By Norman Kretzmann (auth.), John Corcoran (eds.)
During the final part century there was progressive growth in common sense and in logic-related components resembling linguistics. HistoricaI wisdom of the origins of those topics has additionally elevated considerably. hence, it is going to look that the matter of deciding upon the level to which old logical and linguistic theories admit of exact interpretation in smooth phrases is now ripe for research. the aim of the symposium used to be to collect logicians, philosophers, linguists, mathematicians and philologists to provide learn effects concerning the above challenge with emphasis on common sense. shows and discussions on the symposium targeted themselves into 5 components: historic semantics, sleek examine in historical common sense, Aristotle's good judgment, Stoic good judgment, and instructions for destiny examine in historic good judgment and logic-related components. Seven of the papers which look less than have been initially provided on the symposium. In each case, dialogue on the symposium ended in revisions, occasionally to vast revisions. The editor steered nonetheless additional revisions, yet in each case the writer was once the finaljudge of the paintings that looks lower than his name.
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Extra resources for Ancient Logic and Its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972
In the second I consider the passages in the Prior Analytics in which Aristotle refers to mathematics ; my purpose here is to determine whether reflection on mathematics influenced his formulation of syllogistic. In both sections my conclusions are mainly negative. Euclid shows no awareness of syllogistic or even of the basic idea of logic, that validity of an argument depends on its form. And Aristotle's references to mathematies seem to be either supportive of general points about deductive reasoning or, when they relate specifically to syllogistic, false because based on syllogistic itself rather than on an independent analysis of mathematical proof.
When a feature is negative, another set ofresponses is open or permitted. 19. From this point ol' view, therefore, categories are (or are equivalent to) distinct clusters of discourse possibilities. 20. This account has been sketchy and programmatie, and is not intended to establish a definitive reading ofthe Categories. 21. One advantage of such a linguistic reading is that it brings the discussion of categories into a field of active scholarly research. It thereby makes possibie a rational and potentially useful criticism of Aristotle's work.
But now I wish to discuss, as the second preliminary, a question relevant to the issue: How does one decide whether a given mathematical argument or work is influenced by a given logic? In Elements 1,19 Euclid proves that, given two unequal angles of a triangle, the side opposite the greater angle is greater than the side opposite the lesser. He proceeds as follows: l (1) Let ABC be a triangle having the angle ABC greater than the angle BCA; I say that the side AC is also greater than the side AB.