Słupecki's Generalized Mereology and Its Flaws

One of the streams in the early development of set theory was an attempt to use mereology, a formal theory of parthood, as a foundational tool. The first such attempt is due to a Polish logician, Stanis?aw Le?niewski (1886–1939). The attempt failed, but there is another, prima facie more promising attempt by Jerzy S?upecki (1904–1987), who employed his generalized mereology to build mereological foundations for type theory. In this paper I (1) situate Le?niewski's attempt in the development of set theory, (2) describe and evaluate Le?niewski's approach, (3) describe S?upecki's strategy without unnecessary technical details, and (4) evaluate it with a rather negative outcome. The issues discussed go beyond merely historical interests due to the current popularity of mereology and because they are related to nominalistic attempts to understand mathematics in general. The introduction describes very briefly the situation in which mereology entered the scene of foundations of mathematics — it can be safely skipped by anyone familiar with the early development of set theory. Section 2 describes and evaluates Le?niewski's attempt to use mereology as a foundational tool. In Section 3, I describe an attempt by S?upecki to improve on Le?niewski's work, which resulted in a system called generalized mereology. In Section 4, I point out the reasons why this attempt is still not successful. Section 5 contains an explanation of why Le?niewski's use of Ontology in developing arithmetic also is not nominalistically satisfactory.     

Albert le Grand: De ce qui vient avant la logique

Le premier tractatus du commentaire d'Albert le Grand à l'Isagoge de Porphyre consiste en une manière de proème ou d'introduction à l'ensemble de la logique. Comme la plupart des textes d'Albert le Grand, ce traité est d'une très grande richesse, qu'atténuent toutefois son manque d'ordre et son obscurité d'expression. Étant donné que les aspects fondamentaux de la logique y sont touchés—son statut scientifique et philosophique, son utilité, son sujet, sa division, sa relation aux sciences du langage, etc.—, ce petit ouvrage est du plus haut intérêt pour quiconque cherche à mieux comprendre la logique et la philosophie de la logique du XIII^e siècle. L'auteur présente ici une traduction annotée et expliquée de ce texte difficile, faite d'après la version provisoire de la nouvelle édition de Cologne. Le relevé des sources principales de l'ouvrage révèle, sur un fond aristotélicien permanent, une forte influence des traités logiques arabes nouvellement arrivés en Occident.

The first tractatus of Albert the Great's commentary on Porphyry's Isagoge consists of a kind of proem or introduction to the whole of logic. As most of Albert the Great's texts, this tract is of great richness, though it lacks order and is sometimes obscure. Since the fundamental themes of logic are addressed therein—its scientific and philosophical status, its utility, its subject, its division, its relation to the linguistic arts, etc.—, this small work is of high interest for anyone trying to better understand thirteenth-century logic and philosophy of logic. The author presents a translation of this difficult text, made after a preliminary version of the new critical edition and enriched with an introduction and explanatory notes. The survey of the main sources of the tract reveals, apart from a permanent artistotelian background, the strong influence of the Arabic logical treatises which were then coming in the Western world.     

The End(s) of Philosophy: Rhetoric, Therapy and Wittgenstein's Pyrrhonism

In Culture and Value Wittgenstein remarks: ‘Thoughts that are at peace. That's what someone who philosophizes yearns for’. The desire for such conceptual tranquillity is a recurrent theme in Wittgenstein's work, and especially in his later ‘grammatical‐therapeutic’ philosophy. Some commentators (notably Rush Rhees and C. G. Luckhardt) have cautioned that emphasising this facet of Wittgenstein's work ‘trivialises’ philosophy – something which is at odds with Wittgenstein's own philosophical ‘seriousness’ (in particular his insistence that philosophy demands that one ‘Go the bloody hard way’). Drawing on a number of correlations between Wittgenstein's conception of philosophy and that of the Pyrrhonian Sceptics, in this paper I defend a strong ‘therapeutic’ reading of Wittgenstein, and show how this can be maintained without ‘trivialising’ philosophy.     

Excommunication and the philosophy of Spinoza

This paper is an attempt to probe the connection between Spinoza's philosophy and his excommunication from the Synagogue in 1656. It seeks, first, to show the decisive influence of the 1656 excommunication on Spinoza's life and thought, and to demonstrate that this event is the single most important key to understanding his entire philosophy. With this key, the paper seeks, secondly, to illustrate the development and transformation of Spinoza's thought through specific reference to his three major works, Korte Verhandeling, De Emendatione, and Ethica. Underlying these two points is a third, namely, that the inherently dynamic and positive elements of ‘experience’, which have not been fully appreciated thus far, should be given greater attention in the evaluation of Spinoza's philosophy.     

