Syllogistic Premises Research Articles

The Stoic Distinction between Syllogisms and Subsyllogisms

Abstract This paper aims to explain the distinction between syllogisms and subsyllogisms in Stoic logic. Subsyllogisms replace at least one premise in a syllogism with a premise that is, according to Galen and Alexander, equipollent to the respective syllogistic premise. This equipollence is not synonymy of meaning between two linguistic expressions, but obtains between two propositions when they are true or false by the same standard. Subsyllogistic premises are simple propositions that are equipollent to the non-simple premises of the respective syllogisms. For subsyllogistic premises that replace syllogistic premises consist of predicates combining with cases rather than of connectives or negations governing propositions. Because of this difference in their premises, subsyllogisms have a different logical form than syllogisms and are not formally valid.

Aristotle’s Logic of Biological Diversity

Abstract Aristotle’s biology is based on his method of division of animal kinds by multiple differentiae. This results in complex clusters of non-subordinate terms, between which Aristotle seeks to establish universal correlations. The form of these, however, does not correspond to that prescribed by his theory of syllogism. Mereological relations between terms are not linear and quantification is far more complex than the distinction between universal and particular propositions. Thus the axiomatisation of Aristotle’s biology requires a tool designed for analysing such complex universal correlations into valid syllogistic premises. Prosleptic-like premises turn out to be the solution outlined by Aristotle. They make it possible to handle both the logic of consequence which translates from and into mereological relations between term clusters, and the complex quantification required by division based on multiple differentiæ, through the instantiation of a variable ideally consisting of indivisible groups of animals.

Relational abilities index: A experimental study of the procedure at different trial durations

The relational abilities index (RAI) has been shown to consistently correlate with standardized measures of intellectual aptitude, such as the Wechsler Adult Intelligence Scale. However, the procedure has not been systematically studied and, when used with adults, it has problems in discriminating between medium and high-ability participants. Therefore, the aim of this experiment was to study participants’ performance at different levels of analysis and under different trial durations. Sixty-two participants were randomly assigned to one of two groups (30 s or 20 s). We used a version of the RAI involving 55 syllogistic premises (trials), each associated with a YES/NO question. Trials were dived into four blocks, each testing a different relational frame. Results showed that total scores were lower when trials were shortened. However, this reduction was evident only for lower-ability participants. RAI scores in the 20 s group approximated a normal distribution and trial difficulty increased when trial duration decreased. Trial difficulty increased as a function of trial sequence within a block in only half of the blocks. Nodal distance was predictive of trial difficulty. Based on these results, a list of proposed changes to the procedure is provided and discussed.

Models and cognitive change in psychopathology

The hyper-emotion theory attributes psychological illnesses to emotions of aberrant intensity, which in turn prompt better reasoning about their causes. Two experiments in which participants drew their own conclusions from syllogistic premises tested this prediction. Individuals from the same populations as the experimental participants rated the believability of likely conclusions. One experiment compared patients with depression with controls, and the other experiment compared students scoring high on anxiety with controls. Controls tended to draw believable conclusions and not to draw unbelievable conclusions, and this belief bias was greater for invalid inferences. The clinical groups were better reasoners than the controls, and did not show belief bias. As our hypothesis predicted, they drew many more valid conclusions concerning their illness than controls drew valid believable conclusions. But, contrary to the hypothesis, they refrained from drawing invalid conclusions about neutral topics more than controls refrained from drawing invalid unbelievable conclusions.

Large scale brain activations predict reasoning profiles

Deduction is the ability to draw necessary conclusions from previous knowledge. Here we propose a novel approach to understanding the neural basis of deduction, which exploits fine-grained inter-participant variability in such tasks. Participants solved deductive problems and were grouped by the behavioral strategies employed, i.e., whether they were sensitive to the logical form of syllogistic premises, whether the problems were solved correctly, and whether heuristic strategies were employed. Differential profiles of neural activity can predict membership of the first two of these groups. The predictive power of activity profiles is distributed non-uniformly across the brain areas activated by deduction. Activation in left ventro-lateral frontal (BA47) and lateral occipital (BA19) cortices predicts whether logically valid solutions are sought. Activation of left inferior lateral frontal (BA44/45) and superior medial frontal (BA6/8) cortices predicts sensitivity to the logical structure of problems. No specific pattern of activation was associated with the use of a non-logical heuristic strategy. Not only do these findings corroborate the hypothesis that left BA47, BA44/45 and BA6/8 are critical for making syllogistic deductions, but they also imply that they have different functional roles as components of a dedicated network. We propose that BA44/45 and BA6/8 are involved in the extraction and representation of the formal structure of a problem, while BA47 is involved in the selection and application of relevant inferential rules. Finally, our findings suggest that deductive reasoning can be best described as a cascade of cognitive processes requiring the concerted operation of several, functionally distinct, brain areas.

Conditional and syllogistic deductive tasks dissociate functionally during premise integration.

