Aristotle: Necessity and Possibility

In this paper, I compare the Megarian thesis of Metaphysics IX 3 with other sources on the Megarians in order to clarify two questions: that of the unity and nature of the so-called Megarian school and that of Aristotle’s broader argument in IX 3. I first review the disputed issue of the status of the Megarian school and then examine two hypotheses regarding the identity behind Aristotle’s allusion in IX 3. Third, I explore the connection between Megarianism and Plato’s Euthydemus, (...) a task that helps us to contextualize Aristotle’s anti-Megarian polemic. Lastly, I build on the preceding argument in a re-examination of the Eleatic hypothesis with regard both to the Megarians as a whole and to the thesis that Aristotle transmits. (shrink)

There are two distinct but interrelated questions concerning Aristotle’s account of infinity that have been the subject of recurring debate. The first of these, what I call here the interpretative question, asks for a charitable and internally coherent interpretation of the limited pieces of text where Aristotle outlines his view of the ‘potential’ (and not ‘actual’) infinite. The second, what I call here the philosophical question, asks whether there is a way to make Aristotle’s notion of the potential infinite coherent (...) and rigorous with modern tools that can stand as a rival to the widely-accepted view of the infinite as characterized in a mathematical theory of sets. In this paper, I argue that the theoretical roles that Aristotle intends his account of the potential infinite to fulfill lead to a deep and irresoluble tension that can help explain the persistence of debates on both of these questions. I do so by turning to the places where Aristotle attempts to argue for or against the existence of particular infinite processes to show that he slides between different underlying notions of when changes are possible. Making these underlying notions clear can help us better understand the role of Aristotle’s account in the history of philosophy, the possible pitfalls for a contemporary theory of the potential infinite, and what each of these debates might learn from each other. (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)

Although the commentary on Aristotle’s problematic discussion of slavery is vast, his discussion of nobility receives little attention. The fragments of his dialogue On Noble Birth constitute his most extensive examination of nobility, and while their similarity to the παμβασιλεύς of the Politics has recently been recognized, their relevance to natural slavery has hitherto gone unnoticed. Yet by declaring that true nobles – particularly the god-like ἀρχηγός – preternaturally possess superhuman characteristics, Aristotle precludes their easy inclusion in the kind “human” (...) in a manner inversely mirroring the preternatural subhumanity of natural slaves. Building on recent scholarship which argues that Aristotle’s “defense” of natural slaves is better understood as an indictment, On Noble Birth becomes most coherent if read as a hypothetical investigation into what would be required for “nobility” to name something true rather than equivocal, with the conclusion that “true nobility” is an empty set. (shrink)

The intelligibility of nature was a persistent theme of William A. Wallace, OP, one of the most prolific Catholic scholars of the late twentieth century. This Reader aims to make available a representative selection of his work in the history of science, natural philosophy, and theology illustrating his defense and development of this central theme. Wallace is among the most important Galileo scholars of the past fifty years and a key figure in the recent revival of scientific realism. Further, his (...) long and productive scholarly career has been shaped by a continuous effort to bring the resources of the Aristotelian-Thomistic tradition to the solution of contemporary problems of philosophy and science. Through all of these contributions, Wallace has provided the foundation for a renewed confidence in the capacity of human knowers to attain understanding of the natural order. Consequently, the overall aim of this volume is to secure continued access to his scholarship for readers in the new millennium. -/- Intelligibility of Nature contains twenty-nine previously published essays written by Wallace over a period of some forty years. Many of these essays are currently not readily accessible. They are arranged in five thematic groups, each representing a major subject-area of Wallace's scholarly interests. The first group is devoted to essays on making nature intelligible through the use of scientific models. The second group of essays investigates various ways in which the Aristotelian-Thomistic tradition is foundational to contemporary scientific research. Essays in the third group are historical studies on the origins of modern science. The fourth group of essays discuss the viability of the cosmological argument for the existence of God in light of natural science. The final group of essays consider the relation of science and religion. Together these essays provide a representative sample of Wallace's multifaceted contributions to scholarship. (shrink)

In De interpretatione 9, Aristotle argues against the fatalist view that if statements about future contingent singular events (e.g. ‘There will be a sea battle tomorrow,’ ‘There will not be a sea battle tomorrow’) are already true or false, then the events to which those statements refer will necessarily occur or necessarily not occur. Scholars have generally held that, to refute this argument, Aristotle allows that future contingent statements are exempt from either the principle of bivalence, or the law of (...) excluded middle. This paper offers a new interpretation of Aristotle’s refutation of fatalism. According to this interpretation, each member of a pair of contradictory future contingent statements, in virtue of expressing modal necessity, is simply false. (shrink)