Sartre and Bergson: A Disagreement about Nothingness

Abstract

Henri Bergson's philosophy, which Sartre studied as a student, had a profound but largely neglected influence on his thinking. In this paper I focus on the new light that recognition of this influence throws on Sartre's central argument about the relationship between negation and nothingness in his Being and Nothingness. Sartre's argument is in part a response to Bergson's dismissive, eliminativist account of nothingness in Creative Evolution (1907): the objections to the concept of nothingness with which Sartre engages are precisely those raised by Bergson. Even if Sartre's account of nothingness in its entirety is found to be flawed, I argue that the points he makes specifically against Bergson are powerful.

My discussion concludes with a brief examination of the wider philosophical background to Sartre's and Bergson's discussion of nothingness: here I point to some important aspects of Sartre's early philosophy, including some features of his conception of nothingness, that may testify to Bergson's positive influence on his thought.     

Hegel's Critique of Fichte in the 1802/3 Essay on Natural Right

This paper provides a reconstruction and critical assessment of Hegel's critique of Fichte's political philosophy in his 1802/3 essay On the Scientific Ways of Treating Natural Right. I argue that Hegel's critique, while not entirely successful, raises a serious problem for Fichte's political philosophy as presented in the 1796/7 Foundations of Natural Right.     

How Berkeley's Gardener Knows His Cherry Tree

The defense of common sense in Berkeley's Three Dialogues is, first and foremost, a defense of the gardener's claim to know his cherry tree, a claim threatened by both Cartesian and Lockean philosophy. This defense depends on the esse is percipi thesis (EIP). EIP is not something the gardener believes; rather, it is a philosophical analysis of the rules he unreflectively follows in his use of the word ‘exists’. Uncovering these connections between Berkeley's epistemology and philosophy of language will clarify Berkeley's strategy for bringing his reader back to common sense and practical engagement in the ordinary affairs of life.     

‘Mystic Atheism’: Julia Kristeva's Negative Theology

Abstract

This article examines Julia Kristeva's paradoxical concept of a ‘mystic atheism’. It falls into three parts. First, it briefly surveys Kristeva's psychoanalytic account of Christian theology in Au commencement était l'amour (1985). Secondly, it assesses Kristeva's analysis of the Christian mystical tradition from Teresa of Avila to Angela of Foligno in such works as Le féminin et le sacré (1999) and the three volumes on Le génie féminin (1999-2002). For Kristeva, Christian mysticism represents a key moment in the transition from theology to psychoanalysis: what she locates within the work of the female mystics is a so-called ‘mystic atheism’, that is to say, an affirmation of an other within the subject as opposed to the divine other that supposedly lies outside it. Finally, the article offers some critical comments upon Kristeva's own ‘mystic atheism’: I argue that—like much negative theology—Kristeva's psychoanalysis remains ontotheological in form and that this dimension expresses itself in a problematic tendency to anthropomorphize the other within. In conclusion, I will suggest that Kristeva's ‘mystic atheism’ ultimately remains within the theological tradition it seeks to call into question.     

“Bad philosophy” and “derivative philosophy”: Labels that keep women out of the canon

Efforts to include women in the canon have long been beset by reactionary gatekeeping, typified by the charge “That's not philosophy.” That charge doesn't apply to early and mid-analytic female philosophers—Welby, Ladd-Franklin, Bryant, Jones, de Laguna, Stebbing, Ambrose, MacDonald—with job titles like lecturer in logic and professor of philosophy and publications in Mind, the Journal of Philosophy, and Proceedings of the Aristotelian Society. It's hopeless to dismiss their work as “not philosophy.” But comparable reactionary gatekeeping affects them, this paper argues, typified by the labels “bad philosophy” and “derivative philosophy.” Virtue and vice epistemology help explain why these women have been neglected and why their own approaches are epistemically virtuous. Their contemporaries and historians are deficient in scholarly virtues in labelling these women's work “bad” or derived from male mentors with no or specious justification. Their disparaged qualities—intellectual humility, modesty, critical self-reflection, disclosing biases—are often epistemic virtues.     

From Kant to Heidegger. On the path from self-consciousness to self-understanding

In this article I explore the idea that Heidegger's lectures on The Basic Problems of Phenomenology are of particular importance to our understanding of the relationship between Heidegger and Kant. These lectures can be read as a “historical” commentary on Being and Time. Of course, Heidegger does not present himself as a historian of philosophy, but acts as a philosophical reader of Kant in order to expound the principal ideas of his own philosophy. My central claim is that it is through Kant's philosophy of self-consciousness that Heidegger attempts to provide us with a better understanding of his own conception of self-understanding.     

