5.2 Cognitive Use: Taxa ¢» Classification. Aristotle’s logic has been rehabilitated by logicians, though it is a very general and not an especially ‘strong’ logic. Epistemologically, however, its vety generality is crucial, also because it suffices to formulate genus/species reasoning and classi- fication, which are fundamental to human experience, perception and empirical knowledge. In- deed, Kant was right to regard Aristotle’s logic as fully ‘general logic’ (A53-4/B77-8). The addi- tional ‘strength’ of other formal systems of interest to technical logicians is all gained by addi- tional semantic or existence postulates (or both), all of which are non-formal. All such ‘stronger’ logistic systems are /ess general; they are specific logics designed for specific domains, such as Frege’s specifically mathematical logic (Wolff 2009b). It is important yet not surprising that Aris- totle’s logic comports very well with contemporary ‘mental files’ or ‘mental models’ approaches in cognitive sciences (Lopez-Astorga 2016, 2017). Indeed, Kant’s cognitive architecture and the- oty has much to offer contemporary cognitive science, which has yet to avail itself fully of Kant’s Critical resources (Brook 1994, 2016). For good reason, we now know, Kant regarded Aristotle’s logic as profoundly important, nc only for logic, but also for understanding and assessing cognitive judgments. The set of logic: oppositions represented in the traditional Square of Opposition suffices to specify the logical us of ‘none’, ‘some’, ‘all’, ‘not’; affirmation, negation, disjunction, conjunction; and for hypothetic: and disjunctive as well as categorical syllogisms. Using these logical constants and quantifier together with pairs of sentences or propositions, it is easy to generate Aristotle’s paradigmati syllogisms, including both modus ponens ponendo and modus tolens tolendo, i.e., disjunctive syllogist plus negation elimination (Patzig 1969; Kneale ¢» Kneale 1971, 72-3; Parsons 2017). The validit of conversion of terms is also a straight-forward corollary of the logical relations represented b this square. Taken together, Aristotle’s syllogistic logic is in the technical sense complete, becaus every valid argument which can be expressed in his logical system can be deduced within his sys tem of deduction, thus ‘every semantically valid argument is deducible’ (Corcoran 1974).* APPENDIX. 12.4 A recent version using Venn diagrams:
