Online research in philosophy

There is ample evidence that in classical truth table task experiments false antecedents are judged as ?irrelevant?. Instead of interpreting this in support of a suppositional representation of conditionals, Schroyens (2010a, 2010b) attributes it to the induction problem: the impossibility of establishing the truth of a universal claim on the basis of a single case. In the first experiment a truth table task with four options is administered and the correlation with intelligence is inspected. It is observed that ?undetermined? is (...) chosen in one third of the judgements and ?irrelevant? in another third. A positive correlation is revealed between intelligence and the number of ?irrelevant? and ?undetermined? judgements. The data do not exclude that a part of the ?irrelevant? judgements in classical truth table task experiments might be caused by the induction problem. In the second experiment participants are presented with a simplified four-option truth table task and asked for a justification of their judgements. These justifications show the induction problem is not the reason for choosing the ?irrelevant? or ?undetermined? option, which is supportive for a suppositional representation of conditionals. (shrink)

Two types of truth table task are used to examine people's mental representation of conditionals. In two within-participants experiments, participants either receive the same task-type twice (Experiment 1) or are presented successively with both a possibilities task and a truth task (Experiment 2). Experiment 3 examines how people interpret the three-option possibilities task and whether they have a clear understanding of it. The present study aims to examine, for both task-types, how participants' cognitive ability relates to the classification of the (...) truth table cases as irrelevant, and their consistency in doing so. Looking at the answer patterns, participants' cognitive ability influences their classification of the truth table cases: A positive correlation exists between cognitive ability and the number of false-antecedent cases classified as ?irrelevant?, both in the possibilities task and the truth task. This favours a suppositional representation of conditionals. (shrink)

Two types of truth table tasks are used investigating mental representations of conditionals: a possibilities-based and a truth-based one. In possibilities tasks, participants indicate whether a situation is possible or impossible according to the conditional rule. In truth tasks participants evaluate whether a situation makes the rule true or false, or is irrelevant with respect to the truth of the rule. Comparing the two-option version of the possibilities task with the truth task in Experiment 1, the possibilities task yields logical (...) answer patterns whereas the truth task yields defective patterns. Adding the irrelevant option to the possibilities task in Experiment 2 leads to a considerable amount of defective patterns in the possibilities task, but still to more logical patterns in the possibilities task than in the truth task. Experiment 3 shows that directionality matters since rule-to-situation tasks yield more logical answer patterns than do situation-to-rule tasks. We conclude that both task types are not comparable as such since wording, number of options and directionality influence the results. (shrink)

Two types of truth table tasks are used investigating mental representations of conditionals: a possibilities-based and a truth-based one. In possibilities tasks, participants indicate whether a situation is possible or impossible according to the conditional rule. In truth tasks participants evaluate whether a situation makes the rule true or false, or is irrelevant with respect to the truth of the rule. Comparing the two-option version of the possibilities task with the truth task in Experiment 1, the possibilities task yields logical (...) answer patterns whereas the truth task yields defective patterns. Adding the irrelevant option to the possibilities task in Experiment 2 leads to a considerable amount of defective patterns in the possibilities task, but still to more logical patterns in the possibilities task than in the truth task. Experiment 3 shows that directionality matters since rule-to-situation tasks yield more logical answer patterns than do situation-to-rule tasks. We conclude that both task types are not comparable as such since wording, number of options and directionality influence the results. (shrink)

The present paper focuses on the heuristic selection process preceding the actual transitive reasoning process. A part of the difficulty of transitive reasoning lies in the selection of the relevant problem aspects. Two experiments are presented using the paradigm introduced by Markovits, Dumas, and Malfait (1995), in which children were asked to make “higher than” inferences about arrays of coloured blocks. In order to discriminate between genuine transitive inference and a simple strategy of relative position, Markovits et al. interspersed white (...) blocks with the coloured blocks, such that the relative position strategy leads to erroneous responses. However, we argue that the white blocks cause confusion due to their ambiguity, which interferes with the heuristic selection process. Two methodological adaptations were introduced, which are hypothesised to facilitate the selection process and improve transitive reasoning: (1) the white blocks were replaced by coloured blocks, and (2) a less abstract context was added to the experimental design. The colour manipulation leads to a clear increase in the use of a transitive strategy by 9-year-old children; 8-year-old children mainly used the relative position strategy. When adding a context story, 9-year-old children used the transitive strategy regardless of the colour of the interspersed blocks. The overall performance of 8-year-olds improved slightly. These results are interpreted as support for a dual-process model of transitive reasoning. (shrink)

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. (shrink)

