Counterfactual antecedent falsity and the epistemic sensitivity of counterfactuals

Why do utterances of counterfactual conditionals typically, but not universally, convey the message that their antecedents are false? I demonstrate that two common theoretical commitments–commitment to the existence of scalar implicature and of informative presupposition—can be supplemented with an independently motivated theory of the presuppositions of competing conditional alternatives to jointly predict this information when and only when it appears. The view works best if indicative and counterfactual conditionals have a closely related semantics, so I conclude by undermining two familiar arguments for a nonunified semantics of indicative and counterfactual conditionals.     

The Suppositional Ramsey Test and Decision-Instability

I analyse the relationship between the Ramsey Test (RT) for the acceptance of indicative conditionals and the so-called problem of decision-instability. In particular, I argue that the situations which allegedly bring about this problem are troublesome just in case the relevant conditionals are evaluated by non-suppositional versions, e.g. causal/evidential, of the test. In contrast, a suppositional RT, by highlighting the metacognitive nature of the evaluation of indicative conditionals, allows an agent to run a simulation of such evaluation, without yet committing her to the acceptance of such conditionals. I conclude that a suppositional interpretation of RT is superior to its non-suppositional counterparts and by briefly showing that a suppositional RT is compatible with a deliberational decision theory.     

Subjunctive biscuit and stand-off conditionals

Conventional wisdom has it that many intriguing features of indicative conditionals aren’t shared by subjunctive conditionals. Subjunctive morphology is common in discussions of wishes and wants, however, and conditionals are commonly used in such discussions as well. As a result such discussions are a good place to look for subjunctive conditionals that exhibit features usually associated with indicatives alone. Here I offer subjunctive versions of J. L. Austin’s ‘biscuit’ conditionals—e.g., “There are biscuits on the sideboard if you want them”—and subjunctive versions of Allan Gibbard’s ‘stand-off’ or ‘Sly Pete’ conditionals, in which speakers with no relevant false beliefs can in the same context felicitously assert conditionals with the same antecedents and contradictory consequents. My cases undercut views according to which the indicative/subjunctive divide marks a great difference in the meaning of conditionals. They also make trouble for treatments of indicative conditionals that cannot readily be generalized to subjunctives.     

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.     

Reasoning About Uncertain Conditionals

There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view.     

Priming effect on the exceptive conditional ‘except if’

Here we report the results of one priming experiment that examines the comprehension of exceptive conditionals—for example, ‘Mary will go out tonight except if she has an exam tomorrow’—and indicative conditionals—for example, ‘Mary will not go out tonight if she has an exam tomorrow’. The experiment showed that participants read the true possibility ‘Mary is not going out tonight and she has an exam tomorrow’ faster when it was primed by an exceptive conditional than when it was primed by an indicative; other possibilities (‘Mary is going out tonight and she does not have an exam tomorrow’, ‘Mary is going out tonight and she has an exam tomorrow’ and ‘Mary is not going out tonight and she does not have an exam tomorrow’) were primed equally by both connectives. The experiments showed that (1) when people understand ‘B except if A’, they access the true possibilities ‘not-A & B’ and ‘A & not-B’, and (2) when they understand ‘B, if not-A’ they access ‘not-A & B’, but they do not access ‘A & not-B’. We discuss the implications of this for current theories of reasoning.     

Conversation and conditionals

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker’s framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle—concerning so-called ‘reverse Sobel sequences’—can be resolved by conversation dynamics in a theory-neutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called “Gibbard phenomenon” for indicative conditionals.     

On the basis of belief in causal and diagnostic conditionals

According to the suppositional theory of conditionals, people assess their belief in a conditional statement of the form “if p then q” by conducting a mental simulation on the supposition of p in which they assess their degree of belief in q. This leads to them to the judge the probability of a conditional statement to be equal to the conditional probability, P(q|p). Evidence for this conditional probability hypothesis has been adduced in earlier studies for abstract, causal, and counterfactual conditionals. For the realistic conditionals, it is natural to assume that people perform such mental simulations by building causal mental models from prior causes to later effects. However, in the present study we show that the conditional probability hypothesis extends to diagnostic conditionals, which relate effects to causes. This new finding presents a major challenge for theoretical accounts of the mental processing of conditional statements.     

On the basis of belief in causal and diagnostic conditionals

According to the suppositional theory of conditionals, people assess their belief in a conditional statement of the form “if p then q” by conducting a mental simulation on the supposition of p in which they assess their degree of belief in q. This leads to them to the judge the probability of a conditional statement to be equal to the conditional probability, P(q|p). Evidence for this conditional probability hypothesis has been adduced in earlier studies for abstract, causal, and counterfactual conditionals. For the realistic conditionals, it is natural to assume that people perform such mental simulations by building causal mental models from prior causes to later effects. However, in the present study we show that the conditional probability hypothesis extends to diagnostic conditionals, which relate effects to causes. This new finding presents a major challenge for theoretical accounts of the mental processing of conditional statements.     

