On some limits of hypothetical thinking

Faced with extreme demands, hypothetical thinking runs the danger of total failure. Paradoxical propositions such as the Liar (“I am lying”) provide an opportunity to test it to its limits, while the Liar's nonparadoxical counterpart, the Truthteller (“I am telling the truth”), provides a useful comparison. Two experiments are reported, one with abstract materials (“If I am a knave then I live in Emerald City”) and one with belief-laden materials (a judge says: “If I am a knave then I enjoy pop music”). In both experiments, conditionals with Truthteller-type antecedents were “collapsed” to responses of conditional probability closely resembling estimates of control items. Liar-type antecedents, in contrast, dramatically weakened belief in conditionals in which they were embedded. The results are discussed in the framework of the theory of hypothetical thinking.     

充分条件句语义关系知觉对条件推理的影响

作者通过实验考察了大学生被试对五种充分条件句语义关系知觉对其条件推理的影响。两个实验的结果表明,被试对条件句中前后件之间语义关系的知觉理解影响和调节其相应的条件推理的成绩。实验1新发现,被试对充分条件句后件对前件必要性的知觉理解存在难易差异,对许可句和定义句的后件必要性容易知觉,对偶然句、义务句和因果句的后件必要性难以知觉。实验2新发现,被试对充分条件句后件对前件必要性的知觉理解的难易差异导致被试在否定后件式推理成绩上的差异,对许可句和定义句的否定后件式推理成绩显著高于对偶然句、义务句和因果句的否定后件式推理成绩,对充分条件句否定后件式推理成绩随对后件必要性知觉增加而增加。     

Negativity bias in defeasible reasoning

In defeasible reasoning, initially drawn conclusions can be withdrawn in light of new information. In this paper, we examine how the conclusions drawn from conditionals describing positive or negative situations can be defeated by subsequent negative or positive information, respectively. Participants were confronted with conditionals of the form “If [situation], then I am happy/sad” which were either followed by no additional information or by additional information describing situations of the same or the opposite valence. The participant's task was to decide on a question asking for a possible conclusion (“Am I happy?” vs. “Am I sad?”). We found a negativity bias in defeasible reasoning: negative information defeated positively charged conclusions more strongly than positive information defeated negatively charged conclusions. We discuss our results in relation to the new psychology of reasoning.     

对充分条件句语义关系的概念理解与逻辑理解的相关与分离

实验用大学生被试考察了充分条件句语义关系表达形式（逻辑形式和概念形式）和条件句类型（五种条件句）对充分条件句语义关系理解的影响。实验结果发现,语义关系表达形式影响被试对条件句中必要性的语义关系理解,而不影响被试对条件句中充分性的语义关系理解,在对条件句前后件之间语义关系的逻辑理解成绩和概念理解成绩之间既有相关又有分离：对是否充分的语义关系的两种理解成绩之间存在相关一致,而对是否必要的语义关系的两种理解成绩之间存在分离;五种条件句在对后件对前件的必要性的知觉难易程度受条件句意义内容的影响而存在明显差异,这种差异导致被试对许可句和定义句的后件必要性理解成绩高于对偶然句、义务句和因果句的后件必要性理解成绩。     

Reasoning with deontic and counterfactual conditionals

We report two new phenomena of deontic reasoning: (1) For conditionals with deontic content such as, “If the nurse cleaned up the blood then she must have worn rubber gloves”, reasoners make more modus tollens inferences (from “she did not wear rubber gloves” to “she did not clean up the blood”) compared to conditionals with epistemic content. (2) For conditionals in the subjunctive mood with deontic content, such as, “If the nurse had cleaned up the blood then she must have had to wear rubber gloves”, reasoners make the same frequency of all inferences as they do for conditionals in the indicative mood with deontic content. In this regard, subjunctive deontics are different from subjunctive epistemic conditionals: reasoners interpret subjunctive epistemic conditionals as counterfactual and they make more negative inferences such as modus tollens from them. The experiments show these two phenomena occur for deontic conditionals that contain the modal auxiliary “must” and ones that do not. We discuss the results in terms of the mental representations of deontic conditionals and of counterfactual conditionals.     

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.     

Inherent directionality of “even if” counterfactual conditionals

In this research, we investigate whether semifactual conditionals such as “even if there had been an A, there would have been a B” are understood by thinking initially of the antecedent “A”, as was found with factual conditionals. The “inherent directionality” hypothesis assumes that for the comprehension of most relational statements, a presuppositional element (i.e. the “relatum”) is initially established. For “even if”, both terms could work as “relatum”. This is because on the one hand, people tend to infer “B” from “A” and “not-A” and, on the other hand, “B” could work as a pragmatic presupposition. In the present experiment, semifactual and factual conditionals were tested with a sentence-picture verification task. Results were consistent with the “inherent directionality” hypothesis: only “if then” factual conditionals, but not semifactuals, showed a preference for reasoning from the antecedent, with faster verifications.     

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.     

Three Twentieth-century Commonplaces about 'If'

The commonplaces, all grammatically confused, are that ‘conditionals’ are ternary in structure, have ‘antecedents’ and conform to the traditional taxonomy. It is maintained en route that ‘The bough will not break’ is consistent with ‘If the bough breaks …’, that there is no logical difference between “future indicatives” and “subjunctives”, and that there is a difference between the logic of propositions (e.g. ‘The bough broke’) and that of judgments (‘The bough will/might/could/should/must/needn't break’).     