The present study is part of recent attempts to specify the characteristics of the counterexample retrieval process during causal conditional reasoning. The study tried to pinpoint whether the retrieval of stored counterexamples (alternative causes and disabling conditions) for a causal conditional is completely automatic in nature or whether the search process also demands executive working memory (WM) resources. In Experiment 1, participants were presented with a counterexample generation task and a measure of WM capacity. We found a positive relation between (...) search efficiency, as measured by the number of generated counterexamples in limited time, and WM capacity. Experiment 2 examined the effects of a secondary WM load on the retrieval performance. As predicted, burdening WM with an attention-demanding secondary task decreased the retrieval efficiency. Both low and high spans were affected by the WM load but load effects were less pronounced for the most strongly associated counterexamples. Findings established that in addition to an automatic search component, the counterexample retrieval draws on WM resources. (shrink)

Two experiments examined the contribution of working memory (WM) to the retrieval and inhibition of background knowledge about counterexamples (alternatives and disablers, Cummins, 1995) during conditional reasoning. Experiment 1 presented a conditional reasoning task with everyday, causal conditionals to a group of people with high and low WM spans. High spans rejected the logically invalid AC and DA inferences to a greater extent than low spans, whereas low spans accepted the logically valid MP and MT inferences less frequently than high (...) spans. In Experiment 2, an executive-attention-demanding secondary task was imposed during the reasoning task. Findings corroborate that WM resources are used for retrieval of stored counterexamples and that people with high WM spans will use WM resources to inhibit the counterexample activation when the type of counterexample conflicts with the logical validity of the reasoning problem. (shrink)

There are two accounts describing causal conditional reasoning: the probabilistic and the mental models account. According to the probabilistic account, the tendency to accept a conclusion is related to the probability by which cause and effect covary. According to the mental models account, the tendency to accept a conclusion relates to the availability of counterexamples. These two accounts are brought together in a dual-process theory: It is argued that the probabilistic reasoning process can be considered as a heuristic process whereas (...) the mental models account can be seen as its analytic counterpart. Experiment 1 showed that the two processes differ on a temporal dimension: The variation in fast responses was best predicted by the variation in likelihood information, while the variation in slow responses was best predicted by variation in counterexample information. Experiments 2 and 3 validate the override principle: The likelihood conclusion can be overwritten when specific counterexamples are retrieved in time. In Experiment 2 both accounts were compared based on their difference in input. In Experiment 3 we used a verbal protocol analysis to validate the dual-process idea at the output level. The data of the three experiments provide converging support for framing the two reasoning accounts in a dual-process theory. (shrink)

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: "MP", Affirmation of the Consequent "AC") and denial problems (Denial of the Antecedent "DA", and Modus Tollens "MT"). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

In certain contexts reasoners reject instances of the valid Modus Ponens and Modus Tollens inference form in conditional arguments. Byrne (1989) observed this suppression effect when a conditional premise is accompanied by a conditional containing an additional requirement. In an earlier study, Rumain, Connell, and Braine (1983) observed suppression of the invalid inferences "the denial of the antecedent" and "the affirmation of the consequent" when a conditional premise is accompanied by a conditional containing an alternative requirement. Here we present three (...) experiments showing that the results of Byrne (1989) and Rumain et al. (1983) are influenced by the answer procedure. When reasoners have to evaluate answer alternatives that only deal with the inferences that can be made with respect to the first conditional, then suppression is observed (Experiment 1). However, when reasoners are also given answer alternatives about the second conditional (Experiment 2) no suppression is observed. Moreover, contrary to the hypothesis of Byrne (1989), at least some of the reasoners do not combine the information of the two conditionals and do not give a conclusion based on the combined premise. Instead, we hypothesise that some of the reasoners have reasoned in two stages. In the first stage, they form a putative conclusion on the basis of the first conditional and the categorical premise, and in the second stage, they amend the putative conclusion in the light of the information in the second premise. This hypothesis was confirmed in Experiment 3. Finally, the results are discussed with respect to the mental model theory and reasoning research in general. (shrink)

This paper reports three studies of temporal reasoning. A problem of the following sort, where the letters denote common everyday events: A happens before B. C happens before B. D happens while B. E happens while C. What is the relation between D and EEfficacylls for at least two alternative models to be constructed in order to give the right answer for the right reason (D happens after E). However, the (...) first premise is irrelevant to this answer, and so if reasoners were to ignore it, then they would need to construct only one model. Experiment 1 showed that one-model problems were answered faster and more accurately than multiple-model problems. When the question preceded the premises in the statement of the multiple-model problems there was a slight tendency for the latencies of response to speed up in the predicted way. Experiment 2 modified the procedure, in part by using practice problems with many irrelevant premises, so that reasoners might grasp the advantage of ignoring them. Its results showed that when the premises preceded the question, the multiple-model problems were significantly harder than one-model problems. But when the question was presented first, the difference was significantly reduced in line with the theory's prediction. Experiment 3 used only problems with valid conclusions (i.e., one-model problems and multiple-model problems), and so the construction of multiple models was never necessary. However, there was still a significant difference between one-model problems and multiple-model problems. (shrink)

We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that this interaction (...) is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely. (shrink)