In the paper “Math Anxiety,” Aden Evens explores the manner by means of which concepts are implicated in the problematic Idea according to the philosophy of Gilles Deleuze. The example that Evens draws from Difference and Repetition in order to demonstrate this relation is a mathematics problem, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is an historical account of the mathematical problematic that Deleuze deploys in his (...) philosophy, and an introduction to the role that this problematic plays in the develop- ment of his philosophy of difference. One of the points of departure that I will take from the Evens paper is the theme of “power series.”2 This will involve a detailed elaboration of the mechanism by means of which power series operate in the differential calculus deployed by Deleuze in Difference and Repetition. Deleuze actually constructs an alternative history of mathematics that establishes an historical conti- nuity between the differential point of view of the infinitesimal calculus and modern theories of the differential calculus. It is in relation to the differential point of view of the infinitesimal calculus that Deleuze determines a differential logic which he deploys, in the form of a logic of different/ciation, in the development of his proj- ect of constructing a philosophy of difference. (shrink)

The role of mathematics in the development of Gilles Deleuze's (1925-95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze's interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770-1831) presents in the Science of Logic . Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal calculus in his (...) treatment of the problem of the infinitesimal. Against the role that Hegel assigns to integration as the inverse transformation of differentiation in the development of his dialectical logic, Deleuze strategically redeploys Leibniz's account of integration as a method of summation in the form of a series in the development of his philosophy of difference. By demonstrating the relation between the differential point of view of the Leibnizian infinitesimal calculus and the differential calculus of contemporary mathematics, I argue that Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic, and by doing so, sets up the critical perspective from which to construct an alternative logic of relations characteristic of a philosophy of difference. The mode of operation of this logic is then demonstrated by drawing upon the mathematical philosophy of Albert Lautman (1908-44), which plays a significant role in Deleuze's project of constructing a philosophy of difference. Indeed, the logic of relations that Deleuze constructs is dialectical in the Lautmanian sense. (shrink)

Of all twentieth century philosophers, it is Gilles Deleuze whose work agitates most forcefully for a worldview privileging becoming over being, difference over sameness; the world as a complex, open set of multiplicities. Nevertheless, Deleuze remains singular in enlisting mathematical resources to underpin and inform such a position, refusing the hackneyed opposition between ‘static’ mathematical logic versus ‘dynamic’ physical world. This is an international collection of work commissioned from foremost philosophers, mathematicians and philosophers of science, to address the wide range (...) of problematics and influences in this most important strand of Deleuze’s thinking. Contributors are Charles Alunni, Alain Badiou, Gilles Châtelet, Manuel DeLanda, Simon Duffy, Robin Durie, Aden Evens, Arkady Plotnitsky, Jean-Michel Salanskis, Daniel Smith and David Webb. (shrink)

According to the reading of Spinoza that Gilles Deleuze presents in Expressionism in Philosophy: Spinoza, Spinoza's philosophy should not be represented as a moment that can be simply subsumed and sublated within the dialectical progression of the history of philosophy, as it is figured by Hegel in the Science of Logic, but rather should be considered as providing an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Indeed, Deleuze demonstrates, by means of Spinoza, that (...) a more complex philosophy antedates Hegel's which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuze's project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. Deleuze presents Spinoza's metaphysics as determined according to a 'logic of expression', which, insofar as it contributes to the determination of a philosophy of difference, functions as an alternative to the Hegelian dialectical logic. Deleuze's project in Expressionism in Philosophy is therefore to redeploy Spinoza in order to mobilize his philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic. (shrink)

What I plan to do in this paper is to provide a survey of the ways in which Spinoza’s philosophy has been deployed in relation to early modern thought, in the history of ideas and in a number of different domains of contemporary philosophy, and to offer an account of how some of this research has developed. The past decade of research in Spinoza studies has been characterized by a number of tendencies; however, it is possible to identify four main (...) domains that characterize these different lines of research: studies of Spinoza’s individual works, of its problematic concepts, from the point of view of the history of ideas, and comparative studies of Spinoza’s ideas. (shrink)

Maimon’s theory of the differential has proved to be a rather enigmatic aspect of his philosophy. By drawing upon mathematical developments that had occurred earlier in the century and that, by virtue of the arguments presented in the Essay and comments elsewhere in his writing, I suggest Maimon would have been aware of, what I propose to offer in this paper is a study of the differential and the role that it plays in the Essay on Transcendental Philosophy (1790). In (...) order to do so, this paper focuses upon Maimon’s criticism of the role played by mathematics in Kant’s philosophy, to which Maimon offers a Leibnizian solution based on the infinitesimal calculus. The main difficulties that Maimon has with Kant’s system, the second of which will be the focus of this paper, include the presumption of the existence of synthetic a priori judgments, i.e. the question quid facti, and the question of whether the fact of our use of a priori concepts in experience is justified, i.e. the question quid juris. Maimon deploys mathematics, specifically arithmetic, against Kant to show how it is possible to understand objects as having been constituted by the very relations between them, and he proposes an alternative solution to the question quid juris, which relies on the concept of the differential. However, despite these arguments, Maimon remains sceptical with respect to the question quid facti. (shrink)

