Consequential conditionals: invited and suppressed inferences from valued outcomes

Consequential conditionals are defined as "if P then Q" statements, where P is an action, and Q a predicted outcome of this action, which is either desirable or undesirable to the agent. Experiment 1 shows that desirable (viz. undesirable) outcomes invite an inference to the truth (viz. falsity) of their antecedent. Experiment 2 shows that the more extreme the outcome is, the stronger the invited inference is. Experiment 3 shows that modus ponens from premises "If A then C, A" can be suppressed with the introduction of a consequential conditional, "If C then Q," where Q is an undesirable outcome. Experiment 4 shows that the more undesirable Q is, the larger the suppression is. The authors discuss how these results can enrich current approaches of conditional inference on the basis of mental models, complementary necessary conditions, and conditional probabilities.     

A necessity illusion for modal inferences from conditionals

Three experiments examined how people reason about what is possible or necessary when a conditional is true. Participants were asked to indicate whether it was necessary, possible or impossible for a specific instance to conform to one of the truth-table cases (pq, p¬q, ¬pq and ¬p¬q) (¬ = not), given the truth of the conditional. It was found that most participants, inconsistently, judged the pq case as necessary but the ¬pq or ¬p¬q cases as possible. Logically, these two kinds of judgments are contradictory. Moreover, a true conditional doesn’t imply that a specific instance under the conditional must be pq . Therefore, people demonstrate a necessity illusion for pq cases which contradicts their commitment to the possibility of ¬pq or ¬p¬q cases. Existing accounts of conditionals are unable to explain the contradiction and the necessity illusion. We propose an inference dissociation account and explore the theoretical implications of this necessity illusion.     

Generalising the probabilistic semantics of conditionals

Conclusion If assertibility rules are to be important in semantic theory, hypotheses such as this one will need to beiinvestigated. And Slote's observation (see note 12) that what matters for assertibility is not belief but knowledge will turn out to have powerful consequences.Adams' rule is the first well understood assertibility rule in philosophical semantics. I think we should be led by its successes to look for more. In this paper, I have built on his assertibility rule and offered two more. But it is worth observing, finally, that their interest lies, in part, in the contrast with semantic rules stated in terms of truth conditions. Much recent discussion of assertibility conditions derives from Dummett's anti-realist claim that we should perhaps substitute assertibility conditions for truth conditions in general; see Dummett (1973), Wright (1976). This notion of assertibility is not the one I have been working with here: for the anti-realist notion of an assertibility condition is of a condition whose obtaining provides epistemic warrant for the sentence asserted. Dummett and Wright's assertibility conditions are thus to do with the justification of the belief expressed by a sentence and not directly with the justification for asserting it. ¹⁷ But realists may be interested in a more modest role for assertibility conditions — in my sense — which are not derived, by way of ASS, from truth conditions. Realism need not be the claim that all declarative sentences can be given truth conditions; it requires only the view that truth conditions account for the central class of cases. The proposals in this paper presuppose a realist treatment of the antecedents and consequents of unembedded conditionals, and a realist view of the sentences within the scope of the epistemic modality. What could be more central than that?I am very grateful to an anonymous referee for this journal and to its editor for helpful comments on earlier drafts.     

Pronounced inferences: A study on inferential conditionals

An experimental study is reported which investigates the differences in interpretation between content conditionals (of various pragmatic types) and inferential conditionals. In a content conditional, the antecedent represents a requirement for the consequent to become true. In an inferential conditional, the antecedent functions as a premise and the consequent as the inferred conclusion from that premise. The linguistic difference between content and inferential conditionals is often neglected in reasoning experiments. This turns out to be unjustified, since we adduced evidence on the basis of a quantitative and a qualitative analysis that this difference has a manifest psychological relevance. For the inferential conditionals, participants appear to retrieve the order of events of the original content conditional on which it was based, before they start reasoning with it. The implications of this finding for reasoning research and linguistics will be discussed.     

