An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals (...) with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

Claims that necessary and sufficient conditions are not converse relations are discussed, as well as the related claim that If A, then B is not equivalent to A only if B . The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance of distinguishing sufficient-cause conditionals from necessary-cause conditionals. It is concluded that necessary and sufficient conditions, adequately interpreted, are converse relations in (...) all cases. (shrink)

We develop and defend a new approach to counterlogicals. Non-vacuous counterlogicals, we argue, fall within a broader class of counterfactuals known as counterconventionals. Existing semantics for counterconventionals, 459–482 ) and, 1–27 ) allow counterfactuals to shift the interpretation of predicates and relations. We extend these theories to counterlogicals by allowing counterfactuals to shift the interpretation of logical vocabulary. This yields an elegant semantics for counterlogicals that avoids problems with the usual impossible worlds semantics. We conclude by showing how this approach (...) can be extended to counterpossibles more generally. (shrink)

Studies of several languages, including Swahili [swa], suggest that realis (actual, realizable) and irrealis (unlikely, counterfactual) meanings vary along a scale (e.g., 0.0–1.0). T-values (True, False) and P-values (probability) account for this pattern. However, logic cannot describe or explain (a) epistemic stances toward beliefs, (b) deontic and dynamic stances toward states-of-being and actions, and (c) context-sensitivity in conditional interpretations. (a)–(b) are deictic properties (positions, distance) of ‘embodied’ Frames of Reference (FoRs)—space-time loci in which agents perceive and from which they contextually (...) act (Rohrer 2007a, b). I argue that the embodied FoR describes and explains (a)–(c) better than T-values and P-values alone. In this cognitive-functional-descriptive study, I represent these embodied FoRs using Unified Modeling Language (UML) mental spaces in analyzing Swahili conditional constructions to show how necessary, sufficient, and contributing conditions obtain on the embodied FoR networks level. (shrink)

It is argued that contraposition is valid for a class of natural language conditionals, if some modifications are allowed to preserve the meaning of the original conditional. In many cases, implicit temporal indices must be considered, making a change in verb tense necessary. A suitable contrapositive for implicative counterfactual conditionals can also usually be found. In some cases, the addition of certain words is necessary to preserve meaning that is present in the original sentence and would be lost or changed (...) in the contrapositive without them. A distinction is made between adding new meaning and adding new words to preserve existing meaning. For concessive conditionals and relevance conditionals, however, no valid contrapositive can be found. They do not belong to the class of contraposable conditionals, which can be independently defined. Difficult cases are also discussed in which the contradictory of the consequent semantically entails the truth of the antecedent. In such cases the content of the antecedent is implicit in the meaning of the consequent. Contraposition becomes possible if what is implicit in the original consequent is made explicit in the contrapositive antecedent. (shrink)

A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic fallacies (...) disguised by scope ambiguities), and proceed to lay the groundwork for the construction of actual proper de jure objections. (shrink)

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.