This article examines the seventeenth-century debate between the Dutch philosopher Benedict de Spinoza and the British scientist Robert Boyle, with a view to explicating what the twentieth-century French philosopher Gilles Deleuze considers to be the difference between science and philosophy. The two main themes that are usually drawn from the correspondence of Boyle and Spinoza, and used to polarize the exchange, are the different views on scientific methodology and on the nature of matter that are attributed to each correspondent. Commentators (...) have tended to focus on one or the other of these themes in order to champion either Boyle or Spinoza in their assessment of the exchange. This paper draws upon the resources made available by Gilles Deleuze and Felix Guattari in their major work What is Philosophy?, in order to offer a more balanced account of the exchange, which in its turn contributes to our understanding of Deleuze and Guattari’s conception of the difference between science and philosophy. (shrink)

In Hegel ou Spinoza,1 Pierre Macherey challenges the influence of Hegel’s reading of Spinoza by stressing the degree to which Spinoza eludes the grasp of the Hegelian dialectical progression of the history of philosophy. He argues that Hegel provides a defensive misreading of Spinoza, and that he had to “misread him” in order to maintain his subjective idealism. The suggestion being that Spinoza’s philosophy represents, not a moment that can simply be sublated and subsumed within the dialectical progression of the (...) history of philosophy, but rather an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Gilles Deleuze also considers Spinoza’s philosophy to resist the totalising effects of the dialectic. Indeed, Deleuze demonstrates, by means of Spinoza, that a more complex philosophy antedates Hegel’s, which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuze’s project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. It is Spinoza’s role in this project that will be demonstrated in this paper by differentiating Deleuze’s interpretation of the geometrical example of Spinoza’s Letter XII (on the problem of the infinite) in Expressionism in Philosophy, Spinoza,2 from that which Hegel presents in the Science of Logic.3. (shrink)

Within the cognitive science of religion, some scholars hypothesize (1) that minimally counterintuitive (MCI) concepts enjoy a transmission advantage over both intuitive and highly counterintuitive concepts, (2) that religions concern counterintuitive agents, objects, or events, and (3) that the transmission advantage of MCI concepts makes them more likely to be found in the world’s religions than other kinds of concepts. We hypothesized that the memorability of many MCI supernatural concepts was due in large part to other characteristics they possess, such (...) as their frequent and salient association with moral concerns and the alleviation of existential anxieties, and that without such characteristics they would fail to be memorable. We report the results of three experiments designed to test the relative contributions of minimal counterintuitiveness, moral valence, and existential anxiety to the memorability of supernatural ideas. We observed no main effects for minimal counterintuitiveness but did observe main effects for both moral valence and existential anxiety. We also found that these effects did not seem to stem from the greater visualizability of morally valenced concepts or concepts that concerned existential anxieties. These findings challenge important claims made by leading researchers regarding MCI concepts within the cognitive science of religion. (shrink)

Escribir hoy en día un libro sobre hermenéutica, que tal hermenéutica se refiera a la desarrollada por G. Gadamer en su conocido Verdad y método y que se pretenda añadir algo nuevo a lo mucho escrito sobre el tema parecería, a primera vista, empresa irrealizable. Que ambas pretensiones inspiren la sólida monografía de María G. Navarro —titulada Interpretar y argumentar— constituye empresa audaz y arriesgada, plena de coraje innovador, que provoca admiración, curiosidad e interés. Contra lo que pudiera parecer a (...) primera vista, el libro contiene un alto componente de originalidad y creatividad, debido a la estratagema metodoló-gica de que se sirve la autora. A saber, una hermenéutica in obliquo, estrategia consistente en interpretar a la hermenéutica gadameriana a través del prisma de la lógica de la argumentación. (shrink)

Human nature has always been a foundational issue for philosophy. What does it mean to have a human nature? Is the concept the relic of a bygone age? What is the use of such a concept? What are the epistemic and ontological commitments people make when they use the concept? In What’s Left of Human Nature? Maria Kronfeldner offers a philosophical account of human nature that defends the concept against contemporary criticism. In particular, she takes on challenges related to (...) social misuse of the concept that dehumanizes those regarded as lacking human nature (the dehumanization challenge); the conflict between Darwinian thinking and essentialist concepts of human nature (the Darwinian challenge); and the consensus that evolution, heredity, and ontogenetic development results from nurture and nature. After answering each of these challenges, Kronfeldner presents a revisionist account of human nature that minimizes dehumanization and does not fall back on outdated biological ideas. Her account is post-essentialist because it eliminates the concept of an essence of being human; pluralist in that it argues that there are different things in the world that correspond to three different post-essentialist concepts of human nature; and interactive because it understands nature and nurture as interacting at the developmental, epigenetic, and evolutionary levels. On the basis of this, she introduces a dialectical concept of an ever-changing and “looping” human nature. Finally, noting the essentially contested character of the concept and the ambiguity and redundancy of the terminology, she wonders if we should simply eliminate the term “human nature” altogether. (shrink)

In English, discourse reference to time involves grammatical tenses interpreted as temporal anaphors. Recently, it has been argued that conditionals involve modal discourse anaphora expressed by a parallel grammatical system of anaphoric modals. Based on evidence from Kalaallisut, this paper argues that temporal and modal anaphora can be just as precise in a language that does not have either grammatical category. Instead, temporal anaphora directly targets eventualities of verbs, without mediating tenses, while modal anaphora involves anaphoric moods and/or attitudinal verbs.

