I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just (...) one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power. (shrink)

Drawing on the theory of ‘mental models’, I have previously shown that the valid syllogisms in the Aristotelian logical system, including all of its figures and moods, are very easy for the human mind. Indeed, they can even be used to predict inferences that people can make with quantified sentences. In this paper, I further argue that, if mental models theory is correct, then also the Aristotelian conversion rules are not hard for the human mind. My account here again focuses (...) on the distinction made by the mental models theory between canonical and noncanonical models. (shrink)

Since Freges terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this questionBegriffes syntaxhighercorresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcorans theory via predicate logic.

The taxonomy and analysis of fallacies in Aristotle's Sophistical Refutations pre-date the formal logic of his Prior Analytics A4-6. Of the 64 fully described examples of ?sophistical refutations? which are fallacious because they are only apparently valid, 49 have the wrong number of premisses or the wrong form of premiss or conclusion for analysis by the Prior Analytics theory of the categorical syllogism. The rest Aristotle either frames so that they do not look like categorical syllogisms or analyses in a (...) quite different way than by categorical syllogistic. (shrink)