The article aims to reconstruct the seventeenth-century debate of the scientific nature of mathematics and the possibility of conceiving an idea of a positive infinite to address the philosophical implications of mathematics in Spinoza’s work, emphasizing the geometric ordering in his Ethics. We will approach the mathematical thinking of that philosopher from three perspectives: the pedagogical, the epistemological and the ontological. In the pedagogical sense, his synthetic geometry aims to inhabit the evidence as rhetorical and pedagogical expression of a (...) perfect and self-evident concatenation that leads the progress of the reader through philosophical propositions. In the epistemological sense, we have the aim of inhabiting the thing defined by a genetic definition that provides the very acting essence of a thing. That epistemological sense provides us the difference between a definition of a thing by its predicates or through its inner essence. And finally, in the ontological sense of inhabiting the infinite itself, because geometry can bring us the proper way to conceive the positive idea of the absolutely infinite in which we necessarily are and take part. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Meaning in Spinoza’s MethodAlan Nelson and Noa SheinAaron V. Garrett. Meaning in Spinoza’s Method. New York: Cambridge University Press, 2003. Pp. xii + 240. Cloth, $60.00.This is a book about some fundamental aspects of Spinoza's mature metaphysics. The principal focus is on Part I of the Ethics concerning infinite substance, and on Part V concerning the intuitive knowledge that is the goal of philosophy. Within this focus, Garrett (...) concentrates on Spinoza's method. Garrett explains how he has been influenced by interpretations that stress the structural parallel between the synthetic, geometrical presentation of the Ethics and the relations among the ideas of the well-ordered mind. The Ethics proceeds by deriving propositions concerning substance's modes from definitions of substance and related notions while the mind, insofar as it is free from emotions, intuitively knows things as following from God. Garrett's distinctive thesis, however, is that Spinozistic enlightenment depends on the process of emending the intellect as described in one of Spinoza's earliest works, the Treatise on the Emendation of the Intellect. While this work strongly foreshadows many of Spinoza's mature doctrines, its exposition much more closely resembles the analytic, non-geometric approach of Descartes's Meditations. Spinoza's therapy for the emendation of our "inadequate" ideas closely parallels Descartes's analytic therapy for making what he calls confused ideas "clear and distinct."Garrett is on firm ground in arguing that the process of enlightenment cannot be an unbroken chain of intuitive deductions. For one thing, the definitions and axioms printed in a copy of the Ethics are first sensed by the reader and are not likely to produce immediately the requisite adequate ideas (172). An example of one of Garrett's interesting conclusions is that the definition of God as consisting of an infinity of attributes, the sixth of Part I of the Ethics (1D6), is preliminary and replaced in the process of therapeutic emendation by a definition of God as self caused. It is only after our ideas have become adequate at the end of the process that we are able to fully appreciate 1D6 (171).One might think that Garrett does not go far enough here because his point can be naturally extended. Definitions might assist us in the process of bringing our adequate ideas to light, but our cognitive goal is making these ideas themselves adequate. What then are the ideas we can make most adequate and exactly what distinguishes them from highly refined ideas that are nevertheless more inadequate than these? On one interpretation it is divine essence, that is, the attributes of thought and extension that are individually most adequately conceived after successful therapy. It is tempting to suppose that a single idea of God as both thinking and extended would be more adequate still, but Spinoza holds that our conceptions of these attributes are "really distinct" in a sense analogous to Descartes's(1P10). Spinoza's 1D6 definition of God as a substance consisting of both these attributes (and perhaps other inconceivable ones) thus seems to indicate a subsumption of the attributes we can conceive under the image of some printed or spoken words. Such an idea would be more inadequate than our adequate conceptions of the individual attributes. One is here strongly reminded of Descartes's characterization in Article 63 of the first Part of his Principles of Philosophy, "... we more readily understand extended substance or thinking substance than substance alone."In his seventh and concluding chapter, Garrett tackles the grand problems of intuitive knowledge or knowledge of "the third kind" and the sense in which Spinoza thought a part of the human mind is eternal. The discussion is necessarily complex, but one great advantage of Garrett's treatment is that he realizes intuitive knowledge cannot consist in the explicit deduction of particular things from God. The detailed determination of particular "everyday objects" requires sensory knowledge which is, of course, never perfectly determinate and therefore inherently inadequate. But we can acquire the "second kind" of adequate knowledge by understanding what our minds have in common with other determinate, finite things. This finally enables us to ascend to an appreciation of these... (shrink)

