Conditional reasoning and causation (original) (raw)
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Causation and Conditionals in the Cognitive Science of Human Reasoning
The Open Psychology Journal, 2010
This article traces the philosophical and psychological connections between causation and the conditional, if...then, across the two main paradigms used in conditional reasoning, the selection task and the conditional inference paradigm. It is argued that hypothesis testing in the selection task reflects the philosophical problems identified by Quine and Goodman for the material conditional interpretation of causal laws. Alternative formal theories to the material conditional only became available with the advent of possible worlds semantics . The relationship proposed by this semantics between counterfactual and indicative conditionals is outlined and it is concluded that moving away from the abstractions of possible worlds proposes a central role for prior knowledge in conditional inference. This conclusion is consistent with probabilistic approaches to conditional inference which provide measures of the strength of a dependency between the antecedent and the consequent of a conditional similar to those proposed in causal learning. Findings in conditional inference suggest that people are influenced not only by the strength of a dependency but also by the existence of the structural relationship, the broader causal framework in which a dependency is embedded, and the inhibitory and excitatory processes like those required to implement Causal Bayes nets or neural networks. That these findings may have a plausible explanation using the tools of current theories in causal learning suggests a potentially fruitful convergence of research in these two areas.
The Open Psychology Journal, 2010
This article traces the philosophical and psychological connections between causation and the conditional, if...then, across the two main paradigms used in conditional reasoning, the selection task and the conditional inference paradigm. It is argued that hypothesis testing in the selection task reflects the philosophical problems identified by Quine and Goodman for the material conditional interpretation of causal laws. Alternative formal theories to the material conditional only became available with the advent of possible worlds semantics . The relationship proposed by this semantics between counterfactual and indicative conditionals is outlined and it is concluded that moving away from the abstractions of possible worlds proposes a central role for prior knowledge in conditional inference. This conclusion is consistent with probabilistic approaches to conditional inference which provide measures of the strength of a dependency between the antecedent and the consequent of a conditional similar to those proposed in causal learning. Findings in conditional inference suggest that people are influenced not only by the strength of a dependency but also by the existence of the structural relationship, the broader causal framework in which a dependency is embedded, and the inhibitory and excitatory processes like those required to implement Causal Bayes nets or neural networks. That these findings may have a plausible explanation using the tools of current theories in causal learning suggests a potentially fruitful convergence of research in these two areas.
Interpretational factors in conditional reasoning
Memory & Cognition, 1994
on perceived necessity and sufficiency have consistently been shown to be important factors in making and evaluating conditional inferences (e.g., Cummins et al., 1991; Digdon, 1986; Markovits, 1984, 1986; Staudenmayer, 1975; Thompson, in press), we do not know how the use of necessity/sufficiency information may be modified by other interpretational variables, such as pragmatic, contextual relations (e.g., Cheng & Holyoak, 1985) or logical, syntactic relations. Thus, the following experiments examined the role of perceived necessity and sufficiency in the making of inferences about a variety of pragmatic and syntactic relationships. Conditional Reasoning Conditional relationships are often expressed in the generic form "if p, then q," where p and q are referred to as the antecedent and consequent, respectively. In a conditional reasoning task, subjects are typically asked to make inferences about the occurrence of one event, given the occurrence or nonoccurrence ofthe other event. For example, in a conditional arguments task, subjects are asked to indicate the validity of four inferences derived from a conditional statement (e.g., if the car is out of gas, then it stalls). The modus ponens (MP) inference entails concluding q, given p (e.g., the car is out of gas; therefore, it stalls), and modus tollens (MT) entails concluding-p, given-q (e.g., the car has not stalled; therefore, it did not run out ofgas). The denying-the-antecedent (DA) and affirming-the-consequent arguments (AC) involve the inference from 'P to-q (e.g., ifthe car does not run out of gas, it will not stall) and from q to p (the car has stalled; therefore, it has run out of gas), respectively. Logically speaking, the validity of an argument is determined only by its syntactic form; by this criterion, the MP and MT arguments are considered to be valid, and the DA and AC arguments are considered to be fallacies
Processing Inferential Causal Statements: Theoretical Refinements and the Role of Verb Type
Discourse Processes, 2007
An evidential causal relation like Because most distinguished students got bad grades, the teacher made some mistakes in evaluating his students' papers is more difficult to process than a factual one like Because he got tired after a long semester, the teacher made some mistakes in evaluating his students' papers . Two experiments explored the distinguishing characteristics of different types of causal relations. Experiment 1 introduced a third type of causal relation, a deductive causal relation, like Because grading a paper is a subjective process, the teacher made some mistakes in evaluating his students' papers.
