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.     

The negations of conjunctions,conditionals, and disjunctions

How do reasoners understand and formulate denials of compound assertions, such as conjunctions and disjunctions? A theory based on mental models postulates that individuals enumerate models of the various possibilities consistent with the assertions. It therefore predicts a novel interaction: in affirmations, conjunctions, A and B, which refer to one possibility, should be easier to understand than disjunctions, A or B, which refer to more than one possibility; in denials, conjunctions, not(A and B), which refer to more than one possibility, should be harder to understand than disjunctions, not(A or B), which do not. Conditionals are ambiguous and they should be of intermediate difficulty. Experiment 1 corroborated this trend with a task in which the participants selected which possibilities were consistent with assertions, such as: Bob denied that he wore a yellow shirt and he wore blue pants on Tuesday. Experiment 2 likewise showed that participants' own formulations of verbal denials yielded the same trend in which denials of conjunctions were harder than denials of conditionals, which in turn were harder than denials of disjunctions.     

Is everyday causation deterministic or probabilistic?

One view of causation is deterministic: A causes B means that whenever A occurs, B occurs. An alternative view is that causation is probabilistic: the assertion means that given A, the probability of B is greater than some criterion, such as the probability of B given not-A. Evidence about the induction of causal relations cannot readily decide between these alternative accounts, and so we examined how people refute causal assertions. In four experiments most participants judged that a single counterexample of A and not-B refuted assertions of the form, A causes B. And, as a deterministic theory based on mental models predicted, participants were more likely to request multiple refutations for assertions of the form, A enables B. Similarly, refutations of the form not-A and B were more frequent for enabling than causal assertions. Causation in daily life seems to be a deterministic concept.     

Linguistic-pragmatic factors in interpreting disjunctions

' The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature (but not both). We point to a class of situations that ought to predispose disjunctions to inclusive interpretations and to situations that encourage exclusive interpretations. A disjunction's ultimate interpretation is based on its potential informativeness, where the interpretation of the disjunctive utterance having the smallest number of true conditions is considered most informative. Our investigation leads to five experiments employing arbitrary materials. Among the problems expected to encourage inclusive interpretations are those that present disjunctions in the antecedents of conditionals and in question forms. The best candidates to produce implicatures are those disjunctions that underdetermine an expected conjunctive conclusion, although other disjunctive utterances that are more informative as exclusive are discussed and tested.     

Mistaking the instance for the rule: A critical analysis of the truth-table evaluation paradigm

Many studies probe for interpretations of < if A then C> by having people evaluate truth-table cases (<A and C>, < A and not-C>, < not-A and C>, < not-A and not-C>) as making the rule true or false, or being irrelevant. We argue that a single case can never prove a general rule to be true, as philosophy of science has taught any researcher. Giving participants the impossible “true” option would therefore bias results away from this response. In Experiment 1 people judged instead whether cases make a rule false, do not make the rule false, or are irrelevant to the rule. The experimental group (N = 44) showed a significant increase in not-false responses compared with true responses of the control group (N = 39). In Experiments 2 and 3 the experimental groups judged whether cases make a rule true, corroborate it (i.e., make the rule more plausible, but neither true nor false), make it false, or are irrelevant. There was a significant reduction of irrelevant responses as compared to the default true/false/irrelevant task for the control groups. Even < A and C> cases were often no longer considered to make an < if A then C> rule true and were correctly judged to corroborate (vs. verify) rules. Results corroborate our conceptual analyses of the unsuitable “true” response option and put into question arguments that hinge on the presumed likelihood by which people consider truth contingencies to make a rule “true”.     

Interpreting conjoined noun phrases and conjoined clauses: Collective versus distributive preferences

Two experiments are reported that show that introducing event participants in a conjoined noun phrase (NP) favours a single event (collective) interpretation, while introducing them in separate clauses favours a separate events (distributive) interpretation. In Experiment 1, acceptability judgements were speeded when the bias of a predicate toward separate events versus a single event matched the presumed bias of how the subjects' referents were introduced (as conjoined noun phrases or in conjoined clauses). In Experiment 2, reading of a phrase containing an anaphor following conjoined noun phrases was facilitated when the anaphor was they, relative to when it was neither/each of them; the opposite pattern was found when the anaphor followed conjoined clauses. We argue that comprehension was facilitated when the form of an anaphor was appropriate for how its antecedents were introduced. These results address the very general problem of how we individuate entities and events when presented with a complex situation and show that different linguistic forms can guide how we construe a situation. The results also indicate that there is no general penalty for introducing the entities or events separately—in distinct clauses as “split” antecedents.     

Temporal and spatial relations in sentential reasoning

The mental model theory postulates that the meanings of assertions, and knowledge about their context can modulate the logical meaning of sentential connectives, such as "if" and "or". One known effect of modulation is to block the representation of possibilities to which a proposition refers. But, modulation should also add relational information, such as temporal order, to models of possibilities. Three experiments tested this prediction. Experiment 1 showed that individuals spontaneously matched the tense of their conclusions (in Portuguese) to embody implied, but unexpressed, temporal relations in conditional premises. Experiment 2 demonstrated the same phenomenon in inferences from disjunctions. Experiment 3 showed that the number of such implicit relations in inferences from conditionals affects both accuracy and the speed of reasoning. These results support the modulation hypothesis.     

