By Norman Kretzmann (auth.), John Corcoran (eds.)
During the final part century there was innovative development in good judgment and in logic-related components resembling linguistics. HistoricaI wisdom of the origins of those matters has additionally elevated considerably. therefore, it should look that the matter of deciding on the level to which historical logical and linguistic theories admit of actual interpretation in glossy phrases is now ripe for research. the aim of the symposium used to be to assemble logicians, philosophers, linguists, mathematicians and philologists to provide learn effects pertaining to the above challenge with emphasis on common sense. displays and discussions on the symposium concentrated themselves into 5 parts: historical semantics, sleek examine in historic good judgment, Aristotle's common sense, Stoic good judgment, and instructions for destiny study in historical common sense and logic-related components. Seven of the papers which look lower than have been initially awarded on the symposium. In each case, dialogue on the symposium resulted in revisions, now and again to broad revisions. The editor advised nonetheless extra revisions, yet in each case the writer used to be the finaljudge of the paintings that looks less than his name.
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Extra info for Ancient Logic and Its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972
Rather it yields a theory only slightly less concrete than Greek geometry or arithmetic. The theory of book V represents Eudoxus's solution to the problem of dealing mathematicaIly with the relation of one quantity to another when the relation cannot be represented as a ratio between two integers. Aristotle apparently refers to this theory and praises it for a kind of abstraction. Another case is the theorem about proportion, that you can take the terms alternately; this theorem used at one time to be proved separately for numbers, for lines, for solids, and for times, though it admitted of proof by one demonstration.
As far as Chrysippean propositionallogic is concerned, my conclusions are again negative. However, it is clear that at some time logicians, probably Stoic, began to consider mathematical proof on its own terms. Although they never developed what I would call a logic to cover mathematical proof, they at least realized the difference between it and the logicaJ rules formulated in antiquity. C. In conclusion I recapitulate briefly my conclusions about the relation between Greek mathematics and logic.
In the Elements, however, the sumperasma is not so much aresult of inference as a summing up of what has been established. ) From the modem point of view the apodeixis ends with a particular conclusion reached from particular assumptions; GREEK MATHEMATICS AND GREEK LOGIC 43 tacit in the sumperasma are steps of conditionalization to get rid of the assumptions and of quantifier introduction or generalization. Throughout antiquity, indeed down into the nineteenth century, the latter step was not seen as a matter of logic.