Who shows the Unlikelihood Effect - and why?

Recent work shows that people judge an outcome as less likely when they learn the probabilities of all single pathways that lead to that outcome, a phenomenon termed the Unlikelihood Effect. The initial explanation for this effect is that the low pathway probabilities trigger thoughts that deem the outcome unlikely. We tested the alternative explanation that the effect results from people's erroneous interpretation and processing of the probability information provided in the paradigm. By reanalyzing the original experiments, we discovered that the Unlikelihood Effect had been substantially driven by a small subset of people who give extremely low likelihood judgments. We conducted six preregistered experiments, showing that these people are unaware of the total outcome probability and do formally incorrect calculations with the given probabilities. Controlling for these factors statistically and experimentally reduced the proportion of people giving extremely low likelihood judgments, reducing and sometimes eliminating the Unlikelihood Effect. Our results confirm that the Unlikelihood Effect is overall a robust empirical phenomenon, but suggest that the effect results at least to some degree from a few people's difficulties with encoding, understanding, and integrating probabilities. Our findings align with current research on other psychological effects, showing that empirical effects can be caused by participants engaging in qualitatively different mental processes.

Reasoning about possibilities: Modal logics, possible worlds, and mental models

Everyone reasons about possibilities. This article explains how they could do so using mental models. The theory makes four major claims: 1. Correct inferences are necessary, referring only to facts or possibilities to which the premises refer and not ruling any of them out, for example: She left or hid; Therefore, it's possible that she left and possible that she hid. 2. A possibility such as that she hid, which is represented in an intuitive model, presupposes the possibility that it did not occur, she did not hide, which, if reasoners deliberate, is represented in the resulting model. 3. Reasoners condense consistent possibilities, such as the earlier pair, into one possibility: it is possible that she left and she hid. 4. Inconsistencies, such as she left or hid, and she neither left nor hid, refer to no possibilities whatsoever - they have an empty model - and so their only effects are local. Hence, any inference can be withdrawn with impunity if there is knowledge to the contrary. Experiments have corroborated each of these principles. They are incompatible with four essentials of standard modal logics, which concern deductions based on "possible" or "necessary". Their formal deductions correspond to valid inferences, which have no counterexamples in which the premises are true but the conclusion is false. And so the article examines the differences between the two approaches, and explores the adaptation of a modal logic to account for correct human reasoning. Its feasibility is an open question.

How poetry evokes emotions

Poetry evokes emotions. It does so, according to the theory we present, from three sorts of simulation. They each can prompt emotions, which are communications both within the brain and among people. First, models of a poem's semantic contents can evoke emotions as do models that occur in depictions of all kinds, from novels to perceptions. Second, mimetic simulations of prosodic cues, such as meter, rhythm, and rhyme, yield particular emotional states. Third, people's simulations of themselves enable them to know that they are engaged with a poem, and an aesthetic emotion can occur as a result. The three simulations predict certain sorts of emotion, e.g., prosodic cues can evoke basic emotions of happiness, sadness, anger, and anxiety. Empirical evidence corroborates the theory, which we relate to other accounts of poetic emotions.

Recursion in programs, thought, and language

This article presents a theory of recursion in thinking and language. In the logic of computability, a function maps one or more sets to another, and it can have a recursive definition that is semi-circular, i.e., referring in part to the function itself. Any function that is computable - and many are not - can be computed in an infinite number of distinct programs. Some of these programs are semi-circular too, but they needn't be, because repeated loops of instructions can compute any recursive function. Our theory aims to explain how naive individuals devise informal programs in natural language, and is itself implemented in a computer program that creates programs. Participants in our experiments spontaneously simulate loops of instructions in kinematic mental models. They rely on such loops to compute recursive functions for rearranging the order of cars in trains on a track with a siding. Kolmogorov complexity predicts the relative difficulty of abducing such programs - for easy rearrangements, such as reversing the order of the cars, to difficult ones, such as splitting a train in two and interleaving the two resulting halves (equivalent to a faro shuffle). This rearrangement uses both the siding and part of the track as working memories, shuffling cars between them, and so it relies on the power of a linear-bounded computer. Linguistic evidence implies that this power is more than necessary to compose the meanings of sentences in natural language from those of their grammatical constituents.

Can conditionals explain explanations? A modus ponens model of B because A

We suggest a normative model for the evaluation of explanations B because A based on probabilistic conditional reasoning and compare it with empirical data. According to the modus ponens model of explanations, the probability of B because A should equal the joint probability of the conditional if A then B and the explanans A. We argue that B because A expresses the conjunction of A and B as well as positive relevance of A for B. In Study 1, participants (N = 80) judged the subjective probabilities of 20 sets of statements with a focus on belief-based reasoning under uncertainty. In Study 2, participants (N = 376) were assigned to one of six item sets for which we varied the inferential relevance of A for B to explore boundary conditions of our model. We assessed the performance of our model across a range of analyses and report results on the Equation, a fundamental model in research on probabilistic reasoning concerning the evaluation of conditionals. In both studies, results indicate that participants' belief in statements B because A followed model predictions systematically. However, a sizeable proportion of sets of beliefs contained at least one incoherence, indicating deviations from the norms of rationality suggested by our model. In addition, results of Study 2 lend support to the idea that inferential relevance may be relevant for the evaluation of both conditionals and explanations.