In this Chapter, Maria Kronfeldner discusses whether psychological essentialism is a necessary part of dehumanization. This involves different elements of essentialism, and a narrow and a broad way of conceptualizing psychological essentialism, the first akin to natural kind thinking, the second based on entitativity. She first presents authors that have connected essentialism with dehumanization. She then introduces the error theory of psychological essentialism regarding the category of the human, and distinguishes different elements of psychological essentialism. On that basis, Kronfeldner (...) connects historical, socio-psychological, and philosophical insights in order to show that although essentialism can act as a catalyst for dehumanization, it is not necessary for it. Examples relate to dehumanization in the context of colonialism and evolutionary thinking, to the history of dehumanizing women from Aristotle to 19th-century craniology, and to contemporary self-dehumanization and ‘lesser mind’ attribution. (shrink)

Interview with the author of "why We are in Need of Tails." Iguana Books, Toronto, Canada.

Readers are awaiting a new encounter with stories united under the common title Why We Are in Need of Tales. Let me remind you that these deep philosophical books were written by Maria daVenza Tillmanns, a professional philosopher dedicated to the study of philosophizing with children, who has gained valuable experience in this field. Maria’s books are inspired by her work with her students at El Toyon Elementary School in National City (California), with whom Maria held philosophy (...) with children classes for three years before COVID-19. With parental permission, the children provided their drawings, which are used as illustrations for the books. I read Why We Are in Need of Tales, Part III with great pleasure. The focus of this book is on making decisions, sometimes very hard decisions. In Part II, the focus is on dreams — hopes and wishes we have for life. This book looks at how we may best decide how to make those hopes and wishes come true. And the answer Huk and Tuk suggest is deceptively easy: by making decisions “with your eyes wide open.” (5, p. ix). The author of this excellent book managed to describe how to make decisions with your eyes wide open through the playful dialogue between Huk and Tuk. The books are written in dialogue so the reader immediately plunges into the context of a lively conversation. Dialogue not only sharpens attention, but also invites the reader to participate in the conversation. In this way, the reader becomes a listener at the same time. (shrink)

The reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold provides a systematic account of the structure of Leibniz’s metaphysics in terms of its mathematical foundations. However, in doing so, Deleuze draws not only upon the mathematics developed by Leibniz—including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus—but also upon developments in mathematics made by a number of Leibniz’s contemporaries—including Newton’s method of fluxions. He also draws upon a number of subsequent (...) developments in mathematics, the rudiments of which can be more or less located in Leibniz’s own work—including the theory of functions and singularities, the Weierstrassian theory of analytic continuity, and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the Weierstrassian theory of analytic continuity serves to clarify Leibniz’s work, Poincaré’s theory of automorphic functions offers a solution to overcome and extend the limits that Deleuze identifies in Leibniz’s metaphysics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. This essay is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

Michael Hunter, The Boyle Papers: Understanding the Manuscripts of Robert Boyle. With contributions by Edward B. Davis, Harriet Knight, Charles Littleton and Lawrence M. Principe. Aldershot, England; Burlington, VT: Ashgate, 2007. Pp. xiii + 674. US$139.95/£70.00 HB. -/- The publication by Michael Hunter of this revised edition of the catalogue of the Boyle Papers contributes admirably to the renaissance in Boyle studies which has taken place over the past decade and a half. Robert Boyle (1627–91), arguably the most influential British (...) scientist of the late seventeenth century, was a pioneering experimenter, profound thinker, and figure-head of the new science in its early years of development. This volume brings together the materials necessary for understanding the Boyle archive, one of the most important archives from this period, which has been at the Royal Society since 1769. (shrink)

Explications of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in 'The Fold: Leibniz and the Baroque' focus predominantly on the role of the infinitesimal calculus developed by Leibniz.1 While not underestimat- ing the importance of the infinitesimal calculus and the law of continuity as reflected in the calculus of infinite series to any understanding of Leibniz’s metaphysics and to Deleuze’s reconstruction of it in The Fold, what I propose to examine in this paper is the role played by other (...) developments in mathematics that Deleuze draws upon, including those made by a number of Leibniz’s near contemporaries – the projective geometry that has its roots in the work of Desargues (1591–1661) and the ‘proto-topology’ that appears in the work of Du ̈rer (1471–1528) – and a number of the subsequent developments in these fields of mathematics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. What is provided in this paper is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

