Volume 106, Issue 3

The purpose of this paper is to reassess some mathematical examples in Plato’s dialogues which at a first glance may appear to be nothing more than trivial puzzles. In order to provide the necessary background for this analysis, I shall begin by sketching a brief overview of Plato’s mathematical passages and discuss the criteria for aptly selecting them. Second, I shall explain what I mean by ‘mathematical examples,’ and reflect on their function in light of the discussion on παραδείγματα outlined in the Sophist and the Statesman . Against this framework, I shall move to a close examination of specific examples drawn from the Theaetetus (154c–55d), the Republic (523c–24d), and the Phaedo (96d–97b, 100e–101d). By placing these examples in the broader context of pre-Euclidean mathematics, I shall show that their mathematical content is often less elementary than might appear at first sight. Moreover, by placing emphasis on the specific philosophical concerns that motivated their introduction, I shall argue that the examples are not merely nonsensical jokes. Even if their illustrative purpose is not always immediately clear, and even if they can sound playful and bizarre, they in fact fulfil an important function: by virtue of their power to generate wonder or confusion, they serve as exercises and act as a trigger with respect to the difficult philosophical issues they are intended to clarify.

Résumé Dans cet article, j’analyse quelques passages des Commentaires sur la Physique de Simplicius, Philopon et Thémistius afin de : 1) démontrer que ces commentateurs interprètent la phrase d’Aristote, Phys . III 1, 200b16-17, comme affirmant que « continu » est un terme définitoire du mouvement ; 2) identifier la raison pour laquelle ils pensent que parler du mouvement naturel revient à dire que le mouvement est continu, et que, par conséquent, quand Aristote évoque le continu dès le début de sa théorie sur le mouvement, il ne fait qu’affirmer quelque chose d’évident ; 3) montrer que si l’analogie selon laquelle « continu » est un terme définitoire du mouvement, tout comme « mouvement » est un terme définitoire de la nature et « infini » un terme définitoire du continu, n’est pas parfaite (en effet « continu » n’apparaît pas explicitement dans la définition du mouvement), ceci est dû à l’impossibilité de subsumer le mouvement sous une catégorie de l’être. Pour appuyer ce dernier point, j’utilise une citation d’Alexandre par Simplicius, et un passage de Philopon.

I argue that the adjective δαιμόνιος (‘daemonic’) and the substantivized adjective τὸ δαιμόνιον (‘the daemonic’) that occur in Aristotle’s dream treatises basically mean ‘divine-like,’ denoting an illusory appearance of divine intervention, typically in the form of an alleged god-sent prophetic dream. Yet the appearances to which the terms refer are, in fact, neither divine nor supernatural at all, but involve merely coincidental correlations between the dream and the fulfilling event. It is shown that Aristotle’s use of ‘daemonic’ is traditional and reflects the endoxon that prophetic dreams are closely related to the divine. The paper also examines a set of earlier readings of the daemonic in De divinatione in relation to the proposed interpretation.

This paper attempts to reconstruct the views of the Stoic Posidonius on the emotions, especially as presented by Galen’s On the Doctrines of Hippocrates and Plato . This is a well-studied area, and many views have been developed over the last few decades. It is also significant that the reliability of Galen’s account is openly at issue. Yet it is not clear that the interpretative possibilities have been fully demarcated. Here I develop Galen’s claim that Posidonius accepted a persistent, non-rational aspect of the soul that he connects with the merely animal part of humans. The aim is to begin from this testimony in answering two questions: (1) How might the possession of a non-rational element of the soul operate alongside the hêgemonikon (leading-part of the soul) as a source of impulse for Posidonius. (2) How does this persistent animal aspect conform to the Stoic ontological classification found in their scala naturae ? I shall argue in response to these that (a) Posidonius distinguished the merely cognitive aspects of the soul from those that are rational, and (b) that the hêgemonikon itself is not to be identified with what is rational. Accepting a persistent non-rational source of emotional impulses allows Posidonius a richer framework for explaining human affective responses and behaviours. I also briefly address Galen’s motivation for the account he offers. It is in view of Posidonius’ approach to Plato’s Timaeus that Galen’s discussion finds its most plausible interpretation.

In this paper, I attempt to explain one of the most controversial views attributed to the Stoic Chrysippus: that the impossible can follow from the possible. My solution finds in Chrysippus a distinction later made by the medieval logician John Buridan: that between being possible (there being a state of affairs that may occur) and being possibly-true (there being some proposition whose truth-conditions are that state of affairs). Buridan and Chrysippus have radically opposing views on the nature of propositions. What their conceptions share is the conclusion that at least some propositions must be contingent beings. They argue for this while maintaining a rigorous commitment to the view that propositions are strictly bivalent. In 2. I explain the Chrysippean passage in terms of a distinction Buridan makes explicitly. In 3. I show how the distinction follows implicitly from the Stoic theory of quantification. In 4. I compare the modality with other aspects of Stoic logic. In 5. I discuss how the distinction behaves in the future tense.