The probability of conditionals: A review

A major hypothesis about conditionals is the Equation in which the probability of a conditional equals the corresponding conditional probability: p(if A then C) = p(C|A). Probabilistic theories often treat it as axiomatic, whereas it follows from the meanings of conditionals in the theory of mental models. In this theory, intuitive models (system 1) do not represent what is false, and so produce errors in estimates of p(if A then C), yielding instead p(A & C). Deliberative models (system 2) are normative, and yield the proportion of cases of A in which C holds, i.e., the Equation. Intuitive estimates of the probability of a conditional about unique events: If covid-19 disappears in the USA, then Biden will run for a second term, together with those of each of its clauses, are liable to yield joint probability distributions that sum to over 100%. The error, which is inconsistent with the probability calculus, is massive when participants estimate the joint probabilities of conditionals with each of the different possibilities to which they refer. This result and others under review corroborate the model theory.

Beliefs and emotions about social conventions

Deontic assertions concern what people should and shouldn't do. One sort concern moral principles, such as: People should care for the environment; and another sort concern social conventions, such as: People should knock before entering an office. The present research examined such deontic assertions and their corresponding factual assertions, such as: People care for the environment and People knock before entering an office. Experiment 1 showed a correlation between emotions and beliefs for both sorts of deontic assertion, but not for their factual counterparts in which the word "should" had been deleted (as in the preceding examples). Experiment 2 showed that changing the pleasantness of participants' emotions about social conventions changed their strength of belief in them. Experiment 3 showed conversely that changing the participants' strength of belief in social conventions changed the pleasantness of their emotions about them. These results corroborate the mental model theory of deontic assertions, which postulates that emotions and beliefs about deontics depend on parallel systems that interact with one another.

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.

Reasoning about epistemic possibilities

Reasoning about epistemic possibilities - those based on knowledge - is fundamental in daily life. It is formalized in modal logics, of which there are infinitely many, based on the semantics of 'possible worlds'. An alternative psychological theory postulates that possibilities (and probabilities) in daily life are based on the human ability to construct mental models of finite alternatives, which can each be realized in an indefinite number of different ways. This account leads to three main predictions that diverge from normal modal logics. First, the assertion of an epistemic possibility, A, presupposes the possibility of not-A, in default of knowledge to the contrary. Second, reasoners condense multiple possibilities into one, contravening modal logics, but reducing the load on working memory, e.g.: When knowledge shows that this condensation would be inconsistent, reasoners resist it. Epistemic possibilities are akin to non-numerical probabilities, forming a scale that runs from impossible to certain. In contrast, epistemic necessities state a necessary condition for some other proposition, e.g.: "It is necessary that it rains tomorrow for the plants to survive." The article reports five experiments corroborating these predictions. Their results challenge current conceptions of human reasoning.

Possibilities and the parallel meanings of factual and counterfactual conditionals

The mental model theory postulates that the meanings of conditionals are based on possibilities. Indicative conditionals-such as "If he is injured tomorrow, then he will take some leave"-have a factual interpretation that can be paraphrased as It is possible, and remains so, that he is injured tomorrow, and in that case certain that he takes some leave. Subjunctive conditionals, such as, "If he were injured tomorrow, then he would take some leave," have a prefactual interpretation that has the same paraphrase. But when context makes clear that his injury will not occur, the subjunctive has a counterfactual paraphrase, with the first clause: It was once possible, but does not remain so, that he will be injured tomorrow. Three experiments corroborated these predictions for participants' selections of paraphrases in their native Spanish, for epistemic and deontic conditionals, for those referring to past and to future events, and for those with then clauses referring to what may or must happen. These results are contrary to normal modal logics. They are also contrary to theories based on probabilities, which are inapplicable to deontic conditionals, such as, "If you have a ticket, then you must enter the show."

The Analytic Truth and Falsity of Disjunctions

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such as Either A or B, they tended to evaluate the four cases in its 'partition': A and B, A and not-B, not-A and B, not-A and not-B, as 'possible' or 'impossible' in ways that bore out the difference between inclusive disjunctions ('or both') and exclusive disjunctions ('but not both'). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer 'mirror-image' evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.

Possibilities as the foundation of reasoning

Reasoning about possibilities is fundamental in daily life. Yet, it has been little studied in psychology. We present a psychological theory in which it is the foundation of human reasoning. The theory explains how possibilities have distinct interpretations (deontic, epistemic, and alethic), how people represent them in models, and how these models yield inferences. Key principles are that the semantics of possibilities are the same finitary alternatives underlying probabilities, that speech acts can create obligations inexpressible as probabilities, that compound assertions - conditionals and disjunctions - refer to conjunctions of possibilities holding in default of knowledge to the contrary, and that mental models condense multiple consistent possibilities into one. The theory is incompatible with all normal modal logics and with probabilistic logic. Yet, experiments have corroborated its predictions. The article discusses its precursors, rivals, and potentials.

