Aristotle's explanation of what is said ‘of every’ and ‘of none’ has been interpreted either as involving individuals, or as regarding exclusively universal terms. I claim that Alexander of Aphrodisias endorsed this latter interpretation of the dictum de omni et de nullo. This interpretation affects our understanding of Alexander's syllogistic: as a matter of fact, Alexander maintained that the dictum de omni et de nullo is one of the core principles of syllogistic.

Thomas Aquinas maintained that God foreknows future contingent events and that his foreknowledge does not entail that they are necessarily the case. More specifically, he stated that if God knows a future contingent event, this future contingent event will be necessarily the case de sensu composito, but not de sensu diviso. After emphasizing the unified nature of Aquinas’ notion of necessity, we propose an interpretation of his theses by restating them within the framework of non-normal modal logics. In this framework, (...) the K-axiom does not hold, i.e. the necessity operator does not distribute over the material implication. Moreover, assuming that Aquinas rejected the K-axiom is not only consistent, but also leads to a logical framework that allows us to understand other theses maintained by the Doctor Angelicus. In particular, we argue that Aquinas’ remarks on the principle of non-contradiction rest on an impossible worlds semantics for non-normal modal logics. (shrink)

Syllogism is a form of logical argument allowing one to deduce a consistent conclusion based on a pair of premises having a common term. Although Aristotle was the first to conceive and develop this way of reasoning, he left open a lot of conceptual space for further modifications, improvements and systematizations with regards to his original syllogistic theory. From its creation until modern times, syllogism has remained a powerful and compelling device of deduction and argument, used by a variety of (...) figures and assuming a variety of forms throughout history. The Aftermath of Syllogism investigates the key developments in the history of this peculiar pattern of inference, from Avicenna to Hegel. Taking as its focus the longue durée of development between the Middle Ages and the nineteenth century, this book looks at the huge reworking scientific syllogism underwent over the centuries, as some of the finest philosophical minds brought it to an unprecedented height of logical sharpness and sophistication. Bringing together a group of major international experts in the Aristotelian tradition, The Aftermath of Syllogism provides a detailed, up to date and critical evaluation of the history of syllogistic deduction. (shrink)

In this paper I examine Aquinas’s commentary on a text of Aristotle in which the type of order between substance and accidents is discussed. I claim that Aquinas maintains that there cannot be any reference to sensibility, despite any prima facie interpretation of Aristotle’s texts, according to which it could be thought that substance is temporally prior to accidents and, hence, that we must presuppose a perceivable change in the world on the basis of which it is possible to consider (...) something temporally prior to something else. This interpretation – which is possible on the basis of Aristotle’s texts – would be a misinterpretation, according to Aquinas. Aquinas’s assumption is philosophically worthwhile because it confi rms that every metaphysical proposition must abstract from sensibility. (shrink)

According to both Jaakko Hintikka and Simo Knuuttila, Aquinas’ third way to demonstrate that God exists presupposes the acceptance of the principle of plenitude, i.e., of the claim that all possibilities are realized at some time. Aquinas, however, maintained elsewhere that not all possibilities are always realized, and the coherence of his philosophical project may be called into question if one were to accept Hintikka’s and Knuuttila’s reading of the third way. In this paper, I argue that it is difficult (...) to present the third way without invoking the principle of plenitude in Hintikka’s formulation. The corollary of this claim is that third way cannot be a demonstration within the philosophical system outlined by Aquinas, despite his claim to the contrary. Against the backdrop of this exegetical discussion, it is possible to rephrase Aquinas’ third way as a probabilistic argument that shows that God’s existence is highly likely, although not necessarily proven. (shrink)

