Uncertainty and the suppression of inferences (original) (raw)
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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.
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.
8 Uncertain deductive reasoning
The Science of Reason: A Festschrift for …, 2010
Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals).
The science of reason: A Festschrift for …, 2011
Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals).
We asked people to validate conditional inferences (e.g., "A, therefore C" with "if A then C"). People are more likely to look for falsifications ("A and not-C") versus confirmations ("A and C") given a forced choice. Second, falsification rates are lower for logically valid versus invalid inferences. Logically valid inferences are inferences that follow necessarily. Experiment 1 (N ϭ 96) shows that emphasising this logicality constraint increases falsification rates in the validation task and corroborates that validationby-falsification increases logically correct inference evaluations. Experiment 2 (N ϭ 41) corroborates the other way round that people who are more likely to make logically correct evaluations, show higher falsification performance in the validation task. The results support mental-models theory and suggest alternative theories similarly need to specify how people would go about looking for counterexamples. We proffer such a specification for two alternatives to the model theory.
laboratory of experimental Psychology, University of leuven, Belgium rationality, reasoning, conditionals, truth two experiments (N 1 = 117 and N 2 = 245) on reasoning with knowledge-rich conditionals showed a main effect of logical validity, which was due to the negative effect of counter-examples being smaller for valid than for invalid arguments. these findings support the thesis that some people tend to inhibit background inconsistent with the hypothetical truth of the premises, while others tend to abandon the implicit truth-assumption when they have factual evidence to the contrary. Findings show that adhering to the truth-assumption in the face of conflicting evidence to the contrary requires an investment of time and effort which people with a higher general aptitude are more likely to do.
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.
Deductive Rationality in Validating and Testing Conditional Inferences
Canadian Journal of Experimental Psychology
We asked people to validate conditional inferences (e.g., "A, therefore C" with "if A then C"). People are more likely to look for falsifications ("A and not-C") versus confirmations ("A and C") given a forced choice. Second, falsification rates are lower for logically valid versus invalid inferences. Logically valid inferences are inferences that follow necessarily. Experiment 1 (N = 96) shows that emphasising this logicality constraint increases falsification rates in the validation task and corroborates that validation-by-falsification increases logically correct inference evaluations. Experiment 2 (N = 41) corroborates the other way round that people who are more likely to make logically correct evaluations, show higher falsification performance in the validation task. The results support mental-models theory and suggest alternative theories similarly need to specify how people would go about looking for counterexamples. We proffer such a ...
Chains of Inferences and the New Paradigm in the Psychology of Reasoning
Review of Philosophy and Psychology 7 (1):1-16., 2016
The new paradigm in the psychology of reasoning draws on Bayesian formal frameworks, and some advocates of the new paradigm think of these formal frameworks as providing a computational-level theory of rational human inference. I argue that Bayesian theories should not be seen as providing a computational-level theory of rational human inference, where by “Bayesian theories” I mean theories that claim that all rational credal states are probabilistically coherent and that rational adjustments of degrees of belief in the light of new evidence must be in accordance with some sort of conditionalization. The problems with the view I am criticizing can best be seen when we look at chains of inferences, rather than single-step inferences. Chains of inferences have been neglected almost entirely within the new paradigm.
Persuading and dissuading by conditional argument☆
Journal of Memory and Language, 2005
Informal reasoning typically draws on a wider range of inferential behaviour than is measured by traditional inference tasks. In this paper, we developed several tasks to study informal reasoning with two novel types of conditional statements: Persuasions (e.g., if the Kyoto accord is ratified, greenhouse gas emissions will be reduced) and dissuasions (e.g., if the Kyoto accord is ratified, there will be a downturn in the economy). For these statements, the consequent event, q, is offered as an incentive or disincentive for undertaking action p. Forty-eight university students reasoned about the statements from the point of view of the writer; another forty-eight reasoned from their own perspective. We found that reasoning about these statements involves a sophisticated chain of implicit inferences (e.g., a downturn in the economy should be avoided; ratifying the accord will produce a downturn; in order to avoid a downturn the accord should not be ratified) in support of an implicit conclusion (i.e., the accord should not be ratified). When generating arguments to either support or refute a position, reasoners relied on two main strategies: addressing the truth of the conditional or arguing the merits of undertaking action p (i.e., ratifying the Kyoto accord). Finally, using a traditional conditional arguments task, we found that reasoners were more likely to adopt a deductive strategy when reasoning from the writerÕs point of view than their own point of view, even though we did not include any instructions to reason logically. We discuss the relevance of these findings for formal and informal models of reasoning, the writerÕs theory of mind, and the role of pragmatic implicatures in reasoning.