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 innovative growth in common sense and in logic-related parts comparable to linguistics. HistoricaI wisdom of the origins of those topics has additionally elevated considerably. hence, it's going to look that the matter of deciding on the level to which old logical and linguistic theories admit of actual interpretation in sleek phrases is now ripe for research. the aim of the symposium was once to assemble logicians, philosophers, linguists, mathematicians and philologists to give learn effects relating the above challenge with emphasis on common sense. shows and discussions on the symposium targeted themselves into 5 parts: historic semantics, sleek examine in historic good judgment, Aristotle's good judgment, Stoic good judgment, and instructions for destiny study in historic good judgment and logic-related parts. Seven of the papers which look lower than have been initially provided on the symposium. In each case, dialogue on the symposium resulted in revisions, on occasion to vast revisions. The editor advised nonetheless additional revisions, yet in each case the writer was once the finaljudge of the paintings that looks less 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

Aristotle's analysis of reductio is obviously intended to be like S6 IAN MUELLER his analysis of argument from a hypothesis, but the detail s of the analysis of reductio are less clear. Primafacie, one would expect the hypothesis of a reductio to be the assumption refuted; but, if it is, the analogy with argument from a hypothesis breaks down. S0a3S-38). The ob· vious falsehood would seem to be the contradiction derived from the assumption refuted.

The addition of three general premisses is required to correct the reasoning: (Al) (A2) (A3) The angles made by diameters and circumferences of circles are always equal. The two angles made by a chord and the circumference of a circle and on the same side ofthe chord are equal. If equals are subtracted from equals, the results are equal. Quite clearly the proof which AristotIe has in mind here is logically very similar to the apodeixis of Elements 1,1. This proof is slightly more complicated (and less syllogistic) because there is a subtraction involved between steps (2) and (3).

The Stoics make a similar claim when they call "If the first then the second; but the first; therefore the second" valid: any substitution of sentences for ordinal number words produces a correct inference. Of course, artificial indications of form are not likely to occur in applications of logic, but a series of correct deductive arguments cannot be said to show a sense of logic unless it shows a sense of form. But Greek mathematics does not show this sense. In it one finds parallel proofs of separate cases which could be treated simultaneously with only slight generalization.

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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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