In Prior Analytics 1.15, Aristotle attempts to give a proof through the impossible of Barbara, Celarent, Darii, and Ferio with an assertoric first premiss, a contingent second premiss, and a possible conclusion. These proofs have been controversial since antiquity. I shall show that they are valid, and that Aristotle is able to explain them by relying on two meta-syllogistic lemmas on the nature of possibility interpreted as syntactic consistency. It will turn out that Aristotle's proofs are not of the intended (...) schemata. I shall investigate some of the results that the impact of this reconstruction on the modal syllogistic has: the relationship between Aristotle's syllogistic and the logics of relevance; the value of Aristotle's requirement that universal affirmative propositions be taken ‘absolutely’; the destruction of many Aristotelian proofs; the recovery of certain principles of modal opposition from a charge of inconsistency. (shrink)

The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments (...) was Aristotle’s. Indeed, perhaps Aristotle’s finitism applied to magnitude only, not plurality. (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)

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)

"The world is a finite body, and therefore has finite power." John Philoponus is remembered for using this Aristotelian premise to break ranks with Aristotle and argue that the world is not everlasting. This investigation reconsiders Philoponus’s arguments from finite power, and then explores the aftermath of this line of thinking in the works of three lesser-known Arabic intellectuals active in the generation before Avicenna (d. 1037): Abū l-Ḫayr Ibn Suwār (d. after 1017), Abū al-Ḥasan al-ʿĀmirī (d. 992), and Abū (...) Sahl al-Masīḥī (d. after 1025). Each engaged with this dictum in unique and novel ways, and in so doing anticipated a number of central features of Avicenna’s writings. The history of this argument is of crucial importance for understanding the evolution of natural philosophy and metaphysics in this formative period, away from tedious and simplistic arguments about creation and towards a more robust modal ontology based on intrinsic and extrinsic necessity. (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)