Theories of the syllogism: A meta-analysis.

Abstract

Syllogisms are arguments about the properties of entities. They consist of 2 premises and a conclusion, which can each be in 1 of 4 “moods”: All A are B, Some A are B, No A are B, and Some A are not B. Their logical analysis began with Aristotle, and their psychological investigation began over 100 years ago. This article outlines the logic of inferences about syllogisms, which includes the evaluation of the consistency of sets of assertions. It also describes the main phenomena of reasoning about properties. There are 12 extant theories of such inferences, and the article outlines each of them and describes their strengths and weaknesses. The theories are of 3 main sorts: heuristic theories that capture principles that could underlie intuitive responses, theories of deliberative reasoning based on formal rules of inference akin to those of logic, and theories of deliberative reasoning based on set-theoretic diagrams or models. The article presents a meta-analysis of these extant theories of syllogisms using data from 6 studies. None of the 12 theories provides an adequate account, and so the article concludes with a guide—based on its qualitative and quantitative analyses—of how best to make progress toward a satisfactory theory.

Reasoning deficits among illicit drug users are associated with aspects of cannabis use

“…Unlike two and three model problems which generate only a single valid inference, most one model problems generate two valid conclusions. However, Johnson-Laird (1983) has demonstrated that only a minority of participants manage to produce both conclusions for one model syllogisms and although equally valid, some conclusions are produced far more often than others (Khemlani & Johnson-Laird, 2012). Using the example above, individuals are more likely to produce the conclusion: 'Some students are paid money' but less likely to generate the second valid conclusion: 'Some of those who are paid money are students'.…”

Correctness of Syllogistic Reasoning

“…In our study we used scholastic numbering of syllogistic figures, well established in studies of logic, contrary to other researchers of this issue [3], [10], namely: …”

“…In our research, we accepted as valid the subordinate modes too (those that derived a particular conclusion although a universal conclusion could have been generated, starting from the premise that if a universal sentence is true, then its subordinate particular is also true). We also considered valid those modest hat derived a conclusion by legal conversion of a negative universal or an affirmative particular, reasoning that such sentences are equivalent from a logical point of view (which strictly formally involves changing the syllogistic mode from one figure to another); considering also the possibility of conclusion conversion, the number of possible modes is doubled, getting to 512, as performed by Khemlani & Johnson-Laird [10].…”

“…In order to identify sources of fallacies in syllogistic argumentation, heuristic theories invoke the atmosphere effects [15] or the "context effect" [2], , the erroneous interpretation of premises or of the relation between terms [4]; [11]; [1], particularities of how quantifiers are interpreted [13]), limits of working memory etc. In a recent article, Khemlani & Johnson-Laird, [10] consider that there are 12 theories in cognitive psychology about syllogistic reasoning, qualifying the situation as "a small disaster" of any scientific field and they suggest some reference points for a unified theory.…”

The New Paradigm and Mental Models

“…However, the metaanalysis [7] they report comparing PHM with MMT used accuracy as a measure but did not allow PHM to predict no valid conclusion (NVC) responses. This move contradicts PHM in which NVC responses are predicted by one of its main heuristics (the max-heuristic).…”