Advice conditionals about tips and warnings: interpretations and inferences

Two experiments examine how people interpret and reason about advice conditionals, such as tips, for example, “if you study more your grades will improve”, and warnings, for example, “if you stop exercising you will gain weight”. Experiment 1 showed that when participants reason about whether a tip or warning could be true in different situations, their judgments correspond to a biconditional or conditional interpretation on about half of all trials, but to an enabling or tautology interpretation on many others. Experiment 2 showed that participants make few modus ponens and tollens inferences from tips and warnings, and more modus ponens inferences from tips than warnings. The implications for alternative theories are discussed.     

Illusory inferences from a disjunction of conditionals: a new mental models account

(Johnson-Laird, P.N., & Savary, F. (1999, Illusory inferences: a novel class of erroneous deductions. Cognition, 71, 191-229.) have recently presented a mental models account, based on the so-called principle of truth, for the occurrence of inferences that are compelling but invalid. This article presents an alternative account of the illusory inferences resulting from a disjunction of conditionals. In accordance with our modified theory of mental models of the conditional, we show that the way individuals represent conditionals leads them to misinterpret the locus of the disjunction and prevents them from drawing conclusions from a false conditional, thus accounting for the compelling character of the illusory inference.     

Initial models in conditionals: evidence from priming

We examined the comprehension of different types of conditionals. We measured the reading time of sentences primed by different types of conditionals (Experiments 1 and 2). We found that the participants read not-p and not-q faster when it was primed by the conditional form p if q and they were slower to read p and q when it was primed by the conditional form p only if q. This effect disappeared in the second experiment, where the order of the elements was reversed (q and p and not-q and not-p). These results suggest that the conditional form p if q elicits an initial representation "from p to q" with two possibilities, while the conditional form p only if q elicits a reverse representation with only one possibility. The third experiment showed that there were effects of the order only for the conditional if p then q, which confirms the reverse representation hypothesis. We discuss the implications of these results for different theories of conditional comprehension.     

Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models

We report four experiments investigating conjunctive inferences (from a conjunction and two conditional premises) and disjunctive inferences (from a disjunction and the same two conditionals). The mental model theory predicts that the conjunctive inferences, which require one model, should be easier than the disjunctive inferences, which require multiple models. Formal rule theories predict either the opposite result or no difference between the inferences. The experiments showed that the inferences were equally easy when the participants evaluated given conclusions, but that the conjunctive inferences were easier than the disjunctive inferences (1) when the participants drew their own conclusions, (2) when the conjunction and disjunction came last in the premises, (3) in the time the participants spent reading the premises and in responding to given conclusions, and (4) in their ratings of the difficulty of the inferences. The results support the model theory and demonstrate the importance of reasoners' inferential strategies.     

Working memory and inferences: evidence from eye fixations during reading

Eye fixations during reading were monitored to examine the relationship between individual differences in working memory capacity-as assessed by the reading span task-and inferences about predictable events. Context sentences predicting likely events, or non-predicting control sentences, were presented. They were followed by continuation sentences in which a target word represented an event to be inferred (inferential word) or an unlikely event (non-predictable word). A main effect of reading span showed that high working memory capacity was related to shorter gaze durations across sentence regions. More specific findings involved an interaction between context, target, and reading span on late processing measures and regions. Thus, for high- but not for low-span readers, the predicting condition, relative to the control condition, facilitated reanalysis of the continuation sentence that represented the inference concept. This effect was revealed by a reduction in regression-path reading time in the last region of the sentence, involving less time reading that region and fewer regressions from it. These results indicate that working memory facilitates elaborative inferences during reading, but that this occurs at late text-integration processes, rather than at early lexical-access processes.     

The role of inferences about referential intent in word learning: evidence from autism

Young children are readily able to use known labels to constrain hypotheses about the meanings of new words under conditions of referential ambiguity. At issue is the kind of information children use to constrain such hypotheses. According to one theory, children take into account the speaker's intention when solving a referential puzzle. In the present studies, children with autism were impaired in monitoring referential intent, but were equally successful as normally developing 24-month-old toddlers at mapping novel words to unnamed items under conditions of referential ambiguity. Therefore, constraints that lead the child to map a novel label to a previously unnamed object under these circumstances are not solely based on assessments of speakers' intentions.     