This chapter takes a fresh look at 3d2 of Spinoza’s Ethics, an absolutely pivotal definition for the ethical theory that ensues. According to it, “we act when something happens, in us or outside us, of which we are the adequate cause,” whereas we are passive “when something happens in us, or something follows from our nature, of which we are only a partial cause.” The definition of activity has puzzled scholars: how can we be an adequate, i.e. complete, cause (...) of an effect outside us (which clearly involves other causal factors as well)? However, the definition of passivity is hardly unproblematic either: how can something follow from the patient’s nature so that the patient can nevertheless be considered only a partial cause? I begin by outlining 3d2 and situating it in the historical context formed by Descartes, Hobbes, and the Aristotelian tradition. Then I show that the existing interpretations do not solve the problem of activity and argue that unraveling the problem requires taking properly into account the distinction between immanent and transeunt causality. In relation to the definition of passivity, I argue that Spinoza’s geometry-inspired theory of essence constitution offers the key to understanding the nature of passions. (shrink)

At the opening of Spinoza’s Ethics, we find the three celebrated definitions of substance, attribute, and God: E1d3: By substance I understand what is in itself and is conceived through itself, i.e., that whose concept does not require the concept of another thing, from which it must be formed [Per substantiam intelligo id quod in se est et per se concipitur; hoc est id cujus conceptus non indiget conceptu alterius rei, a quo formari debeat]. E1d4: By attribute I understand what (...) the intellect perceives of a substance, as constituting its essence [Per attributum intelligo id, quod intellectus de substantia percipit, tanquam ejusdem essentiam constituens]. E1d6: By God I understand a being absolutely infinite, that is, a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence We are accustomed to think of these paramount definitions as a fixed and settled formulation of the core of Spinoza’s metaphysics, but if we look at the development of Spinoza’s thought, the picture we get is quite different. In the early drafts of the Ethics and in his early works, Spinoza seems to have experimented with various conceptualizations of the relations between substance, attribute, and God. Some of Spinoza’s works make barely any use of the notions of substance and attribute, and the testimony of Spinoza’s letters suggests that, at a certain stage in his philosophical development, the concept of attribute may have been put on the back burner, if not completely dropped. Indeed, another closely related concept—accident [accidens]—was fated to be pulled out of the system (and for good reasons ). The final version of the Ethics makes hardly any use of this notion, but Spinoza’s letters show that in early drafts of the Ethics he used the term ‘accident’ to refer to what cannot be or be conceived without substance. In this paper I will attempt to provide a brief outline of the genealogy of Spinoza’s key metaphysical concepts. This genealogy, like any other, can help us to reexamine and reconsider what seems to us natural, stable and obvious. In the first part of the paper, I rely on Spinoza’s letters to trace the development of his definitions of substance and attribute in the early drafts of the Ethics. The letters, whose dates are more or less established, also provide a temporal grid for our subsequent discussions. The second part surveys Spinoza’s discussion and conceptualization of substance and attributes in the Treatise on the Emendation of the Intellect, the Theological-Political Treatise (1670), and briefly, Spinoza’s 1663 book on Descartes’ Principles of Philosophy, and its appendix on Metaphysical Thoughts, the Cogitata Metaphysica. The third part of the paper is dedicated to Spinoza’s understanding of substance and attribute in the Short Treatise on God, Man, and His Well-Being. I conclude with some remarks on the stability of Spinoza’s final position on the issue, as expressed in the published version of the Ethics . (shrink)

