By Jonathan Lear
Aristotle used to be the 1st and one of many maximum logicians. He not just devised the 1st process of formal common sense, but additionally raised many basic difficulties within the philosophy of good judgment. during this publication, Dr Lear exhibits how Aristotle's dialogue of logical end result, validity and facts can give a contribution to modern debates within the philosophy of good judgment. No historical past wisdom of Aristotle is believed.
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Extra info for Aristotle and Logical Theory
D can be infinite only if some segment of it Ct ••• C1 is dense in the sense that any two members of it are separated by another. e. ) Aristotle's construal of the infinite as potential dictates such an interpretation. To say that a process will terminate is, for Aristotle, equivalent to saying that it will terminate after finitely many steps. The concept of a process terminating after infinitely many steps is one Aristotle would reject. g. g. successively dividing the space between 0 and I. If only one extreme term is fixed, one can imagine an infinite series of predications as a process of addition, moving through an unending series of contiguous terms.
If, however, one takes Aristotle's central concern to be with argumentative role, then two explanations emerge· as to why he says the conclusion is reached not by syllogism but hypothetically. First, in hypothetical argument one is meant to be arguing unconditionally to a conclusion Q. One is not simply deducing Q. from a set of premisses that include 'If P, then Q'. One is attempting to persuade one's interlocutor to admit Q. To this end one secures his agreement to accept Q if P is proved: but this strategy is designed to force him to assent to Q.
The reason, I conjecture, is that Aristotle assimilates the role of supposition in per impossihile syllogisms to the role of agreement in other types of hypothetical syllogisms. What is important about each syllogism is that one must explicitly recognize that a certain step has a special argumentative role; and Aristotle was not careful to distinguish among types of roles. Consider the beginning of Prior Analytics A44: 'Further we must not try to reduce hypothetical syllogisms; for with the given premisses it is not possible to reduce them.