguments. Experimental results provide evidence that inconsistencies in beliefs (...) are more prevalent if the arguments’ components are spatially and temporally dispersed than if they are contiguous in space and time. This supports the idea that assuring the consistency among even a small number of beliefs is difficult to do, especially if the beliefs in question are not brought into consciousness at the same time; but consistency can be enhanced when beliefs are considered simultaneously or nea... (shrink)

The Identity principle says that conditionals with the form 'If p, then p' are logical truths. Identity is overwhelmingly plausible, and has rarely been explicitly challenged. But a wide range of conditionals nonetheless invalidate it. I explain the problem, and argue that the culprit is the principle known as Import-Export, which we must thus reject. I then explore how we can reject Import-Export in a way that still makes sense of the intuitions that support it, arguing that the differences between (...) indicative and subjunctive conditionals play a key role in solving this puzzle. (shrink)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that (...) 'p and might not p', a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not allow substitution of logical equivalents; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a more concrete possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. Then we show how to extend our semantics to explain parallel phenomena involving probabilities and conditionals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...) remove an argumentative form from a logical system without getting entangled in an intricate logical web, since these revisions imply the removal of other parts of a system we want to maintain. Consequently, these revisions are incoherent and unwarranted. At the very least, the usual approach in the analysis of counter-examples of argumentative forms must be seriously reconsidered. (shrink)