Aristotle’s Logic Computed by Parametric Probability and Linear Optimization

Por • 4 jul, 2013 • Sección: Crítica

Joseph W. Norman

Abstract: A new computational method is provided to implement the system of deductive logic presented in Aristotle’s Prior Analytics. Each Aristotelian problem is interpreted as a parametric probability network in which the premises give constraints on probabilities relating the problem’s categorical terms (major, minor, and middle). The problem’s figure (schema) describes which specific probabilities are constrained, relative to those that are queried. Using numerical optimization methods, the minimum and maximum feasible values of certain queried probabilities are computed. These computed values determine whether a syllogism is present and if so, which precise conclusion has been deduced from the premises. This method of analysis prevents existential fallacies, and reveals new complementary patterns of syllogism that were previously unappreciated.

arXiv:1306.6406v1 [math.LO]

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