The work of David R. Lachterman, The Ethics of Geometry, subtitled A Genealogy of Modernity, concerns essentially the status of geometry in Euclid’s Elements and in Descartes’s Geometry. It is a remarkable work, at once by the declared breadth of its ambitions and by the very great precision of its analyses, which are always supported by a prodigious philosophical culture. David Lachterman’s concern is to grasp, by way of an in-depth commentary of certain, particularly crucial passages of these two foundational (...) works, the change in geometry’s status from the one to the other, and this, as a sort of symptom of what the Moderns, since Descartes, will always experience as a necessary, inaugural rupture with regard to tradition. This change is underlaid, according to the author, by a profound change in the philosophical ethos, and in particular, in the geometer’s ethos. One must understand ethos, Lachterman explains, in the manner of Aristotle: those characteristic means that human beings have by which to act in the world or to behave in relation to one another, or to themselves. There is thus an “ethics” of geometry, namely, in the manner and the style of doing geometry, of behaving as a mathematician both toward apprentices and toward the veritable nature of the “entities” which are to be taught or learnt, and which give their discipline its name. That there is a difference of ethos between Euclid and Descartes implies, according to Lachterman, that there is also a difference in the source of intelligibility of the “mathematical,” understood in the most general sense. This in turn implies a deeper difference in the mode of being in general: it suffices to note that, in the ancient case, the source of intelligibility of the geometric figure lies in the nature of the figure itself, and that in the modern case, the same source is found in the “strategies” and “tactics” suited to bringing the figure to its visibility or to its embodiment, 315 in order to notice that this change in the mode of access to intelligibility must have had profound repercussions upon philosophical thought. It is in this sense that the author’s design is also, at the same time, not genetic, but genealogical. The break between ancient and modern mathematics pleas in favor of a consideration of the rupture of modern thought relative to ancient thought; thus, implicitly—and it is one of the great merits of this book that it shows this—against all homogenizing levelling, in Heidegger’s fashion, of the history of thought down to the history of “the” discipline of metaphysics. If there is something Heideggerian, in the best sense of the term, in Lachterman’s way of considering ethos as coextensive with modes of being, there is, on the other hand, and we ought to be very glad of it, something anti-Heideggerian in his original manner of bringing out the effective novelty of modern thought. For, according to him, modern thought is no longer to be defined, explicitly or exclusively, by the so-called “metaphysics of subjectivity.” Instead, it is defined by a self-regulated, operative, and constructive productivity of thought—and this as much with regard to itself as to its objects. To put it briefly, whereas ancient thought is rather polarized by the logico-eidetic, modern thought is polarized by a sort of methodical constructivism, the status of which is, in reality, very complex. If Descartes speaks of “the construction of a problem,” while Leibniz speaks of the “construction of an equation,” and Kant of the “construction of a concept,” everything depends—as we might guess—upon the multiple meanings that the term ‘construction’ may take on. Is it to be taken in the sense of an absolute creation, a quasi ex nihilo creation, which would render mathematics divine? Is it the creation of artefacts, or again, is it the methodical exploration of problems posed to thought by the existence of objects or corresponding ideas, themselves supposed to be somewhere in the divine understanding? We already discern the breadth and the depth of the debate, and we sense that the essential will be played out in Lachterman’s commentaries on the famous Cartesian solution of the problem of Pappus—the birth certificate, as we know, of analytic geometry. (shrink)

In their publications during the 1820s, Jakob Steiner and Julius Plücker frequently derived the same results while claiming different methods. This paper focuses on two such results in order to compare their approaches to constructing figures, calculating with symbols, and representing geometric magnitudes. Underlying the repetitive display of similar problems and theorems, Steiner and Plücker redefined synthetic and analytic methods in distinctly personal practices.

