By Norman Kretzmann (auth.), John Corcoran (eds.)

ISBN-10: 9401021309

ISBN-13: 9789401021302

ISBN-10: 9401021325

ISBN-13: 9789401021326

During the final part century there was progressive development in common sense and in logic-related parts reminiscent of linguistics. HistoricaI wisdom of the origins of those matters has additionally elevated considerably. therefore, it's going to look that the matter of opting for the level to which historic logical and linguistic theories admit of actual 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 offer examine effects concerning the above challenge with emphasis on common sense. displays and discussions on the symposium centred themselves into 5 components: old semantics, sleek examine in historical good judgment, Aristotle's common sense, Stoic common sense, and instructions for destiny examine in historic good judgment and logic-related components. Seven of the papers which seem under have been initially awarded on the symposium. In each case, dialogue on the symposium resulted in revisions, occasionally to broad revisions. The editor urged nonetheless extra revisions, yet in each case the writer was once the finaljudge of the paintings that looks lower than his name.

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**Additional resources for Ancient Logic and Its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972**

**Example text**

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.

The following represent plausible renderings of the proofs of (6) and (7) as categoricai syllo gisms: (B) (C) Straight lines from A to CD B are equal to each other; CA and AB are straight lines from A to CD B; therefore CA and AB are equal to each other. Straight lines from B to ACE are equal to each other; CB and AB are straight lines from B to ACE; therefore CB and AB are equal to each other. The minor premiss of (A) is presumably to be inferred directly from the conclusions of (B) and (C). Clearly it cannot be inferred by a categoricai syllogism since such a syllogism will require five terms, 'CA and AB', 'CB and AB', 'CA and CB', 'equal to each other', and 'equal to the same thing'.

From (l) and 'eDB is a circle' one can infer the definiens of (l) with 'eDB' substituted for 'x'. Such an inference could be referred to Aristotle's syllogistic if one were willing to allow singular terms in syllogisms 8 and to treat the complex term corresponding to the definiens as a term in a categoricaI proposition. But doing these two things will not suffice to recover the whole argument. z) (z is a point within eDB & (u) (v) (u is a straight line fromztoy & v is a straight line from z to y-tu equals v»)].

### Ancient Logic and Its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972 by Norman Kretzmann (auth.), John Corcoran (eds.)

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