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.     

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In defeasible reasoning, initially drawn conclusions can be withdrawn in light of new information.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.     

Conditional Ranking Revision

In the context of a general framework for belief dynamics which interprets revision as doxastic constraint satisfaction, we discuss a proposal for revising quasi-probabilistic belief measures with finite sets of graded conditionals. The belief states are ranking measures with divisible values (generalizing Spohn’s epistemology), and the conditionals are interpreted as ranking constraints. The approach is inspired by the minimal information paradigm and based on the principle-guided canonical construction of a ranking model of the input conditionals. This is achieved by extending techniques known from conditional default reasoning. We give an overview of how it handles different principles for conditional and parallel revision and compare it with similar accounts.     

On the Argumentative Strength of Indirect Inferential Conditionals

Inferential or epistemic conditional sentences represent a blueprint of someone’s reasoning process from premise to conclusion. Declerck and Reed (2001) make a distinction between a direct and an indirect type. In the latter type the direction of reasoning goes backwards, from the blatant falsehood of the consequent to the falsehood of the antecedent. We first present a modal reinterpretation in terms of Argumentation Schemes of indirect inferential conditionals (IIC’s) in Declerck and Reed (2001). We furthermore argue for a distinction between epistemic-modal strong and deontic-modal weak IIC’s. In addition, we extend the category of the indirect inferential conditionals in order to include several other deontic-modal subtypes. On the basis of the undesirability of the consequent the hearer in these cases infers that the antecedent is also undesirable. In this way the rhetoric-argumentative strategy of Reductio ad Absurdum is extended from the realm of deductive reasoning to that of practical reasoning.     

Pronounced inferences: A study on inferential conditionals

An experimental study is reported which investigates the differences in interpretation between content conditionals (of various pragmatic types) and inferential conditionals. In a content conditional, the antecedent represents a requirement for the consequent to become true. In an inferential conditional, the antecedent functions as a premise and the consequent as the inferred conclusion from that premise. The linguistic difference between content and inferential conditionals is often neglected in reasoning experiments. This turns out to be unjustified, since we adduced evidence on the basis of a quantitative and a qualitative analysis that this difference has a manifest psychological relevance. For the inferential conditionals, participants appear to retrieve the order of events of the original content conditional on which it was based, before they start reasoning with it. The implications of this finding for reasoning research and linguistics will be discussed.     

Inference suppression and semantic memory retrieval: Every counterexample counts

Reasoning with conditionals involving causal content is known to be affected by retrieval of counterexamples from semantic memory. In this study we examined the characteristics of this search process in everyday conditional reasoning. In Experiment 1 we manipulated the number (zero to four) of explicitly presented counterexamples (alternative causes or disabling conditions) for causal conditionals. In Experiment 2, using a generation pretest, we measured the number of counterexamples participants could retrieve for a set of causal conditionals. One month after the pretest, participants were presented a reasoning task with the same conditionals. The experiments indicated that acceptance of modus ponens linearly decreased with every additionally retrieved disabler, whereas affirmation of the consequent acceptance linearly decreased as a function of the number of retrieved alternatives. Results for denial of the antecedent and modus tollens were less clear. The findings show that the search process does not necessarily stop after retrieval of a single counterexample and that every additional counterexample has an impact on the inference acceptance.     

Reasoning with conditionals

This paper reviews the psychological investigation of reasoning with conditionals, putting an emphasis on recent work. In the first part, a few methodological remarks are presented. In the second part, the main theories of deductive reasoning (mental rules, mental models, and the probabilistic approach) are considered in turn; their content is summarised and the semantics they assume for if and the way they explain formal conditional reasoning are discussed, in particular in the light of experimental work on the probability of conditionals. The last part presents the recent shift of interest towards the study of conditional reasoning in context, that is, with large knowledge bases and uncertain premises.     

Mental models in deductive reasoning

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.     

Abstract reasoning and the interpretation of basic conditionals

Studies examining the interpretation that is given to if–then statementstypically use what are referred to as basic conditionals, which give contextless relations between two unrelated concrete terms (If the ball is blue, then the shape is square). However, there is some evidence that basic conditionals require a more abstract form of representation. In order to examine this, we presented participants with truth-table tasks involving either basic conditionals or conditionals referring to imaginary categories (If it is a bori, then it has red wings), and standard conditional inference tasks with abstract and familiar premises. As expected, fewer typical defective conditional interpretations were given to basic conditionals. In addition, partial correlations showed a unique relationship between the interpretation of basic conditionals and abstract inferential reasoning. Results suggest that people process basic conditionals as a form of abstract reasoning, and that the interpretation of conditionals must consider the semantic context.     

