The psychology of inferring conditionals from disjunctions: A probabilistic study (original) (raw)
Related papers
The Probability of Conditionals: The Psychological Evidence
Mind and Language, 2003
The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary conditionals in philosophical logic.
Journal of Experimental Psychology: Learning, Memory, & Cognition, 2003
- proffered a Bayesian model in which conditional inferences are a direct function of conditional probabilities. In the current article, the authors first considered this model regarding the processing of negatives in conditional reasoning. Its predictions were evaluated against a large-scale meta-analysis (W. J. Schroyens, W. . This evaluation shows that the model is flawed: The relative size of the negative effects does not match predictions. Next, the authors evaluated the model in relation to inferences about affirmative conditionals, again considering the results of a meta-analysis (W. J. Schroyens, W. . The conditional probability model is countered by the data reported in literature; a mental models based model produces a better fit. The authors conclude that a purely probabilistic model is deficient and incomplete and cannot do without algorithmic processing assumptions if it is to advance toward a descriptively adequate psychological theory.
Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models
The Quarterly Journal of Experimental Psychology Section A, 2001
We report four experiments investigating conjunctive inferences (from a conjunction and two conditional premises) and disjunctive inferences (from a disjunction and the same two conditionals). The mental model theory predicts that the conjunctive inferences, which require one model, should be easier than the disjunctive inferences, which require multiple models. Formal rule theories predict either the opposite result or no difference between the inferences. The experiments showed that the inferences were equally easy when the participants evaluated given conclusions, but that the conjunctive inferences were easier than the disjunctive inferences (1) when the participants drew their own conclusions, (2) when the conjunction and disjunction came last in the premises, (3) in the time the participants spent reading the premises and in responding to given conclusions, and (4) in their ratings of the difficulty of the inferences. The results support the model theory and demonstrate the importance of reasoners' inferential strategies.
Conditional Probability and the Cognitive Science of Conditional Reasoning
Mind and Language, 2003
This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context.
Deductive reasoning from uncertain conditionals
British Journal of Psychology, 2002
This paper begins with a review of the literature on plausible reasoning with deductive arguments containing a conditional premise. There is concurring evidence that people presented with valid conditional arguments such as Modus Ponens and Modus Tollens generally do not endorse the conclusion, but rather find it uncertain, in case (i) the plausibility of the major conditional premise is debatable, (ii) the major conditional premise is formulated in frequentist or probabilistic terms, or (iii) an additional premise introduces uncertainty about the major conditional premise. This third situation gives rise to non monotonic effects by a mechanism that can be characterised as follows: the reasoner is invited to doubt the major conditional premise by doubting the satisfaction of a tacit condition which is necessary for the consequent to occur. Three experiments are presented. The first two aim to generalise the latter result using various types of conditionals and the last shows that performance in conditional reasoning is significantly affected by the representation of the task. This latter point is discussed along with various other issues: we propose a pragmatic account of how the tacit conditions mentioned earlier are treated in plausible reasoning; the relationship of this account with the conditional probability view on conditional sentences is examined; an application of the same account to the Suppression Effect (Byrne, 1989) is proposed and compared with the counterexample availability explanation; and finally some suggestions on how uncertainty could be implemented in a mental logic system are presented.
Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedent
… Symposium on Imprecise Probability: Theories and …, 2007
The modus ponens (A → B, A ∴ B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A → B, ¬A ∴ ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities.
Recent studies indicate that a vast majority of people judge the probability of a conditional as equivalent to the conditional probability of <A, given C>. This means that in evaluating the applicability of a conditional people do not seem to take into account situations in which the antecedent is false. This has been taken as evidence against the model theory of . This theory, however, claims that the conditional interpretation in which false-antecedent cases are relevant is only one of many possible interpretations of "if." We present new evidence that confirms this flexibility of the interpretive system. When people are primed by thinking (1) about truth and the difference between the and or (2) are invited to judge which situations are consistent with the conditional, they are more likely to select a probability estimate that takes into account the false-antecedent cases.
Topoi, 2007
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.