Realizing what might be

Schulz has shown that the suppositional view of indicative conditionals leads to a corresponding view of epistemic modals. But his case backfires: the resulting theory of epistemic modals gets the facts wrong, and so we end up with a good argument against the suppositional view. I show how and why a dynamic view of indicative conditionals leads to a better theory of epistemic modals.     

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.     

Conditional reasoning in context: A developmental dual processes account

The way individuals interpret “if p then q” conditionals varies with content and context, often resulting in a biconditional reading. Surprisingly, truth table tasks reveal the existence of two different types of biconditional interpretations: equivalence, as for promises and threats, and defective biconditional, as for causal conditionals or indicative conditionals involving binary terms. The aim of this study was to determine how the interpretation of indicative conditionals is affected in children, adolescents, and adults, by restricting their context of enunciation to only one possible alternative for both the antecedent and the consequent. Moreover, we wanted to determine what is the exact nature of the biconditional interpretation induced by these restricted contexts. For this purpose, third, sixth, and ninth graders and adults performed a truth-value task on indicative conditionals presented either in restricted on non-restricted contexts. Restricted contexts had no effect on children who have a conjunctive interpretation of the conditional, but elicited a predominant defective biconditional reading in adolescents and adults. These results corroborate the developmental dual process account of conditional reasoning proposed by Gauffroy and Barrouillet (2009).     

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.     

Temporal and spatial relations in sentential reasoning

The mental model theory postulates that the meanings of assertions, and knowledge about their context can modulate the logical meaning of sentential connectives, such as "if" and "or". One known effect of modulation is to block the representation of possibilities to which a proposition refers. But, modulation should also add relational information, such as temporal order, to models of possibilities. Three experiments tested this prediction. Experiment 1 showed that individuals spontaneously matched the tense of their conclusions (in Portuguese) to embody implied, but unexpressed, temporal relations in conditional premises. Experiment 2 demonstrated the same phenomenon in inferences from disjunctions. Experiment 3 showed that the number of such implicit relations in inferences from conditionals affects both accuracy and the speed of reasoning. These results support the modulation hypothesis.     

Defending truth values for indicative conditionals

Philosophical Studies - There is strong disagreement about whether indicative conditionals have truth values. In this paper, I present a new argument for the conclusion that indicative conditionals...     

Word for word: Multiple lexical access in speech production

We report an experiment in which we test the possible influence of the tense of the verb and explicit negatives with indicative conditionals. We tested the effects of systematically negating the constituents of four fundamental inferences based on conditionals in three different tenses (present tense, past tense, future tense): Modus Ponens (i.e., inferences of the form: if p then q; p; therefore q), Modus Tollens (if p then q; not-q; therefore not-p), Affirmation of the Consequent (if p then q; q; therefore p), and Denial of the Antecedent (if p then q; not-p; therefore not-q). The latter two inferences are invalid for true conditionals, but are valid for bi-conditionals (if, and only if, p then q). The participants drew their own conclusions from premises about letters and numbers on cards. We discuss the results in relation to an affirmation premise bias, a negative conclusion bias, and a double negation effect. We outline the importance of our findings for theories about conditional and counterfactual thinking.     

Counterfactuals for Consequentialists

That all subjunctive conditionals with true antecedents and trueconsequents are themselves also true is implied by every plausibleand popularly endorsed account. But I am wary of endorsing thisimplication. I argue that all presently endorsed accounts fail tocapture the nature of certain subjunctive conditionals in contextsof consequentialist reasoning. I attempt to show that we must allowfor the possibility that some subjunctive conditionals with trueantecedents and true consequents are false, if we are to believethat certain types of straightforward consequentialist reasoningare coherent. I begin by evaluating a pair of morally releventcounterfactuals in a case via David Lewis's account. I then turnto a slight modification of the case, arguing that Lewis'ssemantics fails to generate the correct truth values of thesubjunctive conditionals in the modified case. Finally, I presenta modified version of Lewis's semantics that generates the correctresults in all of the cases.     

Vann McGee's counterexample to modus ponens

Conclusion After rejecting some unjustified criticism of McGee's claim about modus ponens, I argued for two conditionals: If the Adams-Appiah theory of conditionals is correct, then modus ponens is saved from McGee's counterexample. If the Lewis-Jackson theory is correct, the same holds. Furthermore, I raised some doubts whether the antecedents of these conditionals are true. But, if one of them were, then, by modus ponens, modus ponens would be generally valid.