Void is at the heart of Stoic metaphysics. As the incorporeal par excellence, being defined purely in terms of lacking body, it brings into sharp focus the Stoic commitment to non-existent Somethings. This article argues that Stoic void, far from rendering the Stoic system incoherent or merely ad hoc, in fact reflects a principled and coherent physicalism that sets the Stoics apart from their materialist predecessors and atomist neighbors.

Hylomorphism is the theory that objects are composites of form and matter. Recently it has been argued that form is structure, or the arrangement of an object's parts. This paper shows that the principle of form cannot be ontologically exhausted by structure. That is, I deny form should be understood just as the arrangement of an object's parts. I do so by showing that structure cannot play the role form is supposed to in a certain domain of objects, specifically, in (...) mereological simples. Thus, I show that Hylomorphism does not reduce to Structuralism. I also draw out some important consequences from my argument for Hylomorphism in general. (shrink)

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...) of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character. (shrink)

I argue that Descartes' Second Causal Proof of God in the Third Meditation evidences, and commits him to, the belief that time is "strongly discontinuous" -- that is, that there is actually a gap between each consecutive moment of time. Much of my article attempts to reconcile this interpretation, the "received view," with Descartes' statements about time, space, and matter in his other writings, including his correspondence with various philosophers.

I defend, against its more recent critics, a literal, factual, and consistent interpretation of Timaeus’ creation of the cosmos and time. My main purpose is to clarify the assumptions under which a literal interpretation of Timaeus’ cosmology becomes philosophically attractive. I propose five exegetical principles that guide my interpretation. Unlike previous literalists, I argue that assuming a “pre-cosmic time” is a mistake. Instead, I challenge the exegetical assumptions scholars impose on the text and argue that for Timaeus, a mere succession (...) of events and the relations derived from it (before, after, simultaneous with) imply no time, given the narrow definition of the term used in the dialogue. For Timaeus, I explain, time is measurable, regular, and dependent on the motion of the celestial bodies. A mere succession of events like the one needed to understand the creation story and the pre-cosmos requires none of these elements. Readers of Plato erroneously assume that a succession of events implies time, but that is to impose a conception of time absent in the text. The chapter offers a detailed reconstruction of the pre-cosmic stage under a literalist interpretation and argues how it is compatible with the immutable relationship between the Demiurge and the cosmos. -/- This is an open access chapter distributed under the terms of the CC BY-NC 4.0 license. chapter 4. (shrink)

The studies that make up this book were written and brought together to honor the memory of Jan Pinborg. His unexpected death in 1982 at the age of forty-five shocked and saddened students of medieval philosophy everywhere and left them with a keen sense of disappoint ment. In his fifteen-year career Jan Pinborg had done so much for our field with his more than ninety books, editions, articles, and reviews and had done it all so well that we recognized him (...) as a leader and counted on many more years of his scholarship, his help, and his friendship. To be missed so sorely by his international colleagues in an academic field is a mark of Jan's achievement, but only of one aspect of it, for historians of philosophy are not the only scholars who have reacted in this way to Jan's death. In his decade and a half of intense productivity he also acquired the same sort of special status among historians of linguistics, whose volume of essays in his memory is being G. L. Bursill-Hall almost simultane published under the editorship of ously with this one. Sten Ebbesen, Jan's student, colleague, and successor as Director of the Institute of Medieval Greek and Latin Philology at the University of Copenhagen, has earned the gratitude of all of us by memorializing Jan 1 in various biographical sketches, one of which is accompanied by a 2 complete bibliography of his publications. (shrink)