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”.     

The Probability of Iterated Conditionals

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth‐table task, and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point.     

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.     

When will is not the same as should: The role of modals in reasoning with legal conditionals

Naïve reasoners reject logically valid conclusions from conditional rules if they can think of exceptions in which the antecedent is true, but the consequent is not. However, when reasoning with legal conditionals (e.g., “If a person kills another human, then this person should be punished for manslaughter”) people hardly consider exceptions but evaluate conclusions depending on their own sense of justice. We show that participants’ reluctance to consider exceptions in legal reasoning depends on the modal auxiliary used. In two experiments we phrased legal conditionals either with the modal “should” (i.e., “ . . . then this person should be punished”), or with “will” (i.e., “ . . . then this person will be punished”) and presented them as modus ponens or modus tollens inferences. Participants had to decide whether the offender should or will be punished (modus ponens) or whether the offender indeed committed the offence (modus tollens). For modus ponens inferences phrased with “should” we replicate previous findings showing that participants select conclusions on the basis of their own sense of justice (Experiments 1 and 2). Yet, when the legal conditional is phrased with the modal “will” this effect is attenuated (Experiments 1 and 2), and exceptions are considered (Experiment 1). The modal auxiliary did not affect modus tollens inferences.     

Indicatives,Subjunctives, and the Falsity of the Antecedent

It is widely held that there are important differences between indicative conditionals (e.g., “If the authors are linguists, they have written a linguistics paper”) and subjunctive conditionals (e.g., “If the authors had been linguists, they would have written a linguistics paper”). A central difference is that indicatives and subjunctives convey different stances toward the truth of their antecedents. Indicatives (often) convey neutrality: for example, about whether the authors in question are linguists. Subjunctives (often) convey the falsity of the antecedent: for example, that the authors in question are not linguists. This paper tests prominent accounts of how these different stances are conveyed: whether by presupposition or conversational implicature. Experiment 1 tests the presupposition account by investigating whether the stances project—remain constant—when embedded under operators like negations, possibility modals, and interrogatives, a key characteristic of presuppositions. Experiment 2 tests the conversational-implicature account by investigating whether the stances can be cancelled without producing a contradiction, a key characteristic of implicatures. The results provide evidence that both stances—neutrality about the antecedent in indicatives and the falsity of the antecedent in subjunctives—are conveyed by conversational implicatures.     

People think about what is true for conditionals,not what is false: Only true possibilities prime the comprehension of “if”

We report the results of two priming experiments that examine the comprehension of conditionals—for example, “if there are apples then there are oranges”—and biconditionals—for example, “if and only if there are apples then there are oranges”. The first experiment showed that participants read a biconditional faster when it was primed by a true possibility, “there were apples and there were oranges” than when it was primed by a false possibility, “there were no apples and there were oranges”; a conditional was primed equally by both possibilities. The second experiment showed that participants read the negated-antecedent conjunction faster when it was primed by a conditional than when it was primed by a biconditional; the affirmative conjunction was primed equally by both connectives. The experiments show that (a) when people understand “if A then B”, they access the true possibilities, “A and B”, and “not-A and B”, and (b) when they understand “if and only if A then B” they access “A and B”, but they do not access “not-A and B”. We discuss their implications for current theories of reasoning.     

The influence of clause order,congruency, and probability on the processing of conditionals

Conditional information can be equally asserted in the forms if p, then q (e.g., “if I am ill, I will miss work tomorrow”) and q, if p (e.g., “I will miss work tomorrow, if I am ill”). While this type of clause order manipulation has previously been found to have no influence on the ultimate conclusions participants draw from conditional rules, we used self-paced reading to examine how it affects the real time incremental processing of everyday conditional statements. Experiment 1 revealed that clause order interacts with presuppositional congruency as readers hypothetically represent counterfactual statements. When if p, then q counterfactuals contained a presupposition that was incongruent with prior context, these statements took longer to read than when the presupposition was congruent, but for q, if p conditionals there was no such congruency effect. Experiment 2 revealed that reading times were influenced by the subjective probability of an indicative conditional regardless of clause order, with a penalty observed for low-probability statements relative to high-probability statements in both conditional clause orders. These data reveal a dissociation whereby clause order mediates the effect of suppositional congruency on reading times, but does not mediate the effect of subjective probability.     

Trust,Testimony, and Prejudice in the Credibility Economy

In this paper I argue for a special kind of injustice I call “trust injustice.” Taking Miranda Fricker's work on epistemic injustice as my starting point, I argue that there are some ethical constraints on trust relationships. If I am right about this, then we sometimes have duties to maintain trust relationships that are independent of the social roles we play.     

Rethinking Gibbard’s Riverboat Argument

According to the Principle of Conditional Non-Contradiction (CNC), conditionals of the form “If p, q” and “If p, not q” cannot both be true, unless p is inconsistent. This principle is widely regarded as an adequacy constraint on any semantics that attributes truth conditions to conditionals. Gibbard has presented an example of a pair of conditionals that, in the context he describes, appear to violate CNC. He concluded from this that conditionals lack truth conditions. We argue that this conclusion is rash by proposing a new diagnosis of what is going on in Gibbard’s argument. We also provide empirical evidence in support of our proposal.     

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.