In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that (...) Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic. (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)

The present paper aims to show that the reconstruction of the formal framework of the proofs in Pr. An. 1.15, as proposed by Malink and Rosen 2013 (‘Proof by Assumption of the Possible in Prior Analytics 1.15’, Mind, 122, 953-85) is due to affront a double impasse. Malink and Rosen argue convincingly that Aristotle operates with two different modal frameworks, one as found in the system of modal logic presented in Prior Analytics 1.3 and 8-22, and one occurring in many (...) of Aristotle’s works, such as the Physics, De Caelo and the Metaphysics. However, they misconstrue the latter framework. More precisely, they misconstrue the domain of significance of what they call the ‘Principle of Necessitation’. As a consequence, bringing the two frameworks into one results into a contradictory modal logic. On the other hand, if the Principle of Necessitation is rectified, the proofs put forward by Malink and Rosen in the same paper are no longer available. (shrink)

Infinite regress arguments are a powerful tool in Aristotle, but this style of argument has received relatively little attention. Improving our understanding of infinite regress arguments has become pressing since recent scholars have pointed out that it is not clear whether Aristotle’s infinite regress arguments are, in general, effective or indeed what the logical structure of these arguments is. One obvious approach would be to hold that Aristotle takes infinite regress arguments to be per impossibile arguments, which derive an infinite (...) sequence. Due to his finitism, Aristotle then rejects such a sequence as impossible. This paper argues that this obvious approach does not work, even for its most amenable cases. The paper argues instead that infinite regress arguments involve domain-specific infinities, and so there is not a general finitism which underpins infinite regress arguments in Aristotle, but rather domain-specific reasons that there cannot be an infinite number of entities in each domain in which Aristotle invokes an infinite regress argument. (shrink)