The modulation of conditional assertions and its effects on reasoning
The Quarterly Journal of Experimental Psychology, 2010
The theory of mental models postulates that conditionals of the sort, if A then C, have a "core" meaning referring to three possibilities: A and C, not-A and C, and not-A and not-C. The meaning of a conditional's clauses and general knowledge can modulate this meaning, blocking certain possibilities or adding relations between the clauses. Four experiments investigated such interpretations in factual and deontic domains. In Experiment 1, the participants constructed instances of what was possible and what was impossible according to various conditionals. The results corroborated the general predictions of the model theory and also the occurrence of modulation. The resulting interpretations governed the conclusions that participants accepted in Experiment 2, which also yielded the predicted effects of a time limit on responding. In Experiment 3, the participants drew the predicted conclusions for themselves. In Experiment 4, modulation led to predicted temporal relations between A and C. We relate these results to current theories of conditionals.
The mental representation of causal conditional reasoning: Mental models or causal models
Cognition, 2011
In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals-such as if P 1 then Q and if P 2 then Q-are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P i causes of Q; or symptoms caused by Q. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a ''collider'' structure where the two causes (P i ) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P i ) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.
Causal conditionals and counterfactuals
Acta Psychologica, 2012
Causal counterfactuals e.g., 'if the ignition key had been turned then the car would have started' and causal conditionals e.g., 'if the ignition key was turned then the car started' are understood by thinking about multiple possibilities of different sorts, as shown in six experiments using converging evidence from three different types of measures. Experiments 1a and 1b showed that conditionals that comprise enabling causes, e.g., 'if the ignition key was turned then the car started' primed people to read quickly conjunctions referring to the possibility of the enabler occurring without the outcome, e.g., 'the ignition key was turned and the car did not start'. Experiments 2a and 2b showed that people paraphrased causal conditionals by using causal or temporal connectives (because, when), whereas they paraphrased causal counterfactuals by using subjunctive constructions (had…would have). Experiments 3a and 3b showed that people made different inferences from counterfactuals presented with enabling conditions compared to none. The implications of the results for alternative theories of conditionals are discussed.
Reasoning with Conjunctive Causes
PsycEXTRA Dataset
Conjunctive causes are causes that all need to be present for an effect to occur. They contrast with independent causes that by themselves can each bring about an effect. We extend existing "causal power" representations of independent causes to include a representation of conjunctive causes. We then demonstrate how independent vs. conjunctive representations imply sharply different patterns of reasoning (e.g., explaining away effects for independent causes as compared to exoneration effects for conjunctive causes). An experiment testing how people reason with independent and conjunctive causes found that their inferences generally matched the model's prediction, albeit with some important exceptions.
Reasoning as we read: Establishing the probability of causal conditionals
Memory & Cognition, 2013
Indicative conditionals of the form if p then q (e.g., if student tuition fees rise, then applications for university places will fall) invite consideration of a hypothetical event (e.g., tuition fees rising) and of one of its possible consequences (e.g., applications falling). Since a rise in tuition fees is an uncertain event with equally uncertain consequences, a reader may believe the statement to a greater or lesser extent. As a conditional is read, the earliest point at which this probabilistic evaluation can take place is as the consequent clause is wrapped up (e.g., as the critical word fall is read in the example above). Wrap-up processing occurs at the end of the clause, as it is evaluated and integrated into the evolving discourse representation. Five sources of probability may plausibly influence the evaluation of a conditional as it is wrapped up; these are P(p), P(q), P(pq), P(q|p), and P(not-p or q). A total of 128 conditionals were constructed, with these probabilities calculated for each item in a pretest. The conditionals were then embedded in vignettes and read by 36 participants on a word-by-word basis. Using linear mixed-effects modeling, we found that wrap-up reading times were predicted by pretest ratings of P(p) and P(q|p). There was no influence of P(q), P(pq), or P(not-p or q) on wrap-up reading times. Our findings are consistent with the suppositional theory of conditionals proposed by Evans and Over (2004) but do not support the mental-models theory advanced by .
Causal relevance of conditionals: semantics or pragmatics?
Linguistics Vanguard
In this paper we argue that the antecedent of a (non-analytic) conditional is causally relevant to the consequent, … at least if standard background conditions hold. Natural counterexamples to the causal relevance analysis are argued to be cases where the standardly assumed background condition(s) do not hold.