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。     

条件推理和选择任务的关系：选择任务中的条件推理逻辑

要求大学生被试在相同的情境和规则下先后完成选择任务和条件推理任务,从而系统考察两项条件命题任务之间的关系。结果表明,当规则的语义表征意义为条件命题和反条件命题时,两项任务的反应模式具有一致性;当为双向条件和非条件命题时,两项任务的反应模式出现了分歧,而且四种推理形式和四张卡片之间不存在直接的对应关系。两项条件命题任务之间的关系表现在,它们可能享有共同的语义关系表征空间,但推理过程和策略有所不同。     

Epistemic comparative conditionals

The interest of epistemic comparative conditionals comes from the fact that they represent genuine ‘comparative epistemic relations’ between propositions, situations, evidences, abilities, interests, etc. This paper argues that various types of epistemic comparative conditionals uniformly represent comparative epistemic relations via the comparison of epistemic positions rather than the comparison of epistemic standards. This consequence is considered as a general constraint on a theory of knowledge attribution, and then further used to argue against the contextualist thesis that, in some cases, considering a new counter- possibility can raise the epistemic standard of knowledge attribution. Instead, the paper shows that considering a new counter-possibility can only lower the epistemic position of a putative knower. Moreover, since the comparison, by the nature of conditionals, is free from any commitment to the truth-values of specific knowledge attributions, my conclusion is free from the debate between contextualism and invariantism on whether the truth-value of a knowledge attribution can actually vary with context.     

The Causal Structure of Utility Conditionals

The psychology of reasoning is increasingly considering agents' values and preferences, achieving greater integration with judgment and decision making, social cognition, and moral reasoning. Some of this research investigates utility conditionals, ‘‘if p then q’’ statements where the realization of p or q or both is valued by some agents. Various approaches to utility conditionals share the assumption that reasoners make inferences from utility conditionals based on the comparison between the utility of p and the expected utility of q. This article introduces a new parameter in this analysis, the underlying causal structure of the conditional. Four experiments showed that causal structure moderated utility‐informed conditional reasoning. These inferences were strongly invited when the underlying structure of the conditional was causal, and significantly less so when the underlying structure of the conditional was diagnostic. This asymmetry was only observed for conditionals in which the utility of q was clear, and disappeared when the utility of q was unclear. Thus, an adequate account of utility‐informed inferences conditional reasoning requires three components: utility, probability, and causal structure.     

Tracking, Epistemic Dispositions and the Conditional Analysis

According to Nozick’s tracking theory of knowledge, an agent a knows that p just in case her belief that p is true and also satisfies the two tracking conditionals that had p been false, she would not have believed that p, and had p been true under slightly different circumstances, she would still have believed that p. In this paper I wish to highlight an interesting but generally ignored feature of this theory: namely that it is reminiscent of a dispositional account of knowledge: it invites us to think of knowledge as a manifestation of a cognitive disposition to form true beliefs. Indeed, given a general account of dispositions in terms of subjunctive conditionals, the two tracking conditionals are satisfied just in case the belief in question results from some cognitive disposition to form true beliefs. Recently, such a conditional account of dispositions has, however, been criticised for its vulnerability to so-called ‘masked’, ‘mimicked’ and ‘finkish’ counterexamples. I show how the classical counterexamples to Nozick’s theory divide smoothly into four corresponding categories of counterexamples from epistemic masking, mimicking and finkishness. This provides strong evidence for the thesis that satisfaction of the two tracking conditionals is symptomatic of knowledge and that knowledge is instead constituted by a dispositional capability to form true beliefs. The attempt to capture such a cognitive, dispositional capability in terms of the tracking conditionals, although providing a good approximation in a wide variety of cases, still comes apart from the real thing whenever the epistemic layout is characterised by masking-, mimicking- and finkish mechanisms. In the last part of the paper I explore the prospect of improving the tracking theory in the light of these findings.     

Induction as conditional probability judgment

Existing research on category-based induction has primarily focused on reasoning about blank properties, or predicates that are designed to elicit little prior knowledge. Here, we address reasoning about nonblank properties. We introduce a model of conditional probability that assumes that the conclusion prior probability is revised to the extent warranted by the evidence in the premise. The degree of revision is a function of the relevance of the premise category to the conclusion and the informativeness of the premise statement. An algebraic formulation with no free parameters accurately predicted conditional probabilities for single- and two-premise conditionals (Experiments 1 and 3), as well as problems involving negative evidence (Experiment 2).     

A Representation Theorem for a Decision Theory With Conditionals

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

Logic programming,probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.     

The probability of causal conditionals

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.     

A puzzle about conditionals

This paper examines a neglected puzzle about conditionals: namely, the fact that each of a pair of conditionals with incompatible consequents, [A>C] and [B>C*], may be properly affirmable in circumstances when one does not believe, and is not entitled to infer, the denial of the conjunction of the antecedents, i.e. [¬(A & B)]. The puzzle is why this should be so, since the conditionals entail the denial of the conjunction on the popular accounts of conditionals. I present a pragmatic solution which distinguishes between two levels of affirmability.