Alexander’s "Infinitesimal. How a dangerous mathematical theory shaped the modern world"(London: Oneworld Publications, 2015) is right to argue that the Jesuits had a chilling effect on Italian mathematics, but I question his account of the Jesuit motivations for suppressing indivisibles. Alexander alleges that the Jesuits’ intransigent commitment to Aristotle and Euclid explains their opposition to the method of indivisibles. A different hypothesis, which Alexander doesn’t pursue, is a conflict between the method of indivisibles and the Catholic doctrine of the Eucharist. (...) This is a pity, for the conflict with the Eucharist has advantages over the Jesuit commitment to Aristotle and Euclid. The method of indivisibles was a method that developed in the course of the seventeenth century, and those who developed ‘beyond the Alps’ relied upon Aristotelian and Euclidean ideals. Alexander’s failure to recognize the importance of Aristotle and Euclid for the development of the method of indivisibles arises from an unwarranted conflation of indivisibles and infinitesimals. Once indivisibles and infinitesimals are distinguished, we observe that the development of the method of indivisibles exhibits an unmistakable sympathy for Aristotle and Euclid. Thus, it makes sense to consider an alternative explanation for the Jesuit abhorrence of indivisibles. And indeed, indivisibles but not infinitesimals conflict with the doctrine of the Eucharist, the central dogma of the Church. (shrink)

This paper identifies two possible versions of the Epicurean 'Symmetry argument', both of which claim that post mortem non-existence is relevantly like prenatal non-existence and that therefore our attitude to the former should be the same as that towards the latter. One version addresses the fear of the state of being dead by making it equivalent to the state of not yet being born; the other addresses the prospective fear of dying by relating it to our present retrospective attitude to (...) the time before birth. I argue that only the first of these is present in the relevant sections of Lucretius (DRN 3.832-42, 972-5). Therefore, this argument is not aimed at a prospective fear of death, or a fear of 'mortality'. That particular fear is instead addressed by the Epicureans through the additional premise (found in the Letter to Menoeceus 125) that it is irrational to fear in prospect an event which is known to be painless when present. This still leaves unaddressed the related fear of 'premature death', which is to be removed through the acceptance of Epicurean hedonism. (shrink)

What is time? Neither the numbering of the motion of things nor their schema, but their way of being. In language, time shows itself as tense. But every verb has both tense and aspect. So what is aspect? Irreducible to tense, it is the way in which anything is at any time whatsoever. Thus the way things are, their being, is not merely temporal – for it is just as aspectual.

La propuesta inmaterialista de Berkeley, elaborada definitivamente en sus Principles (1710), tiene como antecedente remoto los postulados del capadocio Gregorio de Nisa, quien en algunas de sus obras desarrolló argumentos, en relación con la materia, muy semejantes a los que planteó Berkeley casi catorce siglos después. El presente escrito tiene por objetivo mostrar que las concepciones de ambos pensadores tienen elementos en común, lo que permite sostener que el filósofo de Cesarea es un antecede lejano del inmaterialismo berkeleyano. // Berkeley's (...) immaterialism has as a remote antecedent in the postulates of the Cappadocian Gregory of Nyssa, who in some of his works developed arguments, concerning the matter, very similar to those that Berkeley presented almost fourteen centuries later. This paper aims to show that both philosophical conceptions have elements in common, which allows us to assert that the Cappadocian father is a distant precedent of Berkeley's immaterialism. (shrink)

У античкој философској традицији, време је поимано као кинетичка просторност. Св. Августин задржава овакво поимање времена али га такође одређује и као памћење и очекивање, који означују сопство као место пресека вечног и пролазног, које он дефинише као временски простор. Св. Максим Исповедник, ослањајући се на Кападокијске Оце, даје одлучујући допринос конституисању нарочитог хришћанског схватања времена и просторности, сагледавајући га у контексту есхатолошке персоналности. Творевина треба да превазиђе временску и просторну интервалност која истовремено представља услов могућности промене начина постојања творевине (...) кроз ипостасно сједињење са Логосом. Коначну истину творевине св. Максим описује као вечнокрећуће мировање, које представља ипостасно/личносно сједињење са Богом, и тиме личносни преображај спацио темпоралног темеља створених бића. (shrink)

The principles governing elemental composition, variation, and change in Plato’s Timaeus appear to be incompatible, which has led commentators to prioritize some of the principles to the exclusion of others. Call this seeming incompatibility the problem of isomorphic variants. In this paper, I develop the theory of proportionate atomism as a solution to this problem. Proportionate atomism retains the advantages of rival interpretations but allows the principles of material composition, variation, and change to combine into an internally coherent and explanatorily (...) powerful atomic physics. (shrink)

Calosi-Fano_Pre-socratic-discrete-kinematics2.