Baruch Spinoza began his studies learning Hebrew and the Talmud, only to be excommunicated at the age of twenty-four for supposed heresy. Throughout his life, Spinoza was simultaneously accused of being an atheist and a God-intoxicated man. Bertrand Russell said that, compared to others, Spinoza is ethically supreme, 'the noblest and most lovable of the great philosophers'. This book is an exploration of (a) what Spinoza understood God to be, (b) how, for him, the infinite and eternal power of God (...) is expressed, and (c) how finite human beings can have a true idea of this greatest of all entities. Sherry Deveaux begins with an analytic discussion of these three questions, and an explication of three different views held by contemporary commentators on Spinoza. She then shows that the commonly held views about Spinoza are inconsistent with Spinoza's texts, especially his magnum opus, the Ethics. Next comes an analysis of topics in Spinoza that must be understood in order correctly to answer the three questions. For example, the notions of 'power' and 'true idea' are discussed, along with Spinoza's definition of the 'essence' of a thing, which is shown to be central to the discussion of Spinoza's God. Deveaux then claims that Spinoza defines God's essence as 'absolutely infinite and eternal power' and that, contrary to the commonly held view that God's essence is identical with the attributes (e.g., thought and extension), God's essence or "power" is expressed through the attributes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Originality of Descartes’s Conception of Analysis as DiscoveryBenoît TimmermansAccording to Descartes, his Meditations employ the method of analysis. This method of proof, says Descartes, “shows the true way by means of which the thing in question was discovered methodically and as it were a priori.” 1 Such a definition of analysis poses a problem that seems to have attracted little attention among commentators until now, namely, why Descartes (...) considers analysis a method of discovery whereas the Scholastic tradition asserts just the contrary, that synthesis allows the discovery of new things, whereas analysis is a method for judging findings or verifying them a posteriori. What is more, the definition that Descartes gives of his analysis contains another divergence, this time brought up by the commentators, 2 for he curiously considers analysis an a priori movement and not an a posteriori movement as dictated by tradition.These issues are all the more important as the analytical method acquired particular prestige in the seventeenth century. This prestige concerned not only philosophy (Descartes, Leibniz, Locke, etc.) but science as well. Thus algebra lost some of its rough edges and gradually took on the name of “analysis.” 3 Descartes created a type of geometry that was soon dubbed “analytic,” and Leibniz developed his analysis infinitorum or differential and integral calculus. If the scientific revolution and the new philosophies that were associated with it attached so much importance to a method that had already been known in ancient Greece, was it not due to a change of the meaning of analysis or at least a rearranging of some of its functions? This is the question that we propose to [End Page 433] tackle while trying to determine to what extent Cartesian analysis breaks with the forms of analysis that preceded it. 4To do this we shall first examine the teachings of Scholastic philosophy concerning the connections between analysis and discovery in general and then study the logical possibilities of discovery through analysis that draw their inspiration from Aristotle’s Analytics and that were developed extensively by the School of Padua in the sixteenth century. Finally, we shall attempt to determine whether the mathematical definition of analysis derived from the works of Euclid and Pappus gives grounds for the correlation with discovery.The Link Between Analysis and Discovery According to the ScholasticsOne might well think that Descartes was completely unaware of the contradiction between his definition of analysis and the teachings of the Scholastics. Had not he always exhibited a true disdain for the latter? However, in September 1640, that is, four months before writing his text on analysis, Descartes began girding for the Jesuit Fathers’ objections to his Meditations. This involved looking for an “abstract of the whole of scholastic philosophy, this would save the time it would take to read their huge tomes.” 5 He finally found what he was looking for in the shops of Leiden, namely, Eustachius a Sancto Paulo’s Summa Philosophiae. There is reason to believe that Descartes read this opus with interest, for two months later he referred to it as “the best book of its kind ever made.” 6 Later he said that he would definitely have chosen the Summa Philosophiae as the basis for refuting the School’s doctrine if he had not given up such a project. 7 Now, Eustachius a Sancto Paulo’s Summa Philosophiae is categorical on the subject of analysis versus synthesis. Analysis of a definition “is perfectly compatible with the doctrines for teaching and learning; as for the other disciplines of discovery, the other method, that is the composite or synthetic method, must be used.” 8According to the Scholastic doctrine as stated by Eustachius a Sancto Paulo, analysis thus plays a part in the teaching of well-known things and in all processes of appraisal, assessment, or judgment. This is easy to explain if one considers that, etymologically, analysis breaks links (ana-luein), goes backward, or climbs back up from the consequences to the principles. Starting from an observation, proposition, or question, it wends its way back to the simplest, [End Page 434] surest items of knowledge that shed light on and verify said starting... (shrink)