In this paper I compare Philoponus’s account of the laws of conversion for categorical and modal propositions with Alexander’s exposition of the same topic. I argue that Philoponus’s main source was Alexander’s commentary on Aristotle’s Prior Analytics and that Philoponus had no access to independent sources to reconstruct Theophrastus’s proof for the conversion of universal negative propositions. I suggest that the different solutions that Alexander and Philoponus offer to the puzzles of the doctrine of the laws of conversion depend on (...) the two commentators’ different exegetical strategies. Alexander tries to solve the puzzles by means of doctrines, which Aristotle expounded elsewhere. Philoponus instead interprets Aristotle’s passage as implying a hierarchy among propositions - a doctrine which is not explicitly present in Aristotle’s text. (shrink)

This paper offers a syntactic analysis of Aristotle, Sophistical Refutations, 170 b19–26. Several conjectures have been proposed to simplify the passage. We show that no conjectural activity is needed and that the text transmitted by the manuscripts and printed by I. Bekker (1831) fits within the context of Aristotle’s argument and is consistent with his style.

The essays collected in this volume focus on the Ancient Greeks' perception of foreigners and of foreign lands as potential sources of knowledge. They aim at exploring the hypothesis that the most adventurous intellectuals saw foreign lands and foreigners as repositories of knowledge that the Greeks σοφοί had to engage with, in the hope of bringing back home valuables in the form of new ideas. It is a common place to state that the "Greeks" displayed xenophobia, which is probably best (...) exemplified in the binary and ethnocentric division of humanity in two groups: the Greek world (i.e., the hellenophones) and the others, the Barbarians - those who speak foreign languages. This attitude of insularism and defiance, however, did not hinder the curiosity of Greek and Roman societies towards strangers. Lycurgus, Pythagoras, Democritus, etc.: there is a long list of sages and philosophers who travelled around the world for a significant period of time. The Greeks had a rich and varied relationship with foreign lands and people, which made possible a real circulation of knowledge throughout the Archaic, Classical and Hellenistic times; this is also true of the Roman Empire. Each of the articles included in this collective work explore one aspect of the "stranger" as a possible source of knowledge, with contributions mostly focused on Plato, Xenophon, Democritus, Aristotle, Diogenes, Cicero and Galen. (shrink)

According to Philoponus, the activity of drawing syllogisms is a dynamic operation. Following the classical idea that actions are specified by their objects and habitual powers by their actions, Philoponus concludes that only a dynamic power can elicit the act of syllogizing. This power is identified with discursive reasoning (dianoia). Imagination, on the contrary, is a static power, that cannot elicit that particular motion of drawing a syllogistic inference. The issue, however, is not entirely uncontroversial, because Ammonius maintains that sophistical (...) syllogisms can only be formed by imagination, since they involve “empty concepts” as terms and only imagination can form such concepts. In this paper I will reconstruct Philoponus’ and Ammonius’ theories about the “activity” of syllogizing, and I shall explain how Philoponus can deal with sophistical syllogisms in a consistent way. (shrink)

Both W.D. Ross's and J. Brunschwig's editions of Aristotle's Topics contain the following passage: ἔτι εἰ τοῦ αὐτοῦ τινος τὸ μὲν μᾶλλον τὸ δὲ ἧττον τοιοῦτο· καὶ εἰ τὸ μὲν τοιούτου μᾶλλον τοιοῦτο, τὸ δὲ μὴ τοιούτου, δῆλον ὅτι τὸ πϱῶτον μᾶλλον τοιοῦτο. The passage is translated in the revised Oxford translation as follows: ‘Moreover, if in any character one thing exceeds and another falls short of the same standard; also, if the one exceeds something which possesses the character, while (...) the other exceeds something which does not, then clearly the first thing exhibits that character in a greater degree’. (shrink)