Deduction allows us to draw consequences from previous knowledge. Deductive reasoning can be applied to several types of problem, for example, conditional, syllogistic, and relational. It has been assumed that the same cognitive operations underlie solutions to them all; however, this hypothesis remains to be tested empirically. We used event-related fMRI, in the same group of subjects, to compare reasoning-related activity associated with conditional and syllogistic deductive problems. Furthermore, we assessed reasoning-related activity for the two main stages of deduction, namely encoding of premises and their integration. Encoding syllogistic premises for reasoning was associated with activation of BA 44/45 more than encoding them for literal recall. During integration, left fronto-lateral cortex (BA 44/45, 6) and basal ganglia activated with both conditional and syllogistic reasoning. Besides that, integration of syllogistic problems additionally was associated with activation of left parietal (BA 7) and left ventro-lateral frontal cortex (BA 47). This difference suggests a dissociation between conditional and syllogistic reasoning at the integration stage. Our finding indicates that the integration of conditional and syllogistic reasoning is carried out by means of different, but partly overlapping, sets of anatomical regions and by inference, cognitive processes. The involvement of BA 44/45 during both encoding (syllogisms) and premise integration (syllogisms and conditionals) suggests a central role in deductive reasoning for syntactic manipulations and formal/linguistic representations.

Generality and Identity in Late Medieval Discussions of the Prior Analytics

AbstractIn this article, I shall consider medieval discussions of the principles of Aristotelian syllogistic which were called the dictum de omni et nullo and the expository syllogism. I am particularly interested in how theological questions contributed to the introduction of some influential new medieval ideas, such as the extensional sameness of the subject as the basis of predication, the interpretation of the expository syllogism from this point of view, and the explication of the logical subject of universal and particular syllogistic premises with the phrase ‘Anything/something which is A. . .’. I end with some remarks about the increasing medieval awareness that these developments were beyond Aristotle’s purview.

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an "immediate inference" task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' "intended models" of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single "fundamental human reasoning mechanism".

Effects of Belief and Logic on Syllogistic Reasoning

Studies of syllogistic reasoning have demonstrated a nonlogical tendency for people to endorse more believable conclusions than unbelievable ones. This belief bias effect is more dominant on invalid syllogisms than valid ones, giving rise to a logic by belief interaction. We report an experiment in which participants' eye movements were recorded in order to provide insights into the nature and time course of the reasoning processes associated with manipulations of conclusion validity and believability. Our main dependent measure was people's inspection times for syllogistic premises, and we tested predictions deriving from three contemporary mental-models accounts of the logic by belief interaction. Results supported recent "selective processing" theories of belief bias (e.g., Evans, 2000; Klauer, Musch, & Naumer, 2000), which assume that the believability of a conclusion biases model construction processes, rather than biasing the search for falsifying models (e.g., Oakhill & Johnson-Laird, 1985) or a response stage of reasoning arising from subjective uncertainty (e.g., Quayle & Ball, 2000). We conclude by suggesting that the eye-movement analyses in reasoning research may provide a useful adjunct to other process-tracing techniques such as verbal protocol analysis.

Syllogistic reasoning tasks and working memory: Evidence from sequential presentation of premises

An experiment is reported concerning the role of working memory components in syllogistic reasoning. In this study, the syllogistic premises were presented sequentially and subjects attempted the syllogisms with and without three secondary tasks (articulatory suppression; spatial suppression and verbal random generation). Taking account of possible trade-offs among the dual tasks, it appeared that syllogisms with sequentially presented premises markedly loaded the central executive and the phonological loop components of working memory and also showed an involvement of the visuo-spatial scratchpad. It appears that the “slave” systems of working memory were more heavily loaded when sequential presentation of premises was used than was found previously with simultaneous premise presentation (Gilhooly, Logie, Wetherick & Wynn, 1993).

Strategies in Syllogistic Reasoning

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re‐evaluates current theories of syllogistic reasoning in the light of these results.

Strategies in syllogistic reasoning

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants’ use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants’ strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re-evaluates current theories of syllogistic reasoning in the light of these results.

Reasoning about necessity and possibility: A test of the mental model theory of deduction.

This article examined syllogistic reasoning that differs from previous research in 2 significant ways: (a) Participants were asked to decide whether conclusions were possible as well as necessary, and (b) every possible combination of syllogistic premises and conclusions was presented for evaluation with both single-premise (Experiment 1) and double-premise (Experiment 2) problems. Participants more frequently endorsed conclusions as possible than as necessary, and differences in response to the 2 forms of instruction conformed to several predictions derived from the mental model theory of deduction. Findings of Experiments 2 and 3 showed that some fallacies are consistently endorsed and others consistently resisted when people are asked to judge whether conclusions that are only possible follow necessarily. This finding was accounted for by the computational implementation of the model theory: Fallacies are made when the first mental model of the premises considered supports the conclusion presented. Traditional applications of logic concern the validity of arguments, that is, proving that some conclusion is necessary given some premises. However, in everyday reasoning it may be just as important to decide whether some proposition is possible in light of the given information. Inferences of possibility occur whenever rules and regulations constrain a person's behavior rather than determine what it must be. For example, students choosing a degree program within a modular course structure will have many degrees of freedom but will have to respect constraints owing to timetabling restrictions, availability of teaching staff, prerequisite and corequisite relations between modules, and so on. Their decision making here involves inferring what is possible and then deciding between the possibilities identified. Most of the rules by which people live their lives in society, including criminal law, operate in a similar way. It is rarely determined by such rules that people must follow a particular course of action, but they are frequently constrained to act within a set of legal possibilities. The psychological study of deductive reasoning has been steadily increasing in recent years, and there are now many hundreds of experimental studies reported in the literature (see Evans, Newstead, & Byrne, 1993, for a review). In view of the above remarks, however, there is a curious limitation