Baruch Spinoza began his studies learning Hebrew and the Talmud, only to be excommunicated at the age of twenty-four for supposed heresy. Throughout his life, Spinoza was simultaneously accused of being an atheist and a God-intoxicated man. Bertrand Russell said that, compared to others, Spinoza is ethically supreme, 'the noblest and most lovable of the great philosophers'. This book is an exploration of (a) what Spinoza understood God to be, (b) how, for him, the infinite and eternal power of God (...) is expressed, and (c) how finite human beings can have a true idea of this greatest of all entities. Sherry Deveaux begins with an analytic discussion of these three questions, and an explication of three different views held by contemporary commentators on Spinoza. She then shows that the commonly held views about Spinoza are inconsistent with Spinoza's texts, especially his magnum opus, the Ethics. Next comes an analysis of topics in Spinoza that must be understood in order correctly to answer the three questions. For example, the notions of 'power' and 'true idea' are discussed, along with Spinoza's definition of the 'essence' of a thing, which is shown to be central to the discussion of Spinoza's God. Deveaux then claims that Spinoza defines God's essence as 'absolutely infinite and eternal power' and that, contrary to the commonly held view that God's essence is identical with the attributes (e.g., thought and extension), God's essence or "power" is expressed through the attributes. (shrink)

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which (...) all reality can emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

This article is devoted to the question: does the Duhemian argument support the position taken by those contemporary philosophers who--like W. V. O. Quine and M. White--reject the distinction between analytic and synthetic statements? The term "Duhemian argument" is used to refer to the following statement: it is impossible to put to the test one isolated empirical statement; testing empirical statements involves testing a whole group of hypotheses. An analysis of the logical structure of reductive reasoning leads to (...) the conclusion that the Duhemian argument is valid and that it entails the following statements: (1)--experience alone cannot compel us absolutely to the acceptance of any isolated empirical statement whatsoever, independently of our acceptance or rejection of some other statements, and (2)--no isolated empirical statement can be conclusively falsified by experience, independently of our acceptance or rejection of some other statements. The Duhemian argument seems then to establish conclusively the cogency of the claim that, in principle, it is possible to reject or to maintain any particular empirical statement, provided we make appropriate changes in the system of hypotheses which is put to test. The philosophers who reject the distinction between analytic and synthetic statements--in particular Quine--claim that the same line of reasoning supports their contention. It is alleged that: (1)--the Duhemian argument makes impossible a definition of statement synonymy and, consequently, a definition of analyticity in terms of synonymy, and (2)--that the unit of empirical significance is the whole of science or the total science, and (3)--that it is a folly to seek a boundary between synthetic and analytic statements, because all our statements are equally open to revision. The article tries to show that these conclusions do not follow from the Duhemian argument. In particular it is shown: (1)--that the Duhemian argument does not exclude the definition of statement synonymy, (2)--that this argument does not support the contention that the enigmatic entity called "the whole of science" or the "total science" is involved in each and every testing procedure, (3)--that the principle of fundamental revisability of every statement does not change the fact that in scientific practice the situation is never so hopeless as the Duhemian argument seems to imply, because even inconclusive arguments may differ in their adequacy, and (4)--that the term "revision" is ambiguous and only this ambiguity lends an air of plausibility to Quine's formulations. The conclusion is that the Duhemian line of reasoning does not support the contention of philosophers who reject the distinction between analytic and synthetic statements. (shrink)

