Indicative and Subjunctive Conditionals

In any plausible semantics for conditionals, the semantics for indicatives and subjunctives will resemble each other closely. This means that if we are to keep the possible-worlds semantics for subjunctives suggested by Lewis, we need to find a possible-worlds semantics for indicatives. One reason for thinking that this will be impossible is the behaviour of rigid designators in indicatives. An indicative like 'If the stuff in the rivers, lakes and oceans really is H₃O, then water is H₃O' is non-vacuously true, even though its consequent is true in no possible worlds, and hence not in the nearest possible world where the antecedent is true. I solve this difficulty by providing a semantics for conditionals within the framework of two-dimensional modal logic. In doing so, I show that we can have a reasonably unified semantics for indicative and subjunctive conditionals.     

Indicative Conditionals and Graded Information

Journal of Philosophical Logic - I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics,...     

Material Implication and General Indicative Conditionals

This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten , provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – assumed to be merely ( p ⊃ q ) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q.     

Defending a Possible-Worlds Account of Indicative Conditionals

One very popular kind of semantics for subjunctive conditionals is aclosest-worlds account along the lines of theories given by David Lewisand Robert Stalnaker. If we could give the same sort of semantics forindicative conditionals, we would have a more unified account of themeaning of ``if ... then ...' statements, one with manyadvantages for explaining the behaviour of conditional sentences. Such atreatment of indicative conditionals, however, has faced a battery ofobjections. This paper outlines a closest-worlds account of indicativeconditionals that does better than some of its cousins in explaining thebehaviour of such conditionals. The paper then discusses objectionsoffered by Dorothy Edgington and Frank Jackson to closest-worldsaccounts of indicative conditionals, and shows that these objections canbe met by the account outlined.     

Acceptance and Certainty,Doxastic Modals,and Indicative Conditionals

I give a semantics for a logic with two pairs of doxastic modals and an indicative conditional connective that all nest without restriction. Sentences are evaluated as accepted, rejected, or neither. Certainty is the necessity-like modality of acceptance. Inferences may proceed from premises that are certain, or merely accepted, or a mix of both. This semantic setup yields some striking results. Notably, the existence of inferences that preserve certainty but not acceptance very directly implies both failure of modus ponens for the indicative conditional in the logic of acceptance and failure of the deduction theorem for the material conditional in the logic of certainty. The latter failure dissolves, in the logic of certainty, the much - discussed tension between modus ponens and the law of import-export.

     

De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity

Journal of Philosophical Logic - This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti (1936) and...     

De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics

Journal of Philosophical Logic - In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de...     

Antiskeptical Conditionals

Empirical knowledge exists in the form of antiskeptical conditionals , which are propositions like [if I am not undetectably deceived, then I am holding a pen]. Such conditionals, despite their trivial appearance, have the same essential content as the categorical propositions that we usually discuss, and can serve the same functions in science and practical reasoning. This paper sketches out two versions of a general response to skepticism that employs these conditionals. The first says that our ordinary knowledge attributions can safely be replaced by statements using antiskeptical conditionals, which provides a way around the standard sort of skeptical argument while accepting its soundness with respect to the usual targets. The second analyzes the objects of our ordinary knowledge attributions as antiskeptical conditionals, which allows us to refute, not just evade, the skeptic's argument. Both versions compare favorably to the best-known current approaches to skepticism, including semantic contextualism.     

Counterconventional Conditionals

Some philosophical positions maintain that some aspect of reality depends on human practices, cognitive attitudes or sentiments. This paper presents a framework for understanding such positions in a way that renders them immune to a number of natural but allegedly devastating objections.     

Conditionals and Curry

Curry’s paradox for “if.. then..” concerns the paradoxical features of sentences of the form “If this very sentence is true, then 2 + 2 = 5”. Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2 + 2 = 5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. Once we have a sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of “if... then...”. This paper argues that a closest-worlds approach outlined in previous work offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related “contraction conditionals”.     

Conditionals in reasoning

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.     

Conditionals and Actuality

It is known that indicative and subjunctive conditionals interact differently with a rigidifying “actually” operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing “actually” instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they preserve material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed.

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Conditionals and consequences

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.     

Partitions and Conditionals

The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).     

Triviality For Restrictor Conditionals

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals (while also clarifying the sense in which Kratzer's semantics might avoid such results). I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.     

Conditionals As Representative Inferences

According to Adams (Inquiry 8:166–197, 1965), the acceptability of an indicative conditional goes with the conditional probability of the consequent given the antecedent. However, some conditionals seem to be inappropriate, although their corresponding conditional probability is high. These are cases with a missing link between antecedent and consequent. Other conditionals are appropriate even though the conditional probability is low. Finally, we have the so-called biscuit conditionals. In this paper we will generalize analyses of Douven (Synthese 164:19–44, 2008) and others to account for the appropriateness of conditionals in terms of evidential support. Our generalization involves making use of Value, or intensity. We will show how this generalization helps to account for biscuit conditionals and conditional threats and promises. Finally, a link is established between this analysis of conditionals and an analysis of generic sentences.