In this paper, we address an infamous argument against divisibility that dates back to Zeno. There has been an incredible amount of discussion on how to understand the critical notions of divisibility, extension, and infinite divisibility that are crucial for the very formulation of the argument. The paper provides new and rigorous definitions of those notions using the formal theories of parthood and location. Also, it provides a new solution to the paradox of divisibility which does not face some threats (...) that can possibly undermine the standard Lebesgue measure solution to such a paradox. (shrink)

According to three-dimensionalism, objects persist in time by being wholly present at each time they exist; on the contrary, four-dimensionalism asserts that objects persist by having different temporal parts at different times or that they are instantaneous temporal parts of four-dimensional aggregates. Le Poidevin has argued that four-dimensionalism better accommodates two common assumptions concerning persistence and continuity; namely, that time itself is continuous and that objects persist in time in a continuous way. To this purpose, he has offered two independent (...) arguments, each of which moves from a different understanding of continuity. In this paper, both of Le Poidevin’s arguments will be discussed and rejected. (shrink)

This note criticises an argument used by W. L. Craig against an actual infinity of past events. He argues that if Russell's use of the story of Tristram Shandy, who took a year to recount each day of his life, is extended into an infinite past, then Cantor's principle of correspondence leads to the absurd conclusion that Tristram Shandy has already written his last page. I show that no such conclusion can be drawn, and that a ‘past’ version of the (...) story which does allow this principle to be applied leads to no paradox. (shrink)

This paper tries to demonstrate that some passages of Pliny's Naturalis historia on metallurgical materials are influenced by the Stoic philosopher Posidonius' view that surfaces possess a physical existence. Indeed, Pliny reports that copper surfaces are material, both acting towards drawing a patina to themselves, and being acted upon; i.e. they are both chemically modified by air and fire, and subject to mechanical removal. Also relatable to Posidonius, namely to his view of the interaction between soul and body, is Pliny's (...) account of lead and tin, which can be united thanks to the action they mutually exert on each other, since each metal holds together both itself and what is outside itself. A further influence from the ‘aetiologist’ Posidonius is also betrayed in the care Pliny exercises in describing not only metal corrosion and soldering, but also their causes. Both the scientific and the philosophical imports of these passages are compared with passages by Plato and Plutarch on metallurgical subjects; they are also discussed in the light of the theories on ‘mixture’ propounded by Aristotle and by the Old Stoics. It is shown that Pliny's account compares favorably with Posidonius' doctrine, whereas it is at striking variance with the other ancient reports. Introduction Philosophical and literary evidence 2.1 Pliny 2.2 Posidonius 2.3 Plato and Plutarch Discussion Conclusion. (shrink)

The question whether quantum discontinuity can or cannot provide an answer to Zeno’s Paradoxes is reopened. It is observed that what is usually understood by the term “discontinuity”, namely, Einstein’s conception of the photon as described by himself and all others, is unsuitable to the task because, essentially,it reduces to the trivial ‘discontinuity’ of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort of discontinuity (...) required. Discrete quantized orbits, corresponding to eigen-frequencies, are irreducible, and nothing is allowed to stand in-between them in satisfaction of the quantum postulate, furnishing the requisite, and so far missing, immediate nextness of a point to a certain other. In this way, Zeno’s Runner need not postpone his first step indefinitely, always waiting upon an infinity of preceding steps, before it can be taken. There is now a point that is next to a point and so a step on that point, which is the first step. It follows that, if one kind of discontinuity, Einstein’s, is incapable of offerring an answer to Zeno, while another kind can, the two are discrepant. One of them, the former, is not a kind of discontinuity properly so called at all, though evidently the consequence of one. (shrink)

Richmond Campbell and Thomas Vinci have recently presented a Bayesian theory of confirmation by novel evidence (Campbell and Vinci [1983]). I shall review their theory as briefly as possible and present three objections to it.

Platonism and Christian Thought in Late Antiquity examines the various ways in which Christian intellectuals engaged with Platonism both as a pagan competitor and as a source of philosophical material useful to the Christian faith. The chapters are united in their goal to explore transformations that took place in the reception and interaction process between Platonism and Christianity in this period. -/- The contributions in this volume explore the reception of Platonic material in Christian thought, showing that the transmission of (...) cultural content is always mediated, and ought to be studied as a transformative process by way of selection and interpretation. Some chapters also deal with various aspects of the wider discussion on how Platonic, and Hellenic, philosophy and early Christian thought related to each other, examining the differences and common ground between these traditions. -/- Platonism and Christian Thought in Late Antiquity offers an insightful and broad ranging study on the subject, which will be of interest to students of both philosophy and theology in the Late Antique period, as well as anyone working on the reception and history of Platonic thought, and the development of Christian thought. (shrink)

En este artículo se atiende un problema fundamental de la filosofía de la naturaleza: ¿puede fluir el tiempo sin que existan los cambios que de hecho le acompañan? Las dos posturas antiguas más reconocidas, la de Aristóteles y la de los estoicos, se analizan en este ensayo. Por un lado, Aristóteles define al tiempo en función del cambio, de manera que su respuesta a la pregunta arriba planteada tendría que ser negativa; por otro lado, los estoicos sostienen que existen momentos (...) en los que de hecho el tiempo fluye sin que haya cambios,, y, por tanto, el tiempo no presupone la noción de cambio. Presento aquí la siguiente hipótesis: los estoicos heterodoxos aceptaron la idea aristotélica del tiempo que presupone cambio, idea que conocen a través de Eudemo, y que les lleva a proponer cambios transcíclicos para solucionar los problemas que causa la discusión sobre la individuación, la identidad y el cambio a través del tiempo. (shrink)

Scientism is a philosophy which purports to define what the world ‘really is’. It adopts what the philosopher Thomas Nagel called ‘an epistemological criterion of reality’, defining what is real as that which can be discovered by certain quite specific methods of investigation. As a consequence all features of experience not revealed by those methods are deemed ‘subjective’ in a way that suggests they are either not real, or lie beyond the scope of meaningful rational inquiry. This devalues capacities that (...) (we argue) are in fact essential components of good reasoning and virtuous practice. Ultimately, the implications of scientism for statements of value undermine value-judgements essential for science itself to have a sound basis. Scientism has implications, therefore, for ontology, epistemology and also for which claims we can assert as objective truths about the world. Adopting scientism as a world view will have consequences for reasoning and decision-making in clinical and other contexts. We analyse the implications of this approach and conclude that we need to reject scientism if we are to avoid stifling virtuous practice and to develop richer conceptions of human reasoning. (shrink)

This dissertation is a defense of a particular theory of the metaphysics of time which I call "accretivism", but which is popularly known in a form usually called the "Growing Block Theory". The goal of a metaphysics of time is to incorporate the various aspects of our temporal experience into a single, comprehensive whole. To this end I delineate five aspects of our ordinary experience of time: 1) The Tensed Aspect, in virtue of which objects are presented to us as (...) past, present, or future; 2) The Transitory Aspect, in virtue of which time passes or "flows"; 3) The Durational Aspect, in virtue of which entities have a certain temporal extent; 4) The Structural Aspect, in virtue of which entities are given as being in temporal relations to one another, and 5) The Differential-Repetitive Aspect, in virtue of which things are different from one time to another, and yet there is a certain recurrence of aspects of our experience form one time to another. I contrast the accretivist picture of time, according to which that which is past and that which is present both have ontological status, but nothing which is future has ontological status, and in which temporal passage consists in the coming-into-being of new entities at the temporal edge of reality marked by the present, with the two dominant theories of time in the contemporary literature: 1) presentism, according to which only that which is present has ontological status, and 2) four-dimensionalism, according to which time is to be understood on analogy with spatial dimensions. Accretivism, I argue, is superior to the other two views in virtue of the fact that it gives full status to both the Structural Aspect of Time, for which the presentist has difficulty accounting, and the Transitory Aspect of Time, for which the four-dimensionalist has difficulty accounting. I then defend the accretivist picture against a variety of objections that might be raised to it. (shrink)