Emotions and beliefs about morality can change one another

A dual-process theory postulates that belief and emotions about moral assertions can affect one another. The present study corroborated this prediction. Experiments 1, 2 and 3 showed that the pleasantness of a moral assertion - from loathing it to loving it - correlated with how strongly individuals believed it, i.e., its subjective probability. But, despite repeated testing, this relation did not occur for factual assertions. To create the correlation, it sufficed to change factual assertions, such as, "Advanced countries are democracies," into moral assertions, "Advanced countries should be democracies". Two further experiments corroborated the two-way causal relations for moral assertions. Experiment 4 showed that recall of pleasant memories about moral assertions increased their believability, and that the recall of unpleasant memories had the opposite effect. Experiment 5 showed that the creation of reasons to believe moral assertions increased the pleasantness of the emotions they evoked, and that the creation of reasons to disbelieve moral assertions had the opposite effect. Hence, emotions can change beliefs about moral assertions; and reasons can change emotions about moral assertions. We discuss the implications of these results for alternative theories of morality.

The Truth of Conditional Assertions

Given a basic conditional of the form, If A then C, individuals usually list three cases as possible: A and C, not-A and not-C, not-A and C. This result corroborates the theory of mental models. By contrast, individuals often judge that the conditional is true only in the case of A and C, and that cases of not-A are irrelevant to its truth or falsity. This result corroborates other theories of conditionals. To resolve the discrepancy, we devised two new tasks: the "collective" truth task, in which participants judged whether sets of assertions about a specific individual, such as: If A then C, not-A, C, could all be true at the same time; and one in which participants judged the truth of conditional predictions about specific future events. The results consistently matched the three possibilities, thereby corroborating the model theory. They also showed a massive violation of the probability calculus in estimates of the probabilities of the four cases in the partition of conditionals (A and C, A and not-C, not-A and C, and not-A and not-C), which summed to over 200%.

The Relation Between Factual and Counterfactual Conditionals

What is the relation between factual conditionals: If A happened then B happened, and counterfactual conditionals: If A had happened then B would have happened? Some theorists propose quite different semantics for the two. In contrast, the theory of mental models and its computer implementation interrelates them. It postulates that both can have a priori truth values, and that the semantic bases of both are possibilities: states that are possible for factual conditionals, and that were once possible but that did not happen for counterfactual conditionals. Two experiments supported these relations. Experiment 1 showed that, like factual conditionals, certain counterfactuals are true a priori, and others are false a priori. Experiment 2 replicated this result and showed that participants selected appropriate paraphrases, referring, respectively, to real and to counterfactual possibilities, for the two sorts of conditional. These results are contrary to alternative accounts of conditionals.

Facts and Possibilities: A Model-Based Theory of Sentential Reasoning

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities.

Probabilistic representation in syllogistic reasoning: A theory to integrate mental models and heuristics

This paper presents a new theory of syllogistic reasoning. The proposed model assumes there are probabilistic representations of given signature situations. Instead of conducting an exhaustive search, the model constructs an individual-based "logical" mental representation that expresses the most probable state of affairs, and derives a necessary conclusion that is not inconsistent with the model using heuristics based on informativeness. The model is a unification of previous influential models. Its descriptive validity has been evaluated against existing empirical data and two new experiments, and by qualitative analyses based on previous empirical findings, all of which supported the theory. The model's behavior is also consistent with findings in other areas, including working memory capacity. The results indicate that people assume the probabilities of all target events mentioned in a syllogism to be almost equal, which suggests links between syllogistic reasoning and other areas of cognition.

Immediate inferences from quantified assertions

We propose a theory of immediate inferences from assertions containing a single quantifier, such as: All of the artists are bakers; therefore, some of the bakers are artists. The theory is based on mental models and is implemented in a computer program, mReasoner. It predicts three main levels of increasing difficulty: (a) immediate inferences in which the premise and conclusion have identical meanings; (b) those in which the initial mental model of the premise yields the correct conclusion; and (c) those in which only an alternative to the initial model establishes the correct conclusion. These levels of difficulty were corroborated for inferences to necessary conclusions (in a reanalysis of data from Newstead, S. E., & Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning and Verbal Behavior, 22, 535–546), for inferences to modal conclusions, such as, it is possible that all of the bakers are artists (Experiment 1), for inferences with unorthodox quantifiers, such as, most of the artists (Experiment 2), and for inferences about the consistency of pairs of quantified assertions (Experiment 3). The theory also includes three parameters in a stochastic system that predicted quantitative differences in accuracy within the three main sorts of inference.