对相容和不相容析取关系下析取句与条件句之间推理的比较

研究析取句和条件句之间的推理能检验推理心理学中的主要理论解释。一个实验考察了析取句和条件句中两个基本成分之间的关系(相容析取与不相容析取)和推理方向(由析取句推条件句与由条件句推析取句)对析取句与其等值的条件句之间推理的影响。结果发现,推理方向的影响取决于条件句和析取句中基本成分间的关系,在不相容析取关系下的推理成绩好于在相容析取关系下的推理成绩。现有的推理理论不能解释被试的整体反应模式,作者提出的特殊知识启发式与一般的句法意义对比启发式的竞争能统一解释被试的主导反应模式。     

Disjunctive illusory inferences and how to eliminate them

The mental model theory of reasoning postulates that individuals construct mental models of the possibilities in which the premises of an inference hold and that these models represent what is true but not what is false. An unexpected consequence of this assumption is that certain premises should yield systematically invalid inferences. This prediction is unique among current theories of reasoning, because no alternative theory, whether based on formal rules of inference or on probabilistic considerations, predicts these illusory inferences. We report three studies of novel illusory inferences that depend on embedded disjunctions—for example, premises of this sort: A or else (B or else C). The theory distinguishes between those embedded disjunctions that should yield illusions and those that should not. In Experiment 1, we corroborated this distinction. In Experiment 2, we extended the illusory inferences to a more stringently controlled set of problems. In Experiment 3, we established a novel method for reducing illusions by calling for participants to make auxiliary inferences.     

Naive Probability: Model‐Based Estimates of Unique Events

We describe a dual‐process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non‐numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non‐numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P(A), P(B), P(A and B), disjunctions: P(A), P(B), P(A or B or both), and conditional probabilities P(A), P(B), P(B|A). They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning.     

Priming effect in affirmative complex conditional connectives

We report the results of an experiment that examined the mental representations underlying the comprehension of complex conditional connectives (such as “A, on condition that B”) and the conditional if (such as “A, if B”). The mental representations during the comprehension stage were analysed using a “priming methodology”. The experiment showed that participants read the possibility “A and not-B” faster when it was primed by “A, if B” than when it was primed by “A, on condition that B”. The finding suggests that people understand the sentence “A, on condition that B” as biconditional; other possibilities (“A and B”, “not-A and B”, “not-A and not-B”) were primed equally by both connectives. We discuss the implications of this for current theories of reasoning.     

Reasoning from connectives and relations between entities

This article reports investigations of inferences that depend both on connectives between clauses, such as or else, and on relations between entities, such as in the same place as. Participants made more valid inferences from biconditionals—for instance, Ann is taller than Beth if and only if Beth is taller than Cath—than from exclusive disjunctions (Exp. 1). They made more valid transitive inferences from a biconditional when a categorical premise affirmed rather than denied one of its clauses, but they made more valid transitive inferences from an exclusive disjunction when a categorical premise denied rather than affirmed one of its clauses (Exp. 2). From exclusive disjunctions, such as Either Ann is not in the same place as Beth or else Beth is not in the same place as Cath, individuals tended to infer that all three individuals could be in different places, whereas in fact this was impossible (Exps. 3a and 3b). The theory of mental models predicts all of these results.     

The compatibility heuristic in non-categorical hypothetical reasoning: Inferences between conditionals and disjunctions

A new theory explains how people make hypothetical inferences from a premise consistent with several alternatives to a conclusion consistent with several alternatives. The key proposal is that people rely on a heuristic that identifies compatible possibilities. It is tested in 7 experiments that examine inferences between conditionals and disjunctions. Participants accepted inferences between conditionals and inclusive disjunctions when a compatible possibility was immediately available, in their binary judgments that a conclusion followed or not (Experiment 1a) and ternary judgments that included it was not possible to know (Experiment 1b). The compatibility effect was amplified when compatible possibilities were more readily available, e.g., for ‘A only if B’ conditionals (Experiment 2). It was eliminated when compatible possibilities were not available, e.g., for ‘if and only if A B’ bi-conditionals and exclusive disjunctions (Experiment 3). The compatibility heuristic occurs even for inferences based on implicit negation e.g., ‘A or B, therefore if C D’ (Experiment 4), and between universals ‘All A’s are B’s’ and disjunctions (Experiment 5a) and universals and conditionals (Experiment 5b). The implications of the results for alternative theories of the cognitive processes underlying hypothetical deductions are discussed.     