This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause (...) for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist. -/- Friends of the KCA have sought to defend their view that physical reality began to exist in two distinct ways. As I discuss in chapter 2, the first way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a priori arguments meant to show that, as a matter of metaphysical necessity, the past must be finite. If the past is necessarily finite, then the past history of physical reality is necessarily finite. And if having a finite past suffices for having a beginning, then, since the past history of physical reality is necessarily finite, physical reality necessarily began to exist. I show that the arguments which have been offered thus far for the view that the past is necessarily finite do not succeed. Moreover, as I elaborate on in chapter 5, having a finite past does not suffice for having a beginning. -/- As I discuss in chapter 3, the second way in which friends of the KCA have sought to defend their view that physical reality began to exist involves a family of a posteriori arguments meant to show that we have empirical evidence that physical reality has a finite past history. For example, the big bang is sometimes claimed to have been the beginning of physical reality and, since we have excellent empirical evidence for the big bang, we have excellent empirical evidence for the beginning of physical reality. The big bang can be understood in two ways. On the one hand, the big bang can be understood as a theory about the history and development of the observable universe. Understood in that sense, then I agree that the big bang is supported by excellent empirical evidence and by a scientific consensus. On the other hand, some authors (particularly science popularizers, science journalists, and religious apologists) have wrongly interpreted big bang theory as a theory about the beginning of the whole of physical reality. As I argue, while a beginning of physical reality may be consistent with classical big bang theory, classical big bang theory does not provide good reason for thinking that physical reality began to exist. -/- In part II, I turn to discussing three necessary, but not necessarily sufficient, conditions for physical reality to have a beginning. Before discussing the three conditions, in chapter 4, I introduce three metaphysical accounts of the nature of time (A-theory, B-theory, and C-theory) as well as some formal machinery that will subsequently become useful in the dissertation. I introduce the first of the three conditions in chapter 5. According to the Modal Condition, physical reality began to exist only if, at the closest possible worlds without time, physical reality does not exist. I show that this condition helps us to make sense of various views in both theology and philosophy of physics. In chapter 6}, I introduce the second of my three conditions, the Direction Condition, according to which, roughly, physical reality began to exist only if all space-time points agree about the direction of time, so that all space-time points can agree that physical reality's putative beginning took place in their objective past. In chapter 7, I discuss the third condition, the Boundary Condition, according to which physical reality began to exist only if there is a past temporal boundary such that physical reality did not exist before the boundary. I show that there are two senses in which physical reality could be said to have had a past temporal boundary. Lastly, in chapter 8, I show that there is a relationship between my three conditions and classical big bang theory, even though the relationship is not the one usually identified in the literature. -/- In part III, I present four arguments for the view that, at the present stage of philosophical and scientific inquiry, we cannot know whether physical reality satisfies the three necessary conditions to have had a beginning and, consequently, we cannot know whether physical reality had a beginning. As I will prove in chapter 9, no set of observations that we currently have, when conjoined with General Relativity, entails that physical reality satisfies the Direction or Boundary Conditions. As I show in chapter 10, considerations in the philosophical foundations of statistical mechanics entail either that the Cosmos violates the Modal Condition or else that there is a transcendental condition on the possibility of our knowledge of the past that prevents our access to data we would need to gather to determine whether physical reality satisfies the Boundary Condition. In chapter 11, I show that there are a number of live cosmological models according to which physical reality does not satisfy the Boundary Condition. As long as we don't know whether any of those cosmological models are correct, we do not know whether physical reality satisfies the Boundary Condition. Lastly, I turn to confirmation theory and show that, at our present stage of inquiry, ampliative inferences for the conclusion that physical reality satisfies the Modal, Direction, and Boundary Conditions are not successful. (shrink)