Michiel Wielema: The March of the Libertines. Spinozists and the Dutch Reformed Church (1660–1750). ReLiC: Studies in Dutch Religious History. Hilversum: Uitgeverij Verloren, 2004; pp. 221. The Dutch Republic of the seventeenth century is famous for having cultivated an extraordinary climate of toleration and religious pluralism — the Union of Utrecht supported religious freedom, or “freedom of conscience”, and expressly forbade reli- gious inquisition. However, despite membership in the state sponsored Calvinist Dutch Reformed Church not being compulsory, the freedom to (...) gather and worship, or “to air anti-Christian or atheistic opinions” was little tolerated “within” the organized structure of the church, which functioned more as “an exclusive organisation for those willing to submit freely to certain confessional canons and to the disciplinary author- ity of the church’s governing bodies” (10): the consistories, classes, and synods. Those not prepared to submit to Reformed doctrine were free to leave the church without fear of any legal or political repercussions. However, for those not prepared to leave for reasons of personal belief, matters turned out to be quite different. Because the Reformed Church enjoyed full State protection, matters of doctrinal conflict could well evolve into political affairs. And, contrary to the Union of Utrecht, religious inquisition was in some cases actually applied with political approval for “heretics” within the Reformed Church. The main focus of The March of the Libertines is an investigation of this obvious tension. (shrink)

In 1969 Harry Frankfurt published his hugely influential paper 'Alternate Possibilities and Moral Responsibility' in which he claimed to present a counterexample to the so-called 'Principle of Alternate Possibilities' ('a person is morally responsible for what he has done only if he could have done otherwise'). The success of Frankfurt-style cases as counterexamples to the Principle has been much debated since. I present an objection to these cases that, in questioning their conceptual cogency, undercuts many of those debates. Such cases (...) all require a counterfactual mechanism that could cause an agent to perform an action that he cannot avoid performing. I argue that, given our concept of what it is for someone to act, this requirement is inconsistent. Frankfurt-style alleged counterexamples are cases where an agent is morally responsible for an action he performs even though, the claim goes, he could not have avoided performing that action. However, it has recently been argued, e.g. by John Fischer, that a counterexample to the Principle could be a 'Fischer-style case', i.e. a case where the agent can either perform the action or do nothing else. I argue that, although Fischer-style cases do not share the conceptual flaw common to all Frankfurt-style cases, they also fail as counterexamples to the Principle. The paper finishes with a brief discussion of the significance of the Principle of Alternate Possibilities. (shrink)

It is generally agreed that for blame to be appropriate the wrongdoer must be blameworthy. However, blameworthiness is not sufficient for appropriate blame. It has been argued that for blame to be appropriate the blamer must have standing to blame. Philosophers writing on the topic have distinguished several considerations that might defeat someone’s standing to blame. This paper examines the underexplored consideration of how personal relationships can influence who has the standing to express blame. We seem to assume that if (...) we do not stand in the right relation to the wrongdoer, it is not our business to blame them. I identify three challenges to this view. First, we do not know what is wrong with meddling (whether it is morally or prudentially wrong). Second, there are cases where we have no close relation to the wrongdoer, but where we seem to have standing nonetheless – murder and other serious moral offences are examples of this. Third, we don’t seem to have a clear conception of what ‘standing’ means, and this makes it hard to see how discussion on standing can help us determine the propriety of blame. This paper defends the notion of standing as a propriety condition on blame in cases of meddling. I argue that personal relationships influence who has the standing to blame through constitution of relationship-specific norms; and that the role these norms play in developing and regulating our relationships can explain why meddlesome blame is morally wrong. (shrink)

Maria Kronfeldner’s Preface and Introduction to the Routledge Handbook of Dehumanization maps the landscape of dehumanization studies. She starts with a brief portrayal of the history of the field. The systematically minded sections that follow guide the reader through the resulting rugged landscape represented in the Handbook’s contributions. Different realizations, levels, forms, and ontological contrasts of dehumanization are distinguished, followed by remarks on the variety of targets of dehumanization. A discussion on valence and emotional aspects is added. Causes, functions, (...) and consequences of dehumanization, and the prospects for reducing or undoing it, are introduced. The systematic overview closes with a discussion of some important theoretical complexities that arise in studying dehumanization. After these systematic sections, the scholarly work on dehumanization gets situated in the broader intellectual landscape of debates about the ‘human’ in the humanities and social sciences. The Introduction ends with some notes on scope, limitations, and intended readership of the Handbook. (shrink)

This paper advances the view that the history of philosophy is both a kind of history and a kind of philosophy. Through a discussion of some examples from epistemology, metaphysics, and the historiography of philosophy, it explores the benefit to philosophy of a deep and broad engagement with its history. It comes to the conclusion that doing history of philosophy is a way to think outside the box of the current philosophical orthodoxies. Somewhat paradoxically, far from imprisoning its students in (...) outdated and crystallized views, the history of philosophy trains the mind to think differently and alternatively about the fundamental problems of philosophy. It keeps us alert to the fact that latest is not always best, and that a genuinely new perspective often means embracing and developing an old insight. The upshot is that the study of the history of philosophy has an innovative and subversive potential, and that philosophy has a great deal to gain from a long, broad, and deep conversation with its history. (shrink)

We analyze Case in terms of independent constraints on syntactic structures — namely, the Projection Principle (inherent Case), the ECP (marked structural Case), and the theory of extended projections (the nominative, a Caseless nominal projection). The resulting theory accounts for (1) the government constraint on Case assignment, (2) all major Case systems (accusative, ergative, active, three-way, and split), (3) Case alternations (passive, antipassive, and ECM), and (4) the Case of nominal possessors. Structural Case may correlate with pronominal agreement because the (...) former can, and the latter must, involve antecedent-government by a functional head. However, neither phenomenon implies the other. (shrink)

Creativity has often been declared, especially by philosophers, as the last frontier of science. The assumption is that it will defy explanation forever. I will defend two claims in order to oppose this assumption and to demystify creativity: (1) the perspective that creativity cannot be explained wrongly identifies creativity with what I shall call metaphysical freedom; (2) the Darwinian approach to creativity, a prominent naturalistic account of creativity, fails to give an explanation of creativity, because it confuses conceptual issues with (...) explanation. I will close with some remarks on the status and differences in some explanations available in contemporary cognitive science. (shrink)

The central claim of this paper is that surface-faithful word-by-word update is feasible and desirable, even in languages where word order is supposedly free. As a first step, in sections 1 and 2, I review an argument from Bittner 2001a that semantic composition is not a static process, as in PTQ, but rather a species of anaphoric bridging. But in that case the context-setting role of word order should extend from cross-sentential discourse anaphora to sentence-internal anaphoric composition. This can be (...) spelled out as a two-part hypothesis. First, in all languages anaphoric composition derives incremental updates based on the topological order rather than the syntactic hierarchy. And secondly, rigid vs. free word order is simply rigid vs. free mapping from syntax to topology. To formalize this hypothesis, I first present, in section 3, Sevensorted Logic of Change with Centering. This makes it possible, in section 4, to articulate a system of constraints on basic meanings in Kalaallisut — a polysynthetic language with free word order, ideally suited to test the hypothesis of incremental update. The key assumptions about topology as the input to anaphoric composition are spelled out in section 5, which concludes the development of a general formal framework. This formal framework then serves, in sections 6 through 8, t o explicate topologically based incremental updates for increasingly more complex samples of an actual Kalaallisut text. This reveals ubiquitous patterns of prominence-guided anaphora, in all semantic domains, t o increasingly more complex types of discourse referents. These anaphoric patterns show that the context-setting role of word order indeed does extend from discourse to word-to-word anaphora. And this, in turn, strongly supports the hypothesis of topologically based anaphoric composition. Finally, in section 9 I adduce evidence from English that this hypothesis also holds for languages with rigid word order, albeit the fixed mapping keeps the topology close to the syntax. I conclude that both free and rigid word orders receive a natural account if semantic composition is viewed as topologically based anaphoric bridging.. (shrink)

The Eskimo language Kalaallisut (alias West Greenlandic) has traditionally been described as having a rich tense system, with three future tenses (Kleinschmidt 1851, Bergsland 1955, Fortescue 1984) and possibly four past tenses (Fortescue 1984). Recently however, Shaer (2003) has challenged these traditional claims, arguing that Kalaallisut is in fact tenseless.

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this purpose (...) are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (shrink)

This paper describes quantificational structures in Greenlandic Eskimo (Kalaallisut), a language where familiar quantificational meanings are expressed in ways that are quite different from English. Evidence from this language thus poses some formidable challenges for cross-linguistic theories of compositional semantics.

To make sense of what Gilles Deleuze understands by a mathematical concept requires unpacking what he considers to be the conceptualizable character of a mathematical theory. For Deleuze, the mathematical problems to which theories are solutions retain their relevance to the theories not only as the conditions that govern their development, but also insofar as they can contribute to determining the conceptualizable character of those theories. Deleuze presents two examples of mathematical problems that operate in this way, which he considers (...) to be characteristic of a more general theory of mathematical problems. By providing an account of the historical development of this more general theory, which he traces drawing upon the work of Weierstrass, Poincaré, Riemann, and Weyl, and of its significance to the work of Deleuze, an account of what a mathematical concept is for Deleuze will be developed. (shrink)

This paper introduces a framework for direct surface composition by online update. The surface string is interpreted as is, with each morpheme in turn updating the input state of information and attention. A formal representation language, Logic of Centering, is defined and some crosslinguistic constraints on lexical meanings and compositional operations are formulated.

It has long been recognized that temporal anaphora in French and English depends on the aspectual distinction between events and states. For example, temporal location as well as temporal update depends on the aspectual type. This paper presents a general theory of aspect-based temporal anaphora, which extends from languages with grammatical tenses (like French and English) to tenseless languages (e.g. Kalaallisut). This theory also extends to additional aspect-dependent phenomena and to non-atomic aspectual types, processes and habits, which license anaphora to (...) proper atomic parts (cf. nominal pluralities and kinds). (shrink)

This paper argues that the so-called ‘paradox’ of dehumanization is a mirage arising from misplaced abstraction. The alleged ‘paradox’ is taken as a challenge that arises from a skeptical stance. After reviewing the history of that skeptical stance, it is reconstructed as an argument with two premises. With the help of an epistemologically structured but pluralistic frame it is then shown how the two premises of the Skeptic’s argument can both be debunked. As part of that it emerges that there (...) are a couple of ways how dehumanization can be realized, and one such realization can be sufficient for affirming the reality of dehumanization for a specific case. (shrink)

Plato’s philosophy is important to Badiou for a number of reasons, chief among which is that Badiou considered Plato to have recognised that mathematics provides the only sound or adequate basis for ontology. The mathematical basis of ontology is central to Badiou’s philosophy, and his engagement with Plato is instrumental in determining how he positions his philosophy in relation to those approaches to the philosophy of mathematics that endorse an orthodox Platonic realism, i.e. the independent existence of a realm of (...) mathematical objects. The Platonism that Badiou makes claim to bears little resemblance to this orthodoxy. Like Plato, Badiou insists on the primacy of the eternal and immu- table abstraction of the mathematico-ontological Idea; however, Badiou’s reconstructed Platonism champions the mathematics of post-Cantorian set theory, which itself af rms the irreducible multiplicity of being. Badiou in this way recon gures the Platonic notion of the relation between the one and the multiple in terms of the multiple-without-one as represented in the axiom of the void or empty set. Rather than engage with the Plato that is gured in the ontological realism of the orthodox Platonic approach to the philosophy of mathematics, Badiou is intent on characterising the Plato that responds to the demands of a post-Cantorian set theory, and he considers Plato’s philosophy to provide a response to such a challenge. In effect, Badiou reorients mathematical Platonism from an epistemological to an ontological problematic, a move that relies on the plausibility of rejecting the empiricist ontology underlying orthodox mathematical Platonism. To draw a connec- tion between these two approaches to Platonism and to determine what sets them radically apart, this paper focuses on the use that they each make of model theory to further their respective arguments. (shrink)

Continuing Franz Boas' work to establish anthropology as an academic discipline in the US at the turn of the twentieth century, Alfred L. Kroeber re-defined culture as a phenomenon sui generis. To achieve this he asked geneticists to enter into a coalition against hereditarian thoughts prevalent at that time in the US. The goal was to create space for anthropology as a separate discipline within academia, distinct from other disciplines. To this end he crossed the boundary separating anthropology from biology (...) in order to secure the boundary. His notion of culture, closely bound to the concept of heredity, saw it as independent of biological heredity (culture as superorganic) but at the same time as a heredity of another sort. The paper intends to summarise the shifting boundaries of anthropology at the beginning of the twentieth century, and to present Kroeber?s ideas on culture, with a focus on how the changing landscape of concepts of heredity influenced his views. The historical case serves to illustrate two general conclusions: that the concept of culture played and plays different roles in explaining human existence; that genetics and the concept of Weismannian hard inheritance did not have an unambiguous unidirectional historical effect on the vogue for hereditarianism at that time; on the contrary, it helped to establish culture in Kroeber's sense, culture as independent of heredity. (shrink)

The aim of this chapter is to test the degree to which Deleuze’s philosophy can be reconciled with the subject naturalist approach to pragmatism put forward by Macarthur and Price.

: This study describes a new field method, suited for investigating scope relations — and other aspects of truth conditional meaning — with native speaker consultants who may speak no other language and have no background in linguistics or logic. This method revealed a surprising scope contrast between the antipassive and the ergative construction in Greenlandic Eskimo. The results of this field work are described in detail and a crosslinguistic scope generalization is proposed based on Greenlandic Eskimo, Basque, Polish, Russian, (...) Finnish and English. (shrink)

The theme of the conflict between the different interpretations of Spinoza’s philosophy in French scholarship, introduced by Christopher Norris in this volume and expanded on by Alain Badiou, is also central to the argument presented in this chapter. Indeed, this chapter will be preoccupied with distinguishing the interpretations of Spinoza by two of the figures introduced by Badiou. The interpretation of Spinoza offered by Gilles Deleuze in Expressionism in Philosophy provides an account of the dynamic changes or transformations of the (...) characteristic relations of a Spinozist finite existing mode, or human being. This account has been criticized more or less explicitly by a number of commentators, including Charles Ramond. Rather than providing a defence of Deleuze on this specific point, which I have done elsewhere, what I propose to do in this chapter is provide an account of the role played by “joyful passive a affections” in these dynamic changes or transformations by distinguishing Deleuze’s account of this role from that offered by one of his more explicit critics on this issue, Pierre Macherey. An appreciation of the role played by “joyful passive affections” in this context is crucial to understanding how Deleuze’s interpretation of Spinoza is implicated in his broader philosophical project of constructing a philosophy of difference. The outcome is a position that, like Badiou in the previous chapter, rules out “intellect in potentiality” but maintains a role for the joyful passive affects in the development of adequate ideas. (shrink)

Much has been made of Deleuze’s Neo-Leibnizianism,3 however not very much detailed work has been done on the specific nature of Deleuze’s critique of Leibniz that positions his work within the broader framework of Deleuze’s own philo- sophical project. The present chapter undertakes to redress this oversight by providing an account of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold. Deleuze provides a systematic account of the structure of Leibniz’s metaphys- ics in terms of its mathematical underpinnings. (...) However, in doing so, Deleuze draws upon not only the mathematics developed by Leibniz – including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus – but also the developments in mathematics made by a number of Leibniz’s contemporaries – including Newton’s method of fluxions – and a number of subsequent developments in mathematics, the rudiments of which can be more or less located in Leibniz’s own work – including the theory of functions and singularities, the theory of continuity and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the theory of continuity serves to clarify Leibniz’s work, Poincaré’s theory of automorphic functions offers a solution to overcome and extend the limits that Deleuze identifies in Leibniz’s metaphysics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. What is provided in this chapter is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