This dissertation includes an introduction, five main chapters, and a conclusion. In the chapter “The Definition of Change”, I expound Aquinas’ account of change. I maintain that Aquinas’ account is meant to describe both spiritual and material changes. Hence, the hylomorphic account of change as the passage from form-less matter to enformed matter is unable to describe all changes. Contrary to Brower, I suggest that Aquinas’ favorite model involves a passage from potentiality to actuality. In addition, I state that ‘change’ (...) is identical to the second potentiality/first actuality of a process that includes three steps, a first potentiality, a second potentiality, and a second actuality. In the chapter on “Aquinas, Presentism, and Adverbialism”, I analyze the semantics of propositions that describe changing processes. I maintain that Aquinas subscribed to the view that past and future tense statements can have a truth-value. Chapter 4 is devoted to the so-called principle of plenitude, i.e. the thesis that all possibilities are realized at some point in the future. Aquinas is believed to have subscribed to the principle, whereas Aristotle’s texts are much more disputed. In this chapter, I offer a new interpretation, according to which Aristotle accepted a restricted version of the principle of plenitude, but Aquinas rejected the principle in all its formulations. In chapter 5 “Aquinas on Future Contingents”, I expound Aquinas’ theory of future contingents events. In this chapter, I make two claims. I state that Aquinas’ theory entails that future events do not exist, according to the ‘actual’ sense of existence. My second claim is about the logic of future contingents. I claim that Aquinas’ argument is logically sound, but presupposes that the so-called K-formula is not a tautology of Aquinas’ modal system. In chapter 6 I expound Aquinas’ definition of time. I maintain that Aquinas’ definition is not circular and time is distinct in both definition and in essendo from change. I conclude by stating that time has extra-mental existence. (shrink)

In his paper “Aquinas, Geach, and Existence”, D. Costa maintains that Aquinas’ solution to the puzzle of future contingent events entails that future contingent entities already exist. This is tantamount to state that Aquinas endorsed a form of eternalism, since he maintained that past, present and future timelessly exist in God’s sight. I object that Aquinas’ texts are also compatible with another reading. In any statement of the form “S will be P”, the verb “will be” simply states the truth (...) of the predicative link between S and P, not the existence of either S or P. In other words, I take the verb “to be” occurring in sentences describing future events as having the meaning of the “esse ut verum”. (shrink)

Aristotelian philosophers have been always puzzled by the ambiguous status of essences: it is not clear whether an Aristotelian should admit that an essence, taken in itself, is real, even though essences do not exist over and above particular things, as Platonists posit; furthermore, it is not clear whether an Aristotelian should endorse the view that essences have a certain unity, even if they are taken in themselves, namely, by abstracting from the individuals of which they are essences. I tackle (...) Thomas Cajetan’s analysis of this problem: this analysis is more sophisticated than that developed by Aquinas—whose texts had been commented upon by Cajetan. Cajetan distinguishes two senses of “real” and of “unity,” in order to speak of the reality and of the unity of essences, taken in themselves, though not endorsing a Platonist’s ontology. I suggest that his solution is appealing for the contemporary debate about this problem. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

ABSTRACTIn Physics VIII, 5, 256b8-13, Aristotle maintains that it is impossible that there is no motion, because he proved earlier on that it is necessary that there is always motion. In Physics VIII, 1, 251b23-28, Aristotle said that it is necessary that if time is eternal, then motion is also eternal. In Physics VIII, 5, 256b8-13, Aristotle speaks on the contrary about the necessity of eternal motion. In this paper, we show that the argument expounded in Physics VIII, 1, 251b23-28 (...) entails that eternal motion is also necessary de sensu diviso. (shrink)

In today’s academia, scholars are compelled to be productive. The result is an overabundance of publications that often are formulaic follow-ups to the debates du jour. The essays included in this collection are a fortunate exception to this rule—they are original and make refreshingly bold claims. The articles are devoted to the reception of Aristotle’s logic and metaphysics in the Middle Ages and show the vitality of the cluster of scholars known as the “Copenhagen School of Medieval Philosophy.” Even though (...) the school does not identify as “neo-scholastic”, many of its members accept the idea that scholastic interpretations are relevant to our understanding of Aristotle’s thought. Undoubtedly, this is a... (shrink)

In this paper the author demonstrates that Teophilus of Antioch had the pseudo-Platonic dialogue Alcibiades I in mind when he wrote the apologetic treatise Ad Autolycum. It is worth noting that this implicit reference occurs in the context of Teophilus’s description of the soul’s ascent to God.