Intellectual intuition and Kant's epistemology

In order to construct culture‐inclusive theories of psychology to establish an autonomous academic tradition of Confucian humanism, this article provides a commentary on Zongshan Mou's philosophy of intellectual intuition (智的直覺) as well as his systematic bias in translating Kant's epistemology of transcendental idealism (先驗理念論) into Chinese as ‘transcendent idealism’ (超越觀念論). I will demonstrate that his systematic bias in translating Kant's epistemology into Chinese may hinder his followers in developing a comprehensive understanding of the dialectical relationships among various paradigms of the Western philosophy of science, while his philosophy of intellectual intuition not only deviates from the original philosophical stance of pre‐Qin Confucians towards Heaven (天) and Dao (道), but also leads to his misunderstanding of Zhu Xi's philosophy and exploration of human nature (性), which may help us to understand the necessity of a psychodynamic model of cultural psychology with its emphasis on collective unconsciousness instead of the metaphor of Height Psychology.     

From Kant to Sade: a fragment of the history of philosophy in the Dialectic of Enlightenment

In this paper, I set out (1) to consider the extent to which Horkheimer and Adorno's account of the transition from Kant's philosophy to key features of the novels of the Marquis de Sade in the Second Excursus of their Dialectic of Enlightenment can be viewed as a fragment of the ‘history of philosophy’ and (2) to explain this account in a way that allows us to ask whether it succeeds in establishing a necessary connection between Kant's philosophy and Sade's novels. In connection with (2), a particular problem emerges. This problem concerns the role played by a non-instrumental form of reason in Horkheimer and Adorno's attempt to establish an essential connection between Kant's theoretical philosophy and Sade's novels, in which the practical implications of the theoretical employment of reason allegedly become explicit. It will be shown that, despite appearances to the contrary, an employment of reason of the relevant type is not identified by Kant in the Critique of Pure Reason.     

Redrawing Kant's philosophy of mathematics

This essay offers a strategic reinterpretation of Kant's philosophy of mathemat- ics in Critique of Pure Reason via a broad, empirically based reconception of Kant's conception of drawing. It begins with a general overview of Kant's philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant's constructivism takes up these issues, largely inspired by Hintikka's unorthodox conception of Kantian intuition. Third, it offers further analyses of three Kantian concepts vitally linked to that of drawing. It concludes with an etymologically based exploration of the seven clusters of meanings of the word drawing to gesture toward new possibilities for interpreting a Kantian philosophy of mathematics.     

Kant's Criticism of Common Moral Rational Cognition

There is a consensus that Kant's aim in the Groundwork is to clarify, systematize and vindicate the common conception of morality. Philosophical theory hence serves a restorative function. It can strengthen agents' motivation, protect against self‐deception and correct misunderstandings produced by uncritical moral theory. In this paper, I argue that Kant also corrects the common perspective and that Kant's Groundwork shows in which senses the common perspective, even considered apart from its propensity to self‐deception and without being influenced by misleading theory, is deficient. Critical practical philosophy needs to set right agents about the stringency of some of their duties, and agents need to be made aware that they have certain other duties. I discuss how Kant corrects the common agent's notion of the stringency of the duty to not make false promises and how Kant corrects the common agent's notion of duties to self. I finally discuss how his critical practical philosophy can become popular and achieve the correction of the common perspective. I stress the role of education informed by philosophical theory for this and contrast it with so called ‘popular philosophy’.     

Heidegger's Descartes and Heidegger's Cartesianism

Abstract: Heidegger's Sein und Zeit (SZ) is commonly viewed as one of the 20^th century's great anti‐Cartesian works, usually because of its attack on the epistemology‐driven dualism and mentalism of modern philosophy of mind or its apparent effort to ‘de‐center the subject’ in order to privilege being or sociality over the individual. Most who stress one or other of these anti‐Cartesian aspects of SZ, however, pay little attention to Heidegger's own direct engagement with Descartes, apart from the compressed discussion in SZ §§19–21. I here show through a careful reading of Heidegger's lectures on Descartes from the years immediately preceding SZ that, while he has sharp criticisms of Descartes and certain ‘Cartesian’ aspects of modern philosophy along the lines commonly recognized, he also aims to disclose what he calls the ‘positive possibilities’ in Descartes and the philosophy he inspired. I detail a number of these and then show that they force us to see Heidegger's own early project as largely unconcerned with dualism and mentalism per se, and much more with questions of the philosophical methodology that gives rise to them. Moreover, I show that a careful reading of Heidegger's treatment of the cogito makes clear that he is no serious way attempting to ‘de‐center the subject’ and that the fundamental question of the ‘analytic of Dasein’ is one that takes Descartes as an immediate jumping off point: how can I articulate what I understand myself to be as the general kind of entity I am, and on what besides me does my being depend?     