In the face of causal complexity, scientists reconstitute phenomena in order to arrive at a more simplified and partial picture that ignores most of the 'bigger picture.' This paper will distinguish between two modes of reconstituting phenomena: one moving down to a level of greater decomposition (toward organizational parts of the original phenomenon), and one moving up to a level of greater abstraction (toward different differences regarding the phenomenon). The first aim of the paper is to illustrate that phenomena are (...) moving targets, i.e., they are not fixed once and for all, but are adapted, if necessary, on the basis of the preferred perspective adopted for pragmatic reasons. The second aim is to analyze in detail the second mode of reconstituting phenomena. This includes an exposition of the kind of pragmatic-pluralistic picture resulting from the fact that phenomena are reconstituted by a move up to a level of greater abstraction. (shrink)

Important empirically informed proposals of virtue cultivation invoke techniques of goal pursuit. This paper argues that these techniques are effective in changing behavior due to the attention narrowing they bring about, and further show that such attention narrowing can threaten the appropriate exercise of phronetic-related capacities. When these phronetic-related capacities are threatened, two derivative problems arise: (1) One can end up acting in morally inappropriate ways, and (2) Even in cases where one performs the morally appropriate action, one nonetheless can (...) fail to notice and appreciate features of moral value. In light of these concerns, such techniques of goal pursuit – at least, by themselves – serve the most good for those who are merely trying to avoid vice, rather than cultivate virtue. And so, I suggest that such accounts of virtue cultivation are incomplete. I then go on to argue that these undesirable effects of attention narrowing brought about by these goal pursuit techniques may be ameliorated by also engaging in certain indirect modifications of cognition, particularly those which broaden attention. The suggestion, then, is that attention narrowing techniques of goal pursuit, along with attention broadening modifications, might best facilitate virtue cultivation when employed together. While the particulars of how we might best go about this are currently unclear, this paper ends by looking at empirical research on Open Monitoring Meditation as providing a hopeful option that might be further investigated. (shrink)

Recent philosophical work on the concept of human nature disagrees on how to respond to the Darwinian challenge, according to which biological species do not have traditional essences. Three broad kinds of reactions can be distinguished: conservative intrinsic essentialism, which defends essences in the traditional sense, eliminativism, which suggests dropping the concept of human nature altogether, and constructive approaches, which argue that revisions can generate sensible concepts of human nature beyond traditional essences. The different constructive approaches pick out one or (...) two of the three epistemic roles that are fused in traditional essentialist conceptions of human nature: descriptive, explanatory, definitional, or explanatory and definitional. These turns towards diverging epistemic roles are best interpreted pluralistically: there is a plurality of concepts of human nature that have to be clearly distinguished, each with a legitimate role in respective scientific contexts. (shrink)

This paper spells out the ways in which we need to be pluralists about “human nature”. It discusses a conceptual pluralism about the concept of “human nature”, stemming from post-essentialist ontology and the semantic complexity of the term “nature”; a descriptive pluralism about the “descriptive nature” of human beings, which is a pluralism regarding our self-understanding as human beings that stems from the long list of typical features of, and relations between, human beings; a natural kind term pluralism, which is (...) a pluralism that concerns the choices we have in deciding how to apply the kind term “human”; and an explanatory pluralism that results from the causal complexity of life. Because of the complexity of being human, which gives rise to these pluralisms, being human is, the paper claims, a kaleidoscopic affair, and one far from concerning the life sciences only. (shrink)

Over the last four decades arguments for and against the claim that creative hypothesis formation is based on Darwinian ‘blind’ variation have been put forward. This paper offers a new and systematic route through this long-lasting debate. It distinguishes between undirected, random, and unjustified variation, to prevent widespread confusions regarding the meaning of undirected variation. These misunderstandings concern Lamarckism, equiprobability, developmental constraints, and creative hypothesis formation. The paper then introduces and develops the standard critique that creative hypothesis formation is guided (...) rather than blind, integrating developments from contemporary research on creativity. On that basis, I discuss three compatibility arguments that have been used to answer the critique. These arguments do not deny guided variation but insist that an important analogy exists nonetheless. These compatibility arguments all fail, even though they do so for different reasons: trivialisation, conceptual confusion, and lack of evidence respectively. Revisiting the debate in this manner not only allows us to see where exactly a ‘Darwinian’ account of creative hypothesis formation goes wrong, but also to see that the debate is not about factual issues, but about the interpretation of these factual issues in Darwinian terms. (shrink)

This paper focuses on negative exemplarity-related emotions (NEREs) and on their educational implications. In this paper, we will first argue for the nonexpendability of negative emotions broadly conceived (section 2) by defending their instrumental and intrinsic role in a good and flourishing life. In section 3, we will make the claim more specific by focusing on the narrower domain of NEREs and argue for their moral and educational significance by evaluating whether they fit the arguments provided in the previous section. (...) In section 4, we will propose three educational strategies to foster NEREs’ positive moral role. In conclusion, we will point out that an exemplarist approach to character education would greatly benefit from a more fine-grained account of the emotions involved in the educational process and from a broader perspective on which of these emotions should be taken as valuable for educational purposes. (shrink)

