The Interaction of ‘If’ and ‘Would’

The chapter argues that ‘would’ is associated with a suppositional heuristic analogous to that for ‘if’ but sensitive to the contextual restriction on ‘would’. This heuristic has structurally analogous consequences to those for ‘would’; in particular, it generates the appearance that ‘would’ commutes with negation, and correspondingly that counterfactuals obey the principles of Conditional Excluded Middle (CEM) and Conditional Non-Contradiction (CNC). However, to play its central cognitive role properly, ‘would’ must be able to generalize over more than one world at a time, thereby invalidating CEM, which is thus an artefact of the heuristics (as is CNC). Connections between ‘would’, ‘will’, ‘might’, and ‘not’ are explored. In particular, the relation between ‘will’ and ‘would’ corresponds to the relation between online prediction and offline imagination.

Conditionals and Abduction

The chapter gives a preliminary sketch of some cognitive differences between indicative conditionals and counterfactual conditionals relevant to the testing of hypotheses by experiment. They especially concern cases where the indicative conditional can be decided without new evidence while the counterfactual conditional cannot. They also show that the antecedent of a ‘counterfactual’ conditional need not be presupposed to be false. Differences connected with the past tense morphology of ‘would’ are explored. Cases are given where the morphology should be understood as expressing a ‘fake past’, modal rather than temporal.

Consequences of the Suppositional Rule

This chapter argues that the Suppositional Rule is a fallible heuristic, because it has inconsistent consequences. They arise in several ways: (i) it implies standard natural deduction rules for ‘if’, and analogous but incompatible rules for refutation in place of proof; (ii) it implies the equation of the probability of ‘If A, C’ with the conditional probability of C on A, which is subject to the trivialization results of David Lewis and others; (iii) its application to complex attitudes generates further inconsistencies. The Suppositional Rule is compared to inconsistent principles built into other linguistic practices: disquotation for ‘true’ and ‘false’ generate Liar-like paradoxes; tolerance principles for vague expressions generate sorites paradoxes. Their status as fallible, semantically invalid but mostly reliable heuristics is not immediately available to competent speakers.

Worlds and Meaning

This chapter discusses the possible world framework for intensional semantics, used for the semantics of ‘would’. It does not depend on any particular metaphysics of worlds, but the standard compositional clauses for the logical constants are a significant constraint. Semantic theories which invoke ‘impossible worlds’ flouting those constraints typically turn out to violate the principle of compositionality; since synonymy is not epistemically transparent to speakers, attempts to craft epistemically possible but metaphysically impossible worlds also tend to violate compositionality. Since worlds are best understood as objectively possible, in a broad sense, the proposed semantics makes counterfactuals with metaphysically impossible antecedents vacuously true; appearances to the contrary are an artefact of the suppositional heuristic (similar phenomena are noted for vacuous universal generalizations). This makes trouble for some prominent versions of fictionalist theories in metaphysics and various other philosophical theories which assume that counterpossibles vary in truth-value.

Is ‘Would If’ Hyperintensional?

This chapter responds to Fine’s arguments that counterfactual conditionals are hyperintensional because the result of substituting a truth-functionally equivalent antecedent can change the truth-value of a counterfactual. Fine’s descriptions of his alleged examples of hyperintensionality are inconsistent but seem consistent as a result of contextual shifts between different components, for which there is independent evidence, and which can be explained by the application of the suppositional heuristic, which makes some worlds verifying the antecedent relevant. Different senses of ‘hyperintensional’ are distinguished, one based on sameness of intension, another on logical equivalence, but the objection to Fine’s arguments works for both.

The Interaction of ‘If’ and ‘Would’: Semantics and Logic

This chapter argues that the difference between indicative and counterfactual conditionals traces to the overt difference in verb forms and not to any alleged covert ambiguity or context-dependence in ‘if’. ‘Would’ has a life beyond conditionals; the best hypothesis is that it is a necessity modal restricted to contextually relevant worlds. In standard counterfactual conditionals, ‘would’ scopes over ‘if’; given the invariant truth-functional semantics of ‘if’, the compositional semantics then makes counterfactual conditionals contextually restricted strict conditionals. The chapter explores the consequences of this for the logic of counterfactuals: principles such as transitivity, contraposition, and strengthening the antecedent hold, with appearances to the contrary being explained by context-shifting caused by the application of the suppositional heuristic. However, modus ponens fails because the contextual restriction may exclude the actual world.

The Role of Conditional Propositions

This chapter explains why the practice of using conditionals assessed by the primary (suppositional) and secondary (testimonial) heuristics is best understood on a material, truth-functional semantics. The aptness of the testimony-based heuristic supports a semantics on which the semantic contribution of ‘if’ is context-insensitive; the aptness of the supposition-based heuristic supports a semantics on which the probability of a conditional is not overestimated by being treated like the conditional probability, and compatibly with that underestimates it as little as possible. A formal result shows that in almost all cases these desiderata mandate the truth-functional interpretation. But that does not imply that the truth-functional interpretation will be transparent to speakers: it does not grant them epistemic access to the truth-conditional equivalence of ‘If A, C’ and ‘Not A or C’. This non-transparent ‘synonymy’ is compared to our understanding in cases of vagueness.

The Suppositional Rule

The chapter describes the role of suppositions in conditional thinking, from everyday decision-making to mathematical proof, and the cognitive role of imagination in developing the consequences of suppositions. It proposes that the primary way of assessing a conditional ‘If A, C’ is to suppose A and on that basis assess C; whatever attitude you take to C conditionally on A (such as acceptance, rejection, or something in between) take unconditionally to ‘If A, C’; this corresponds to the Ramsey Test or Suppositional Rule. Such offline assessment’s similarities to, and differences from, online updating on new information are discussed. Other ways of assessing ‘If A, C’ are also considered, including experimental testing by making A true, and reliance on memory or testimony without new first-hand testing.

The Value of Conditionals

This introductory chapter sketches the near-ubiquitous role of conditional statements, questions, and commands in human cognitive life and decision-making. It emphasizes that the standard way of instantiating a known or hypothesized generalization ‘Every F is a G’ is with a conditional, ‘If this is an F, it is a G’; this matters in both everyday life and science. The chapter also sketches how conditionals are passed from one context to another by memory and testimony. These features of our use of conditionals suggest desiderata for the semantics of conditionals. In particular, various kinds of computational complexity and context-sensitivity would tend to unfit conditionals for the cognitive role they are expected to play.

More on the Interaction of ‘Would’ with Context

This chapter discusses the contrast between Sobel sequences of counterfactuals and reverse Sobel sequences, where adding a conjunct to the antecedent generates an apparent counterexample to the (valid) principle of strengthening the antecedent, but subtracting it again does not. The difference corresponds to the pragmatic difference that adding items to the contextually relevant domain (here, of worlds) is easier than taking them away again. The pressure to add worlds is explained by the use of the suppositional heuristic, which makes some worlds verifying the antecedent (if there are any) relevant. For indicative conditionals, similar apparent counterexamples arise, for the difference in suppositions remains even in the absence of a context-sensitive element in the semantics: the basic explanation of the apparent counterexamples is cognitive rather than semantic. However, a recent attempt by Moss to explain the difference on epistemic grounds in a way consistent with a Lewis-style semantics is shown not to cover all the data.