Processing inferences at the semantics/pragmatics frontier: Disjunctions and free choice

Linguistic inferences have traditionally been studied and categorized in several categories, such as entailments, implicatures or presuppositions. This typology is mostly based on traditional linguistic means, such as introspective judgments about phrases occurring in different constructions, in different conversational contexts. More recently, the processing properties of these inferences have also been studied (see, e.g., recent work showing that scalar implicatures is a costly phenomenon). Our focus is on free choice permission, a phenomenon by which conjunctive inferences are unexpectedly added to disjunctive sentences. For instance, a sentence such as “Mary is allowed to eat an ice-cream or a cake” is normally understood as granting permission both for eating an ice-cream and for eating a cake. We provide data from four processing studies, which show that, contrary to arguments coming from the theoretical literature, free choice inferences are different from scalar implicatures.     

The psychology of inferring conditionals from disjunctions: A probabilistic study

There is a new probabilistic paradigm in the psychology of reasoning that is, in part, based on results showing that people judge the probability of the natural language conditional, if $A$then $B$, $P\left(ifAthenB\right)$, to be the conditional probability, $P(B\mid A)$. We apply this new approach to the study of a very common inference form in ordinary reasoning: inferring the conditional if not-$A$then $B$ from the disjunction $A$ or $B$. We show how this inference can be strong, with $P$(if not-$A$then $B$) “close to” $P\left(AorB\right)$, when $A$ or $B$ is non-constructively justified. When $A$ or $B$ is constructively justified, the inference can be very weak. We also define suitable measures of “closeness” and “constructivity”, by providing a probabilistic analysis of these notions.     

Suppression of valid inferences and knowledge structures: the curious effect of producing alternative antecedents on reasoning with causal conditionals

These studies looked at the difficulty that reasoners have in accepting conditional ("If P then Q") major premises that are not necessarily true empirically, as a basis for deductive reasoning. Preliminary results have shown that when reasoners are asked to produce possible alternate antecedents to the major premise ("If A then Q"), they paradoxically tend to deny the modus ponens (MP) inference ("If P is true, then Q is true"). Three studies further explored these results. The first study gave university students paper-and-pencil tests in which instructions to "suppose that the major premise is true" was followed by a request to determine the next number in a sequence, to retrieve information unrelated to the premises, or to retrieve a possible case of "If A then Q." Relative to a control group, reasoners asked to produce an alternative antecedent showed a significant tendency to deny the MP inference, whereas no such tendency was observed for the two other tasks used. A second study compared performance on a condition in which reasoners were asked to produce an alternative antecedent with that when they were given an explicit alternative. Premises used in this study were such that the latter alternative antecedent was also spontaneously produced by over 70% of reasoners. Results showed that the tendency to refuse the MP premise could not be accounted for by the specific nature of the alternative produced. A third study found that the tendency to refuse the MP inference after producing an alternative antecedent was affected by the number of "disabling conditions" (i.e., conditions that allow "P to be true" and "Q to be false") available for the major premise. These results are interpreted as being consistent with a model that supposes that logical reasoning requires selective inhibition of real-world knowledge.     

The semantics of prosody: acoustic and perceptual evidence of prosodic correlates to word meaning

This investigation examined whether speakers produce reliable prosodic correlates to meaning across semantic domains and whether listeners use these cues to derive word meaning from novel words. Speakers were asked to produce phrases in infant-directed speech in which novel words were used to convey one of two meanings from a set of antonym pairs (e.g., big/small). Acoustic analyses revealed that some acoustic features were correlated with overall valence of the meaning. However, each word meaning also displayed a unique acoustic signature, and semantically related meanings elicited similar acoustic profiles. In two perceptual tests, listeners either attempted to identify the novel words with a matching meaning dimension (picture pair) or with mismatched meaning dimensions. Listeners inferred the meaning of the novel words significantly more often when prosody matched the word meaning choices than when prosody mismatched. These findings suggest that speech contains reliable prosodic markers to word meaning and that listeners use these prosodic cues to differentiate meanings. That prosody is semantic suggests a reconceptualization of traditional distinctions between linguistic and nonlinguistic properties of spoken language.     

Children’s causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference.     

The logic of conditionals 1

The standard use of the propositional calculus ('P.C.’) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ‘safely’ used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn.