Dynamic inference and everyday conditional reasoning in the new paradigm

Coherence, not conditional meaning, accounts for the relevance effect

Missing-link conditionals like "If bats have wings, Paris is in France" are generally felt to be unacceptable even though both clauses are true. According to the Hypothetical Inferential Theory, this is explained by a conventional requirement of an inferential connection between conditional clauses. Bayesian theorists have denied the need for such a requirement, appealing instead to a requirement of discourse coherence that extends to all ways of connecting clauses. Our experiment compared conditionals ("If A, C"), conjunctions ("A and C"), and bare juxtapositions ("A. C."). With one systematic exception that is predicted by prior work in coherence theory, the presence or absence of an inferential link affected conditionals and other statement types in the same way. This is as expected according to the Bayesian approach together with a general theory of discourse coherence.

Inferences from the negation of counterfactual and semifactual conditionals

Our goal was to study how people understand the negation of counterfactuals (such as “Antonio denied/said that it is false that if Messi had played, then Barcelona would have won”) and semifactuals (such as “Antonio denied that even if Messi had played, Barcelona would have won”). Previous studies have shown that participants negated basic conditionals using small-scope interpretations by endorsing a new conditional with the negated consequent, but also by making large-scope interpretations, endorsing a conjunction with the negated consequent. Three experiments showed that when participants were asked whether the negation of a counterfactual (Experiments 1 and 2) or semifactual (Experiment 3) conditional was followed by a new conditional, they made a small-scope interpretation, endorsing the same conditional with the negated consequent (e.g., “if/even if Messi had played, Barcelona would not have won”). However, they also accepted the conditional with the negated antecedent for semifactuals (e.g., “even if Messi had not played, Barcelona would have won”). When participants were asked whether the negation of a counterfactual or semifactual conditional is followed by a conjunction, they endorsed the conjunction with both the negated antecedent and the consequent (e.g., “Messi did not play and Barcelona did not win”), but again they accepted the conjunction with the negated antecedent only for semifactuals (e.g., “Messi did not play and Barcelona did win”). These results have implications for the main theories of reasoning.

Conceptual spaces and the strength of similarity-based arguments

Central to the conceptual spaces framework is the thought that concepts can be studied mathematically, by geometrical and topological means. Various applications of the framework have already been subjected to empirical testing, mostly with excellent results, demonstrating the framework's usefulness. So far untested is the suggestion that conceptual spaces may help explain certain inferences people are willing to make. The experiment reported in this paper focused on similarity-based arguments, testing the hypothesis that the strength of such arguments can be predicted from the structure of the conceptual space in which the items being reasoned about are represented. A secondary aim of the experiment concerned a recent inferentialist semantics for indicative conditionals, according to which the truth of a conditional requires the presence of a sufficiently strong inferential connection between its antecedent and consequent. To the extent that the strength of similarity-based inferences can be predicted from the geometry and topology of the relevant conceptual space, such spaces should help predict truth ratings of conditionals embodying a similarity-based inferential link. The results supported both hypotheses.

Specificity effects in reasoning with counterintuitive and arbitrary conditionals

When people have prior knowledge about an inference, they accept conclusions from specific conditionals (e.g., “If Jack does sports, then Jack loses weight”) more strongly than for unspecific conditionals (e.g., “If a person does sports, then the person loses weight”). But can specific phrasings also elevate the acceptance of conclusions from unbelievable conditionals? In Experiment 1, we varied the specificity of counterintuitive conditionals, which described the opposite of what is expected according to everyday experiences (“If Lena/a person studies hard, then Lena/the person will not do well on the test”). In Experiment 2, we varied the specificity of arbitrary conditionals, which had no obvious link between antecedent and consequent (“If Mary/a person goes shopping, then Mary/ the person gets pimples”). All conditionals were embedded in MP and AC inferences. Participants were instructed to reason as in daily life and to evaluate the conclusions on a 7-point Likert scale. Our results showed a specificity effect in both experiments: participants gave higher acceptance ratings for specific than for unspecific conditionals.