This book investigates what change is, according to Aristotle, and how it affects his conception of being. Mark Sentesy argues that change leads Aristotle to develop first-order metaphysical concepts such as matter, potency, actuality, sources of being, and the teleology of emerging things. He shows that Aristotle’s distinctive ontological claim—that being is inescapably diverse in kind—is anchored in his argument for the existence of change. -/- Aristotle may be the only thinker to have given a noncircular definition of change. When (...) he gave this definition, arguing that change is real was a losing proposition. To show that it exists, he had to rework the way philosophers understood reality. His groundbreaking analysis of change has long been interpreted through a Platonist lens, however, in which being is conceived as unchanging. Offering a comprehensive reexamination of the relationship between change and being in Aristotle, Sentesy makes an important contribution to scholarship on Aristotle, ancient philosophy, the history and philosophy of science, and metaphysics. (shrink)

In this essay, I consider some logical treatises and commentaries from the first decades of the 12th century (many of which are still unedited) which contain a discussion on modalities and modal logic. After presenting a short catalogue of these sources and a description of their common features, I shall focus on some definitions of the modal term “necessarium” which are provided in them. As we will see, Abelard and logicians of his time advanced three different characterizations of this term: (...) necessity was either defined in terms of unavoidability (ineuitabilitas), or in terms of immutability and omnitemporality (impermutabilitas, sempiternitas), or again in terms of absolute necessity as opposed to conditioned one (necessitas absoluta vs. determinata). I argue that the temporal understanding of necessity in terms of omnitemporality, inherited from ancient sources and extensively used by Abelard and others in the first years of the twelfth-century, started to disappear in texts datable from around the 1120, perhaps due to several difficulties that were related to this definition when applied in logical contexts. I also discuss how the notion of necessitas determinata was used by Abelard’s contemporaries to qualify the modal status of present and past events, which were generally believed to be necessary only in a “weak” and harmless sense that did not prevent them from being contingent. -/- . (shrink)

This paper focuses on two short dubitationes on animal’s technical abilities, which Pietro Pomponazzi discussed in 1514 and in 1519 while teaching at the University of Bologna and commenting on Aristotle’s Physica, II, t. 80. A comparative analysis between the respective positions, expressed at a distance of five years, allows to retrace the change in Pomponazzi’s thoughts from the period immediately preceding the composition of De immortalitate animae to the writing of the De incantationibus and De fato.

Aristotle is no exception in seeing a connection between causation and necessity, and teleological causation is no exception for Aristotle. His discussions of teleology in the Physics and in Parts of Animals i 1 both make this connection explicitly, by presenting final causation as involving necessity ‘from a hypothesis (ex hupotheseôs)’, usually referred to in the literature as ‘hypothetical necessity’. Hypothetical necessity is evidently invoked to express the thought that, given the functions and activities of living things, certain of their (...) features cannot be otherwise. Further, it appears that these necessity claims are meant to have explanatory force: that is, it seems that according to Aristotle, to grasp that A hypothetically necessitates B is to understand, at least in part, why B is the case. The trouble is that while Aristotle and his commentators do indeed seem to think that his appeals to hypothetical necessity are supposed to have explanatory power, their various glosses on the notion make it difficult to see how this could be the case. That is, he and his commentators seem, contrary to their intentions, to present appeals to hypothetical necessity as exemplifying patterns of inference that do not, in fact, have explanatory power. The challenge, then, is to provide an understanding of hypothetical necessity that allows us say how the patterns of inference invoking it are successful as explanations, and to distinguish them from patterns of inference that are not. I suggest that if we look in closer detail at the patterns of explanation Aristotle associates with hypothetical necessity, and the ways in which these are supposed to be distinctive, we can offer an account of what hypothetical necessity is and how it can have explanatory power. (shrink)

According to most scholars, in the Parts of Animals Aristotle frequently provides explanations in terms of material necessity, as well as explanations in terms of that-for-the-sake-of-which, i.e., final causes. In this paper, I argue that we misunderstand both matter and the way that Aristotle explains things using necessity if we interpret Aristotle as explaining things in terms of material necessity. Aristotle does not use the term “matter” very frequently in his detailed discussions of animal parts; when he does use it, (...) he typically identifies blood as matter. I argue that this is because blood is, for Aristotle, what properly nourishes and grows the other parts of the body and he views nourishment and growth as types of coming-to-be. The second half of the paper turns to necessity as a cause in the Parts of Animals. I argue that in the Parts of Animals Aristotle is not interested in distinguishing between what Aristotle elsewhere treats as very different types of necessity. (shrink)

In Contingency, Time and Possibility, Pascal Massie explores the inquiries of Aristotle and Duns Scotus into contingency and possibility, as well as the complex and fascinating questions they raise.

Some commentators have argued that there is no room in Aristotle's natural science for simple, or unconditional, physical necessity, for the only necessity that governs all natural substances is hypothetical and teleological. Against this view I argue that, according to Aristotle, there are two types of unconditional physical necessity at work in the material elements, the one teleological, governing their natural motions, and the other non-teleological, governing their physical interaction. I argue as well that these two types of simple necessity (...) also govern everything made out of the elements, that is, all other natural substances and artifacts. (shrink)