This paper studies the theories defended by John Buridan and Nicole Oresme on the presence of the soul in the body, with a special focus on the interpretation of the Augustinian principle – or ‘holenmeric’ principle – according to which the soul is in the whole body and is wholly present in every part of it. The first part of the paper introduces the different types of composition involved in the medieval discussions over the soul and its parts and shows how different psychological theories prior to 1350 employed this typology of part/whole relations to clarify the soul’s presence in the body. The next part of the paper presents how the theories designed by John Buridan and Nicole Oresme were motivated by problems raised by these earlier accounts of the soul’s presence and undertook to solve them from the perspective of a reductionist conception of parthood. It is argued that, despite their common commitment to a reductionist stance, the solutions endorsed by Buridan and Oresme represent two opposite ways of applying a nominalist metaphysics of parts to psychological matters.

This paper argues that Shaftesbury differs from other moral sentimentalists (Hutcheson, Hume, Smith) because he conceives of the moral sentiments as partial and first-personal, rather than impartial and spectatorial. This difference is grounded in Shaftesbury’s distinctive notion that moral self-governance consists in the self-examination of soliloquy. Breaking with his Stoic influences, Shaftesbury holds that the moral sentiments play the role of directing and guiding soliloquy. Because soliloquy is first-personal reflection that is directed to achieving happiness, claiming that the moral sentiments direct soliloquy leads Shaftesbury to conceive of the moral sentiments as arising from the internal perspective of an agent focused on her own happiness. This provides Shaftesbury with a stronger framework for understanding moral sentiments, for it avoids the difficulty of explaining why the sentiments of others or those arising from an imagined spectator’s perspective are motivating or authoritative for us.

According to a common interpretation, most explicitly defended by Onora O’Neill and Patricia Kitcher, Kant held that epistemic obligations normatively depend on moral obligations. That is, were a rational agent not bound by any moral obligation, then she would not be bound by any epistemic obligation either. By contrast, in this paper, I argue that, according to Kant, some epistemic obligations are normatively independent from moral obligations, and are indeed normatively absolute. This view, which I call epistemicism , has two parts. First, it claims that in the absence of other kinds of obligations, rational agents would still be bound by these epistemic obligations, i. e., that the latter are normatively independent. Second, it claims that, no matter what other obligations are at stake, rational agents are bound by these epistemic obligations, i. e., the normativity of these epistemic obligations is absolute in that it cannot be undercut by any moral or other sort of obligation. The argument turns on an exploratory reading of Kant’s remarks in “What Is Orientation in Thinking?” (1786) about the maxim of “thinking for oneself” as the “supreme touchstone of truth”. In contrast to O’Neill and Kitcher, I argue that if we interpret this maxim as stating the unifying principle of theoretical and practical reason, then we must interpret it as stating an epistemic, and not merely practical imperative. This result, I argue, vindicates epistemicism and illuminates interesting lessons about Kant’s conception of the category of “epistemic” norms. Further, it helps us make headway with Kant’s enigmatic remarks about the unity of practical and theoretical reason in the Groundwork , the first and second Critiques , and the Lectures on Logic . On my proposal, principles of the practical and theoretical uses of reason are unified through a formal epistemic principle.

In Marx’s posthumously published manuscripts from 1857–1863, we find a systematic exposition of his concept of subsumption. Though much has been written about it, significant interpretative gaps persist. In this article, I begin filling these gaps by examining the emergence of Marx’s concept of subsumption. I will argue that in the Grundrisse Marx brings together distinct but complementary elements from Hegel’s theories of judgment and teleology to coin two new and well delineated concepts of subsumption that prefigure his later concepts of formal and real subsumption. These two concepts may be defined as: (a) the process of acquiring the social relational property of being a means to an end; (b) the process by which changes in non-relational properties occur in something due to this acquisition – and occur to better suit said end.

This paper argues that the ‘scientific dispute’ between Hermann Cohen and Rudolf Stammler is symptomatic of a philosophical movement of left-wing Kant interpretations at the turn of the twentieth century. By outlining influential predecessors that shaped Cohen’s and Stammler’s thinking, I show that their Kantian justifications of socialism differ regarding their conception of law, history, and the political implications that follow from their practical philosophies. Against scholars who suggest that the Marburg School’s view on socialism was a coherent school of thought, I introduce the concept of ‘left-Kantianism’ as an open term that includes a wide variety of novel socialist approaches to Kant at the time.