Explaining Away, Augmentation, and the Assumption of Independence

In reasoning about situations in which several causes lead to a common effect, a much studied and yet still not well-understood inference is that of explaining away. Assuming that the causes contribute independently to the effect, if we learn that the effect is present, then this increases the probability that one or more of the causes are present. But if we then learn that a particular cause is present, this cause "explains" the presence of the effect, and the probabilities of the other causes decrease again. People tend to show this explaining away effect in their probability judgments, but to a lesser extent than predicted by the causal structure of the situation. We investigated further the conditions under which explaining away is observed. Participants estimated the probability of a cause, given the presence or the absence of another cause, for situations in which the effect was either present or absent, and the evidence about the effect was either certain or uncertain. Responses were compared to predictions obtained using Bayesian network modeling as well as a sensitivity analysis of the size of normative changes in probability under different information conditions. One of the conditions investigated: when there is certainty that the effect is absent, is special because under the assumption of causal independence, the probabilities of the causes remain invariant, that is, there is no normative explaining away or augmentation. This condition is therefore especially diagnostic of people's reasoning about common-effect structures. The findings suggest that, alongside earlier explanations brought forward in the literature, explaining away may occur less often when the causes are assumed to interact in their contribution to the effect, and when the normative size of the probability change is not large enough to be subjectively meaningful. Further, people struggled when given evidence against negative evidence, resembling a double negation effect.

Causal conflicts produce domino effects

Inconsistent beliefs call for revision-but which of them should individuals revise? A long-standing view is that they should make minimal changes that restore consistency. An alternative view is that their primary task is to explain how the inconsistency arose. Hence, they are likely to violate minimalism in two ways: they should infer more information than is strictly necessary to establish consistency and they should reject more information than is strictly necessary to establish consistency. Previous studies corroborated the first effect: reasoners use causal simulations to build explanations that resolve inconsistencies. Here, we show that the second effect is true too: they use causal simulations to reject more information than is strictly necessary to establish consistency. When they abandon a cause, the effects of the cause topple like dominos: Reasoners tend to deny the occurrence of each subsequent event in the chain. Four studies corroborated this prediction.

Conditionals and testimony

Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much-perhaps most-of what we believe through the testimony of others, the simple matter of acquiring conditionals via others' assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning - a challenge which no account presently fully meets.

The Suppression of Inferences From Counterfactual Conditionals

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, "if she watered the plants they bloomed," when beliefs about additional background conditions, for example, "if the sun shone they bloomed" decrease the frequency of inferences such as modus tollens (from "the plants did not bloom" to "therefore she did not water them"). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, "if she had watered the plants they would have bloomed," when beliefs about the known or presupposed facts, "she did not water the plants and they did not bloom" increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from "she did not water the plants" to "therefore they did not bloom") is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new "switched-suppression" effect for conditionals with negated components, for example, "if she had not watered the plants they would not have bloomed": modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning.

The ecological rationality of explanatory reasoning

There is growing evidence that explanatory considerations influence how people change their degrees of belief in light of new information. Recent studies indicate that this influence is systematic and may result from people's following a probabilistic update rule. While formally very similar to Bayes' rule, the rule or rules people appear to follow are different from, and inconsistent with, that better-known update rule. This raises the question of the normative status of those updating procedures. Is the role explanation plays in people's updating their degrees of belief a bias? Or are people right to update on the basis of explanatory considerations, in that this offers benefits that could not be had otherwise? Various philosophers have argued that any reasoning at deviance with Bayesian principles is to be rejected, and so explanatory reasoning, insofar as it deviates from Bayes' rule, can only be fallacious. We challenge this claim by showing how the kind of explanation-based update rules to which people seem to adhere make it easier to strike the best balance between being fast learners and being accurate learners. Borrowing from the literature on ecological rationality, we argue that what counts as the best balance is intrinsically context-sensitive, and that a main advantage of explanatory update rules is that, unlike Bayes' rule, they have an adjustable parameter which can be fine-tuned per context. The main methodology to be used is agent-based optimization, which also allows us to take an evolutionary perspective on explanatory reasoning.

