In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...) interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates the (...) assertoric syllogistic. I argue that this mereological validation offers advantages over recent discussions in Morison, Malink, Ebert and Vlasits. (shrink)

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)

In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science. This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative (...) science. (shrink)

Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the relation of divisibility on positive integers. The adequacy of this interpretation, labeled here ‘arithmetical dictum’, is assessed both theoretically and textually with respect to the existing interpretations, especially the so-called ‘mereological dictum’.