Mental Models vs Integrated Models: Explanations of Syllogistic Reasoning

To compare mental versus integrated models explanations of syllogistic reasoning, we administered a multiple-choice questionnaire containing 19 pairs of syllogistic premises with valid conclusions (given in a C-A order) to 72 psychology undergraduates. Association between our integrated models classification and the empirical difficulty of items was strong.

‘Atmosphere’, matching, and logic in syllogistic reasoning

The frequency of error in syllogism solving suggests that not all subjects are using logic. The atmosphere and matching hypotheses suggest what they might be doing instead but predict some of the same (correct and incorrect) responses. Reexamination of the data supporting the atmosphere hypothesis (Sells, 1936) shows that the procedure employed was unsatisfactory and that the results obtained support the matching hypothesis as well as they support the atmosphere hypothesis. It is argued on theoretical grounds that the matching hypothesis should be preferred. An experiment is reported in which subjects (N=71) were required to draw conclusions from syllogistic premises and to construct premises from which given conclusions followed. It is shown that subjects may be divided into three groups: (n=16) consisting of subjects who used logic and made few errors; (n=25) of subjects whose correct and incorrect responses were in accordance with the matching hypothesis; and (n=30) of subjects who were not matching but trying to do logic and not doing it well.

Children'S Syllogistic Reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.

Conversion and possibility in syllogistic reasoning

Previous research on syllogistic reasoning has identified two bases of error on this task. One basis is the illicit conversion of universal affirmative and particular negative propositions. The second basis is the selection of propositional conclusions on indeterminate nonconversion syllogisms. The present study explores possible explanations for these phenomena. Data are presented that cast doubt on the explanation of conversion based upon the similarity between syllogistic premises and definitional statements. Even when the premises are modified so that they no longer resemble definitional statements, conversion still occurs. Bias toward symmetrical relations is discussed as an alternative explanation. Data are also presented to show that poor performance on indeterminate nonconversion syllogisms in large part reflects the failure of subjects to differentiate between possible and necessary conclusions. When this issue is clarified, performance significantly improves.

The belief-bias effect in formal reasoning: the influence of knowledge on logic.

The present study examines the applicability of a rational model of categorical inference (e.g., Revlis, 1975b) to account for the apparently irrational decisions students reach on categorical syllogisms. In Experiment 1, students judged the logical validity of emotionally neutral conclusions to controversial premises. Of the reasoners’ decisions, 80% can be accounted for by the application of rational rules to their idiosyncratic encoding of the syllogistic premises. In Experiment 2, students were asked to solve syllogisms whose conclusions varied in truth value. When asked to reason about controversial, if not emotional, material, students do not suspend rational choice, but rather, their decisions are judicious ones, flowing logically from their idiosyncratic understanding of the materials reasoned about. When errors do occur, they result from an interrupt to rational processes and reflect conflict between competing goals rather than a switch to irrational decision processes.

The psychology of syllogisms

Two experiments were carried out in which subjects had to draw conclusions from syllogistic premises. The nature of their responses showed that the figure of the syllogisms exerted a strong effect on the accuracy of performance and on the nature of the conclusions that were drawn. For example, premises such as “Some of the parents are scientists; All of the scientists are drivers” tend to elicit the conclusion, “Some of the parents are drivers” rather than its equally valid converse, “Some of the drivers are parents”. In general, premises of the form iE$ created a bias towards conclusions of the form A-C, whereas premises of the form $=fi created a bias towards conclusions of the form C-A. The data cast doubt on current theories of syllogistic inference; a new theory was accordingly developed and implemented as a computer program. The theory postulates that quantified assertions receive an analogical mental representation which captures their logical properties structurally. A simple heuristic generates putative conclusions from the combined representations of premises, and such conclusions are put to logical tests which, if exhaustively conducted, invariably yield a correct response. Erroneous responses may occur if there is a failure to test exhaustively.

Sources of error in syllogistic reasoning

The experiment attempted to provide evidence that errors in reasoning do not imply that reasoning is not occurring at all. One suggestion has been that errors occur because Ss misinterpret syllogistic premises in order to refer to simpler class relations. When Ss were given modified syllogisms having these simpler relations as premises, they performed considerably better than when given traditional syllogisms. Furthermore, they responded to the traditional syllogisms as if they were the modified syllogisms, which accounted for their errors. A second source of error was traced to the logical structure of the syllogism. It was found that the more alternatives generated by a set of premises, the more difficult was the syllogism. It was argued that errors in reasoning are not the result of illogical or alogical processes, but are the result of an incomplete analysis of the logical structure of the syllogism.