The present book is the English version of a monograph 'Die aristotelische Syllogistik', which first appeared ten years ago in the series of Abhand 1 lungen edited by the Academy of Sciences in Gottingen. In the preface to the English edition, I would first like to express my indebtedness to Mr. J. Barnes, now fellow of Oriel College, Oxford. He not only translated what must have been a difficult text with exemplary precision and ingenuity, but followed critically every argument and (...) check ed every reference. While translating it, he has improved the book. Of those changes which I have made on Mr. Barnes' suggestion I note only the more important ones on pages 4, 12, 24sq, 32, 39, 6lsq, and 158. Since the second edition of the German text appeared in 1963 some further reviews have been published, or come to my notice, which I have 2 been able to make use of in improving the text of this new edition. I must mention here especially the detailed critical discussions of my results and arguments published by Professor W. Wieland in the Philosophische Rundschau 14 (1966), 1-27 and by Professor E. Scheibe in Gnomon 39 (1967), 454-64. Both scholars, while agreeing with the main drift and method of my interpretation, criticise some of my results and disagree with some of my arguments. It would not be possible to discuss these technical matters here with the necessary thoroughness. (shrink)

I consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue that ecthesis (...) for Aristotle really means ?setting out? the case to be proved using letters. Aristotle?s remarks about the use of letters in mathematical proofs suggest that he had some understanding of rules equivalent to universal generalization and existential instantiation; the ?proofs through ecthesis? are so called because they rest on the latter rule, with which use of letters is involved in a special way. (shrink)

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In this paper, the theory of syllogistic reasoning proposed by Johnson-Laird is shown to be inadequate and an alternative theory is put forward. Protocols of people attempting to solve syllogistic problems and explaining to another person how they reached their conclusions were obtained. Two main groups of subjects were identified. One group represented the relationship between classes in a spatial manner that was supplemented by a verbal representation. The other group used a primarily verbal representation. A detailed theory of the (...) processes for both groups is given. (shrink)

Existing accounts of syllogistic reasoning oppose rule-based and model-based methods. Stenning \& Oberlander show that the latter are isomorphic to well-known graphical methods, when these are correctly interpreted. We here extend these results by showing that equivalent sentential implementations exist, thus revealing that all these theories are members of a family of abstract {\it individual identification algorithms} variously implemented in diagrams or sentences. This abstract logical analysis suggests a novel {\it individual identification task} for observing syllogistic reasoning processes. Comparison of (...) the results of this task with the Standard Task confirms that the tasks are psychologically closely related, throwing light on sources of error, on subjects' sensitivity to metalogical properties, and on term ordering phenomena. Since it avoids posing the sub-task of formulating a quantified conclusion, the new task allows comparison of explanations of problem difficulty in terms of the number of models with alternatives in terms of the difficulty of choosing a quantifier for the conclusion. Logical concepts of {\it source} and {\it conditional} premisses provide a comprehensive account of term order data, including figural effects, at a level abstract with regard to imagistic or sentential representations. These results argue that much richer empirical evidence will be required to discriminate phenomenologically distinct reasoning processes than has hitherto been supposed. (shrink)