While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that (...) do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ϕ entails conditional-free ψ, “if ϕ then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional. (shrink)

Most instantiations of the inference ‘y; so if x, y’ seem intuitively odd, a phenomenon known as one of the paradoxes of the material conditional. A common explanation of the oddity, endorsed by Mental Model theory, is based on the intuition that the conclusion of the inference throws away semantic information. We build on this explanation to identify two joint conditions under which the inference becomes acceptable: (a) the truth of x has bearings on the relevance of asserting y; and (...) (b) the speaker can reasonably be expected not to be in a position to assume that x is false. We show that this dual pragmatic criterion makes accurate predictions, and contrast it with the criterion defined by the mental model theory of conditionals, which we show to be inadequate. (shrink)

There is an Aristotelian thesis that can be considered controversial. That is the thesis related to a denied conditional with only one propositional variable and in which, in addition, one of its clauses is also denied. While the thesis is not a tautology, people tend to accept it as true. Pfeifer’s approach can account for this fact. However, I try to show that this problem can also be explained from other alternative frameworks, in particular, from that of the mental models (...) theory, that of López-Astorga based on the pragmatic phenomenon of conditional perfection, and that of the mental logic theory. Likewise, I indicate the difficulties regarding Aristotle’s thesis of the mental models theory and López-Astorga’s proposal, and conclude that the account of the mental logic theory is the strongest alternative to Pfeifer’s explanation and that what is clearly obvious is that conditional should not be materially interpreted. (shrink)

I take up the four issues considered by Johnson -Laird, Byrne and Girotto in their reply to Politzer. Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one and can be attenuated about the second one. However, I maintain and refine my criticisms on the last two, backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals.

There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a (...) whole spectrum of consequence relations, flexible enough to be tailored for choices from a variety of contexts. We do so by investigating semantic constraints on classical entailment which give rise to a family of infra-classical logics with appealing properties. More specifically, our infra-classical reasoning demands (beyond ${\alpha\models\beta}$ ) that Mod(β) does not run wild, but lies within the scope (whatever that may mean in some specific context) of Mod(α), and which can be described by a sentence ${\bullet\alpha}$ with ${\beta\models\bullet\alpha}$ . Besides being infra-classical, the resulting logic is also non-monotonic and allows for non-trivial reasoning in the presence of inconsistencies. (shrink)