How falsity dispels fallacies

From certain sorts of premise, individuals reliably infer invalid conclusions. Two Experiments investigated a possible cause for these illusory inference: Reasoners fail to think about what is false. In Experiment 1, 24 undergraduates drew illusory and control inferences from premises based on exclusive disjunctions (“or else”). In one block, participants were instructed to falsify the premises of each illusory and control inference before making the inference. In the other block, participants did not receive these instructions. There were more correct answers for illusory disjunctions whose premises had been falsified than there were for illusory disjunctions that had not been falsified. A second Experiment introduced illusory inferences in a real world context that accentuated falsification of premises. Accuracy also improved. Knowledge of how to falsify premises and to consider their implications for true premises transferred to a new problem introduced at the end of the Experiment without the falsification instruction. The participants' ratings of the difficulty of the inferences showed that they did not err simply because illusory inferences are perceived to be more difficult than control problems. The model theory predicts these results because it postulates that the limitations of working memory preclude the representation of false information.     

The consistency of disjunctive assertions

In two experiments, we established a new phenomenon in reasoning from disjunctions of the grammatical form either A or else B, where A and B are clauses. When individuals have to assess whether pairs of assertions can be true at the same time, they tend to focus on the truth of each clause of an exclusive disjunction (and ignore the concurrent falsity of the other clause). Hence, they succumb to illusions of consistency and of inconsistency with pairs consisting of a disjunction and a conjunction (Experiment 1), and with simpler problems consisting of pairs of disjunctions, such as eIther there is a pie or else there is a cake and Either there isn't a pie or else there is a cake (Experiment 2), that appear to be consistent with one another, but in fact are not. These results corroborate the theory that reasoning depends on envisaging models of possibilities.     

Naive causality: a mental model theory of causal meaning and reasoning

This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B , and A allows not-B , and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not-A and B, and not-A and not-B, with the temporal constraint that B does not precede A; and the stronger relation conveys only the first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules.     

Mental representation of logical connectives

Logical connectives, such as “AND”, “OR”, “IF . . . THEN”, and “IF AND ONLY IF” are ubiquitous in both language and cognition; however, reasoning with logical connectives is error-prone. We argue that some of these errors may stem from people's tendency to minimize the number of possibilities compatible with logical connectives and to construct a “minimalist” one-possibility representation. As a result, connectives denoting a single possibility (e.g., conjunctions) are likely to be represented correctly, whereas connectives denoting multiple possibilities (e.g., disjunctions or conditionals) are likely to be erroneously represented as conjunctions. These predictions were tested and confirmed in three experiments using different paradigms. In Experiment 1, participants were presented with a multiple-choice task and asked to select all and only those possibilities that would indicate that compound verbal propositions were true versus false. In Experiment 2, a somewhat similar task was used, except that participants were asked later to perform a cued recall of verbal propositions. Finally, Experiment 3 used an old/new recognition paradigm to examine participants' ability to accurately recognize different logical connectives. The results of the three experiments are discussed in relation to theories of representation of possibilities and theories of reasoning.     

Unless reasoning

We report the results of two experiments investigating conditional inferences from conditional unless assertions, such as Juan is not in León unless Nuria is in Madrid. Experiments 1 and 2 check Fillenbaum's hypothesis about the semantic similarity of unless with if not and only if assertions; both also examine inferential endorsements (Experiment 1) and endorsements and latencies (Experiment 2) of the four logically equivalent conditional formulations: if A then B, if not-B then not-A, A only if B and notA unless B. The results of these experiments show the similarity of unless and only if confirming that the representation of both conditionals from the outset probably include two possibilities directionally oriented from B to A; results also confirm the especial difficulty of unless assertions. The implications of the results are discussed in the context of recent psychological and linguistic theories of the meaning of unless.     

Estimating valence from the sound of a word: Computational,experimental, and cross-linguistic evidence

It is assumed linguistic symbols must be grounded in perceptual information to attain meaning, because the sound of a word in a language has an arbitrary relation with its referent. This paper demonstrates that a strong arbitrariness claim should be reconsidered. In a computational study, we showed that one phonological feature (nasals in the beginning of a word) predicted negative valence in three European languages (English, Dutch, and German) and positive valence in Chinese. In three experiments, we tested whether participants used this feature in estimating the valence of a word. In Experiment 1, Chinese and Dutch participants rated the valence of written valence-neutral words, with Chinese participants rating the nasal-first neutral-valence words more positive and the Dutch participants rating nasal-first neutral-valence words more negative. In Experiment 2, Chinese (and Dutch) participants rated the valence of Dutch (and Chinese) written valence-neutral words without being able to understand the meaning of these words. The patterns replicated the valence patterns from Experiment 1. When the written words from Experiment 2 were transformed into spoken words, results in Experiment 3 again showed that participants estimated the valence of words on the basis of the sound of the word. The computational study and psycholinguistic experiments indicated that language users can bootstrap meaning from the sound of a word.     

Cessation and integration in classical yoga

In this paper I challenge and attempt to correct conclusions about Classical Yoga philosophy drawn by traditional and modern interpretations of Patañjali's Yoga‐sūtras. My interpretation of Patañjali's Yoga—which focuses on the meaning of “cessation” (nirodha) as given in Patañjali's central definition of Yoga (YS 1.2)—counters the radically dualistic and ontologically‐oriented interpretations of Yoga presented by many scholars, and offers an open‐ended, epistemologically‐oriented hermeneutic which, I maintain, is more appropriate for arriving at a genuine assessment of Patañjali's system (dar?ana) of Yoga.