David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 3 (2):113-127 (1982)
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
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References found in this work BETA
Michael Clark (1980). The Place of Syllogistic in Logical Theory. Nottingham University Press.
John Corcoran (1973). A Mathematical Model of Aristotle's Syllogistic. Archiv für Geschichte der Philosophie 55 (2):191-219.
John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.
Jonathan Lear (1980). Aristotle and Logical Theory. Cambridge University Press.
Citations of this work BETA
Michael V. Wedin (1990). Negation and Quantification in Aristotle. History and Philosophy of Logic 11 (2):131-150.
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