New Paradigms in the Psychology of Reasoning

The psychology of verbal reasoning initially compared performance with classical logic. In the last 25 years, a new paradigm has arisen, which focuses on knowledge-rich reasoning for communication and persuasion and is typically modeled using Bayesian probability theory rather than logic. This paradigm provides a new perspective on argumentation, explaining the rational persuasiveness of arguments that are logical fallacies. It also helps explain how and why people stray from logic when given deductive reasoning tasks. What appear to be erroneous responses, when compared against logic, often turn out to be rationally justified when seen in the richer rational framework of the new paradigm. Moreover, the same approach extends naturally to inductive reasoning tasks, in which people extrapolate beyond the data they are given and logic does not readily apply. We outline links between social and individual reasoning and set recent developments in the psychology of reasoning in the wider context of Bayesian cognitive science.

Moral judgment as reasoning by constraint satisfaction

May's careful examination of empirical evidence makes a compelling case against the primacy of emotion in driving moral judgments. At the same time, emotion certainly is involved in moral judgments. We argue that emotion interacts with beliefs, values, and moral principles through a process of coherence-based reasoning (operating at least partially below the level of conscious awareness) in generating moral judgments and decisions.

Why the Conjunction Effect Is Rarely a Fallacy: How Learning Influences Uncertainty and the Conjunction Rule

In this article we explore the relationship between learning and the conjunction fallacy. The interpretation of the conjunction effect as a fallacy assumes that all observers share the same knowledge, and that nobody has access to privileged information. Such situations are actually quite rare in everyday life. Building on an existing model of surprise, we prove formally that in the more typical scenarios, where observers are alert to the possibility of learning from event outcomes, the conjunction rule does not apply. Scenarios which have been engineered to produce the so-called conjunction “fallacy” (e.g., Tverksy and Kahneman, 1983) often imply subjective uncertainty and hence the possibility of learning. In Experiment 1 we demonstrate that when these scenarios are rephrased so as to eliminate subjective uncertainty, the effect is mitigated. In Experiment 2 we demonstrate that when subjective uncertainty is reduced by allowing participants to learn about the mechanism behind a conjunction-inducing scenario, the conjunction effect again diminishes. We conclude that the conjunction effect arises due to the unnaturalness of interpreting verbal descriptions in terms of a situation in which all observers share the same knowledge. Instead, when people hear descriptions of real world situations, they are likely to assume that learning is possible, and that subjective rather than objective uncertainty applies.

Utilitarian Moral Judgment Exclusively Coheres with Inference from Is to Ought

Faced with moral choice, people either judge according to pre-existing obligations (deontological judgment), or by taking into account the consequences of their actions (utilitarian judgment). We propose that the latter coheres with a more general cognitive mechanism – deontic introduction, the tendency to infer normative (‘deontic’) conclusions from descriptive premises (is-ought inference). Participants were presented with vignettes that allowed either deontological or utilitarian choice, and asked to draw a range of deontic conclusions, as well as judge the overall moral rightness of each choice separately. We predicted and found a selective defeasibility pattern, in which manipulations that suppressed deontic introduction also suppressed utilitarian moral judgment, but had little effect on deontological moral judgment. Thus, deontic introduction coheres with utilitarian moral judgment almost exclusively. We suggest a family of norm-generating informal inferences, in which normative conclusions are drawn from descriptive (although value-laden) premises. This family includes deontic introduction and utilitarian moral judgment as well as other informal inferences. We conclude with a call for greater integration of research in moral judgment and research into deontic reasoning and informal inference.

Defeasible reasoning with legal conditionals

Valid conclusions can be defeated if people can think of conditions that prevent the consequent to occur although the antecedent is given. The goal of the present research was to investigate how people consider these conditions when reasoning with legal conditionals such as "If a person kills another human, then this person should be punished for manslaughter." In Experiments 1 and 2 legal conditionals were presented to participants together with exculpatory circumstances, i.e., counterexamples. The participants' task was to decide whether they would adhere to the legal conditional rule and punish the offender. Participants were either lawyers (i.e., advanced law students and graduate lawyers) or legal laypeople. We found that laypeople often ignore exculpatory circumstances and adhere to the conditional rule when offences evoked high levels of moral outrage. Lawyers did not show this effect. In Experiment 3 laypeople showed difficulties even when asked to simply imagine exculpatory circumstances for highly morally outrageous offences. Results provide new evidence for the role of emotions--like moral outrage--in the consideration of counterexamples to legal conditionals.