KARL BARTH AND THE RELATIONSHIP BETWEEN PHILOSOPHY AND THEOLOGY

It is commonly held that Karl Barth emphatically rejected the usefulness of philosophy for theology. In this essay I explore the implications of Barth's theological epistemology for the relationship and proper boundaries between philosophy and theology, given its origin in Barth's theology of revelation. I seek to clarify Barth's position with respect to philosophy by distinguishing the contingency of its offence from any necessary incompatibility. Barth does not reject philosophy per se, but the way in which philosophy is typically conducted. This is made explicit through an analysis of Barth's censure of the uncritical acceptance in theology of modernist philosophical presuppositions. I nuance Barth's response to a collection of philosophical assumptions that are rarely distinguished in theological literature. Finally, I highlight a representative instance of Barth's reflections on philosophy in relationship to theology, to demonstrate that the criterion for evaluating the usefulness of philosophical assumptions and methods in the service of theology is the same criterion by which theology is itself evaluated.     

Hegel's critique of Kant

In this paper we present a reconstruction of Hegel's critique of Kant. We try to show the congruence of that critique in both theoretical and practical philosophy. We argue that this congruence is to be found in Hegel's criticism of Kant's hylemorphism in his theoretical and practical philosophy. Hegel is much more sympathetic to Kant's response to the distinction between matter and form in his theoretical philosophy and he credits Kant with ‘discovering’ here that thinking is an activity that always takes place within a greater whole. He, however, argues that the consequences of this are much more significant than Kant suspects and that, most importantly, the model of cognition in which thought (form) confronts something non-thought (matter) is unsustainable. This leads to Hegel's appropriation of Kantian reflective judgements, arguing that the greater whole in which thinking takes place is a socially shared set of meanings, something resembling what Kant calls a sensus communis. From here, it is not far to Hegel's Geist, which eventually gains self-consciousness in Sittlichkeit, a whole of social practices of mutual recognition. In practical philosophy, Hegel argues for the importance of situating oneself within such a whole in order to attain the self-knowledge required for autonomous, or ethically required, action. For this to happen, he claims, it is necessary to recognise the status of Kantian Moralität as a form of Sittlichkeit or social practice. This would justify our practices without an appeal to a ‘fact of reason’ and also allow a wider range of actions that could count as autonomous.     

When Does Truth Matter? Spinoza on the Relation between Theology and Philosophy

One of the aims of Spinoza's Tractatus Theologico‐Politicus is to vindicate the view that philosophy and theology are separate forms of enquiry, neither of which has any authority over the other. However, many commentators have objected that this aspect of his project fails. Despite his protestations to the contrary, Spinoza implicitly gives epistemological precedence to philosophy. I argue that this objection misunderstands the nature of Spinoza's position and wrongly charges him with inconsistency. To show how he can coherently allow both that theology and philosophy employ independent epistemological standards, and that philosophy is epistemologically superior to theology, we need to step back from the immediate disputes to which the Tractatus is a response and examine a Ciceronian distinction on which Spinoza indirectly draws. As well as enabling us to vindicate Spinoza's position, it places his alleged naturalism in a new light and portrays philosophizing as a form of piety.     

HEGEL'S LEGACY

Answering the challenge of G. W. F. Hegel's idealism and its perceived logocentrism has arguably been a defining feature of nineteenth‐ and twentieth‐century continental philosophy. Today, in the midst of a Hegel renaissance, Hegel's legacy within continental philosophy is far more ambivalent. In this essay, I cut across debates about the status of Hegel's idealism in order to offer a reflection on the legacy of Hegel by reconstructing a Hegelian notion of legacy. I develop this notion in response to Jacques Derrida's discussion of inheritance in Specters of Marx (1993). Both Hegel and Derrida articulate the structure of legacy, inheritance, and history on the basis of the strictures of gathering. For both, gathering is an act of memory that determines a legacy as a legacy, a history as a history. Gathering determines an event, norm, idea, or institution as something to be passed on for a future to come. While Derrida concludes that inheritance implies decision, Hegel's recollection provides the basis for what I will call a critical history, which contributes to any such decision in crucial ways.