Online research in philosophy

(i) Inferences from the (assumed) truth of the asserted sentence. Hearers may have conditional beliefs (if p, q) and upon hearing p asserted they can infer q by Modus Ponens (with suitable caveats about the reliability of their initial conditional belief and the new information that p).

The paper presents a non-monotonic inference relation on a language containing a conditional that satisfies the Ramsey Test. The logic is a weakening of classical logic and preserves many of the ‘paradoxes of implication’ associated with the material implication. It is argued, however, that once one makes the proper distinction between supposing that something is the case and accepting that it is the case, these ‘paradoxes’ cease to be counterintuitive. A representation theorem is provided where conditionals are given a non-bivalent semantics and epistemic states are represented via preferential models.

The empirical phenomenon at the center of this paper is projection, which we define (uncontroversially) as follows: (1) Definition of projection An implication projects if and only if it survives as an utterance implication when the expression that triggers the implication occurs under the syntactic scope of an entailment-cancelling operator. Projection is observed, for example, with utterances containing aspectual verbs like stop, as shown in (2) and (3) with examples from English and Paraguayan Guaraní (Paraguay, Tupí-Guaraní).1 The Guaraní example in (2) and its English translation have at least the following implications: (i) Carla has previously smoked, and (ii) Carla stopped smoking. The first but not the second of these implications is also conveyed by the question version of sentence (2), as in (3a), or when (2) is embedded under entailment-cancelling sentential operators, such as negation, as in (3b), the antecedent of a conditional, as in (3c), or an epistemic modal, as in (3d). Hence, by the definition in (14), the first but not the second implication of (2) projects.

This paper is concerned with Sir Peter Strawson’s critical discussion of Paul Grice’s defence of the material implication analysis of conditionals. It argues that although Strawson’s own ‘consequentialist’ suggestion concerning the meaning of conditionals cannot be correct, a related and radically contextualist account is able to both account for the phenomena that motivated Strawson’s consequentialism, and to undermine the material implication analysis by providing a simpler account of the processes that we go through when interpreting conditionals.

This paper presents a unified, more-or-less complete, and largely pragmatic theory of indicative conditionals as they occur in natural language, which is entirely truth-functional and does not involve probability. It includes material implication as a special—and the most important—case, but not as the only case. The theory of conditional elements, as we term it, treats if-statements analogously to the more familiar and less controversial other truth-functional compounds, such as conjunction and disjunction.

In this paper Grice’s requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz’s conclusion-relevant consequence relation.

It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius' Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which instances of CEM are derivable. We also investigate the systems CIw and CI of consequential implication, corresponding to the modal logics K and KD respectively, with occasional remarks about stronger systems. While unrestricted CEM produces modal collapse in all these systems, CEM restricted to contingent formulas yields the Alt2 axiom (semantically, each world can see at most two worlds), which corresponds to the symmetry of consequential implication. It is proved that in all the main systems considered, a given instance of CEM is derivable if and only if the result of replacing consequential implication by the material biconditional in one or other of its disjuncts is provable. Several related results are also proved. The methods of the paper are those of propositional modal logic as applied to a special sort of conditional.

This article introduces the classic accounts of the meaning of conditionals (material implication, strict implication, variably strict conditional) and discusses the difference between indicative and subjunctive/counterfactual conditionals. Then, the restrictor analysis of Lewis/Kratzer/Heim is introduced as a theory of how conditional meanings come about compositionally: if has no meaning other than serving to mark the restriction to an operator elsewhere in the conditional construction. Some recent alternatives to the restrictor analysis are sketched. Lastly, the interactions of conditionals (i) with modality and (ii) with tense and aspect are discussed. Throughout the advanced research literature is referenced while the discussion stays largely non-technical.