Two conceptions of motivating reasons, i.e. the reasons for which we act, can be found in the literature: (1) the dominant 'psychological conception', which says that motivating reasons are an agent's believing something; and (2) the 'non-psychological' conception, the minority view, which says that they are what the agent believes, i.e. his beliefs. In this paper I outline a version of the minority view, and defend it against what have been thought to be insuperable difficulties - in particular, difficulties concerning (...) 'error cases' (cases where what the agent believes is false); and difficulties concerning the explanation of action. Concerning error cases, I argue that if we are motivated by something believed that is true, what motivates us to act is a motivating reason. By contrast, if we are motivated by something believed that is false, then what motivates us to act is merely an apparent motivating reason. Either way, what motivates us is, as the non-psychological conception says, what we believe and not our believing it. I offer an account of the relation between motivating reasons and the explanation of action, and argue that this account helps bring out two important points. One is that the fact that we often do, and indeed sometimes must, use explanations such as 'He did it because he believed that p' does not vindicate the psychological conception of motivating reasons. The other is that endorsing the non-psychological conception of motivating reasons does not commit one to a non-factive view of explanations of action. (shrink)

Human nature is a concept that transgresses the boundary between science and society and between fact and value. It is as much a political concept as it is a scientific one. This chapter will cover the politics of human nature by using evidence from history, anthropology and social psychology. The aim is to show that an important political function of the vernacular concept of human nature is social demarcation (inclusion/exclusion): it is involved in regulating who is ‘us’ and who is (...) ‘them.’ It is a folk concept that is used for dehumanization, for denying (a) membership in humankind or (b) full humanness to certain people in order to include or exclude them from various forms of politically relevant aspects of human life, such as rights, power, etc. (shrink)

This thesis sets out an argument in defence of moral objectivism. It takes Mackie as the critic of objectivism and it ends by proposing that the best defence of objectivism may be found in what I shall call Kantian intuitionism, which brings together elements of the intuitionism of Ross and a Kantian epistemology. The argument is fundamentally transcendental in form and it proceeds by first setting out what we intuitively believe, rejecting the sceptical attacks on those beliefs, and by then (...) proposing a theory that can legitimize what we already do believe. Chapter One sets out our intuitive understanding of morality: that morality is cognitive, moral beliefs can be true or false; that morality is real, we do not construct it; that morality is rational, we can learn about it by rational investigation; and that morality places us under an absolute constraint. The chapter ends by clarifying the nature of that absolute demand and by arguing that the critical idea within morality is the idea of duty. In Chapter Two Mackie’s sceptical attack on objectivism is examined. Four key arguments are identified: that moral beliefs are relative to bfferent agents; that morality is based upon on non-rational causes; that the idea of moral properties or entities is too queer to be sustainable; and that moral objectivism involves queer epistemological commitments. Essentially all of these arguments are shown to be ambiguous; however it is proposed that Mackie has an underlying epistemological and metaphysical theory, scientific empiricism, which is hostile to objectivism and a theory that many find attractive for reasons that are independent of morality. Chapter Three explores the nature of moral rationality and whether scientific empiricism can use the idea of reflective equilibrium to offer a reasonable account of moral rationality. It concludes that, while reflective equilibrium is a useful account of moral rationality, it cannot be effectively reconciled with scientific empiricism. In order to function effectively as a rational process, reflective equilibrium must be rationally constrained by our moral judgements and our moral principles. Chapter Four begins the process of exploring some alternative epistemologies and argues that the only account that remains true to objectivism and the needs of reflective equilibrium is the account of intuitionism proposed by Ross. However this account can be developed further by drawing upon number of Kantian ideas and using them to supplement Ross’s intuitionism. So Chapter Five draws upon a number of Kant's ideas, most notably some key notions from the Critique of Judgement. These ideas are: that we possess a rational will that is subject to the Moral law and determined by practical reason; that we possess a faculty of judgement which enables us to become aware of moral properties and that these two faculties together with the third faculty of thought can function to constitute the moral understanding. Using these ideas the thesis explores whether they can serve to explain how intuitions can be rational and how objectivism can be justified. (shrink)

This chapter discusses the topics of trust and expertise from the perspective of political epistemology. In particular, it addresses four main questions: (§1) How should we characterise experts and their expertise? (§2) How can non-experts recognize a reliable expert? (§3) What does it take for non-experts to trust experts? (§4) What problems impede trust in experts?

Crosslinguistically, causative constructions conform to the following generalization: If the causal relation is syntactically concealed, then it is semantically direct. Concealed causatives span a wide syntactic spectrum, ranging from resultative complements in English to causative subjects in Miskitu. A unified type-driven theory is proposed which attributes the understood causal relation—and other elements of constructional meaning—to type lifting operations predictably licensed by type mismatch at LF. The proposal has far-reaching theoretical implications not only for the theory of compositionality and causation, but (...) also for the underlying theory of events, space, and time, in natural language discourse. (shrink)