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.

Imaging deductive reasoning and the new paradigm

There has been a great expansion of research into human reasoning at all of Marr’s explanatory levels. There is a tendency for this work to progress within a level largely ignoring the others which can lead to slippage between levels (Chater et al., 2003). It is argued that recent brain imaging research on deductive reasoning—implementational level—has largely ignored the new paradigm in reasoning—computational level (Over, 2009). Consequently, recent imaging results are reviewed with the focus on how they relate to the new paradigm. The imaging results are drawn primarily from a recent meta-analysis by Prado et al. (2011) but further imaging results are also reviewed where relevant. Three main observations are made. First, the main function of the core brain region identified is most likely elaborative, defeasible reasoning not deductive reasoning. Second, the subtraction methodology and the meta-analytic approach may remove all traces of content specific System 1 processes thought to underpin much human reasoning. Third, interpreting the function of the brain regions activated by a task depends on theories of the function that a task engages. When there are multiple interpretations of that function, interpreting what an active brain region is doing is not clear cut. It is concluded that there is a need to more tightly connect brain activation to function, which could be achieved using formalized computational level models and a parametric variation approach.

Bayesian reasoning with ifs and ands and ors

The Bayesian approach to the psychology of reasoning generalizes binary logic, extending the binary concept of consistency to that of coherence, and allowing the study of deductive reasoning from uncertain premises. Studies in judgment and decision making have found that people’s probability judgments can fail to be coherent. We investigated people’s coherence further for judgments about conjunctions, disjunctions and conditionals, and asked whether their coherence would increase when they were given the explicit task of drawing inferences. Participants gave confidence judgments about a list of separate statements (the statements group) or the statements grouped as explicit inferences (the inferences group). Their responses were generally coherent at above chance levels for all the inferences investigated, regardless of the presence of an explicit inference task. An exception was that they were incoherent in the context known to cause the conjunction fallacy, and remained so even when they were given an explicit inference. The participants were coherent under the assumption that they interpreted the natural language conditional as it is represented in Bayesian accounts of conditional reasoning, but they were incoherent under the assumption that they interpreted the natural language conditional as the material conditional of elementary binary logic. Our results provide further support for the descriptive adequacy of Bayesian reasoning principles in the study of deduction under uncertainty.

The empirical study of norms is just what we are missing

This paper argues that the goals people have when reasoning determine their own norms of reasoning. A radical descriptivism which avoids norms never worked for any science; nor can it work for the psychology of reasoning. Norms as we understand them are illustrated with examples from categorical syllogistic reasoning and the “new paradigm” of subjective probabilities. We argue that many formal systems are required for psychology: classical logic, non-monotonic logics, probability logics, relevance logic, and others. One of the hardest challenges is working out what goals reasoners have and choosing and tailoring the appropriate logics to model the norms those goals imply.

Normativity, interpretation, and Bayesian models

It has been suggested that evaluative normativity should be expunged from the psychology of reasoning. A broadly Davidsonian response to these arguments is presented. It is suggested that two distinctions, between different types of rationality, are more permeable than this argument requires and that the fundamental objection is to selecting theories that make the most rational sense of the data. It is argued that this is inevitable consequence of radical interpretation where understanding others requires assuming they share our own norms of reasoning. This requires evaluative normativity and it is shown that when asked to evaluate others' arguments participants conform to rational Bayesian norms. It is suggested that logic and probability are not in competition and that the variety of norms is more limited than the arguments against evaluative normativity suppose. Moreover, the universality of belief ascription suggests that many of our norms are universal and hence evaluative. It is concluded that the union of evaluative normativity and descriptive psychology implicit in Davidson and apparent in the psychology of reasoning is a good thing.