Definitions Axioms Prop. I. Substance is by nature prior to its modifications Prop. II. Two substances, whose attributes are different, have nothing in common Prop III. Things, which have nothing in common, cannot be one the cause of the other Prop. IV. Two or more distinct things are distinguished one from the other either by the difference of the attributes of the substance, or by the differences of their modifications Prop. V. There cannot exist in the universe two or more (...) substances having the same nature or attribute Prop. VI. One substance cannot be produced by another substance Prop. VII. Existence belongs to the nature of substance Prop. VIII. Every substance is necessarily infinite Prop. IX. The more reality or being a thing has, the greater the number of its attributes Prop. X. Each particular attribute of the one substance must be conceived through itself Prop. XI. God, or substance consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists Prop. XII. No attribute of substance can be conceived, from which it would follow that substance can be divided Prop. XIII. Substance absolutely infinite is indivisible Prop. XIV. Besides God no substance can be granted or conceived Prop. XV. Whatsoever is, is in God, and without God nothing can be, or be conceived Prop. XVI. From the necessity of the divine nature must follow an infinite number of things in infinite ways--that is, all things which fall within the sphere of infinite intellect Prop. XVII. God acts solely by the laws of his own nature and is not constrained by anyone Prop. XVIII. God is the indwelling and not the transient cause of all things Prop. XIX. God and all the attributes of God are eternal Prop. XX. The existence of God and his essence are one and the same Prop. XXI. All things, which follow from the absolute nature of any attribute of God, must always exist and be infinite, or, in other words, are eternal and infinite through the said attribute Prop.. (shrink)

The present paper is an attempt to give an account of the analytic-synthetic distinction both inside and outside of physical theory. It is hoped that the paper is sufficiently nontechnical to be followed by a reader whose background in science is not extensive; but it has been necessary to consider problems connected with physical science (particularly the definition of 'kinetic energy,' and the conceptual problems connected with geometry) in order to bring out features of the analytic-synthetic (...) distinction that seem to me to be the most important. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting (...) with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

Spinoza's Mediate Infinite Mode TAD M. SCHMALTZ IN PART I of the Ethics, Spinoza argued that a modification is infinite just in case it either "follows from the absolute nature of any attribute of God" or "follows from some attribute of God, as it is modified by such a modification" that is infinite. 1 The main purpose of this argument is to bolster the claim later in this text that a finite modification can follow from a divine attribute only insofar (...) as that attribute is modified by another finite modification. 2 Thus it is understandable that in the section that contains the argument Spinoza did not actually affirm the existence of the two kinds of infinite modifications he mentioned, which following standard practice I call "immediate infinite modes" and "mediate infinite modes," respectively.3 Yet in this section he did 'E IP21,D-22,D, G II 65-66/Curley 429-3 o. In the text and notes of this paper I use the following abbreviations pertaining to Spinoza's writings: E: Ethics ; Ep.: Letters ; RDPP: Descartes' Principles of Philosophy ; CM: Appendix containing Metaphysical Thoughts ; KV: Short Treatise ; TdlE: Treatise on the Emendation of the Intellect ; G: C. Gebhardt, ed., Spinoza Opera, 4 vols. , cited by volume and page; Curley: E. Curley, trans, and ed., The Collected Works of.. (shrink)

DESCARTES was a dualist and Spinoza a monist. If this marks a contrast between them, there ought to be a question to which Descartes’s answer was “two” and Spinoza’s “one”. (a) How many substances are there? Spinoza: “One.” Descartes: “Strictly speaking, one; but if we relax the criteria for substantiality a little, millions.” On no interpretation of the question did Descartes answer, “Two.” (b) How many basic kinds of substance are there? Descartes: “Two.” Spinoza: “Two; though there is only one (...) substance, and it is of both kinds.” Descartes is usually called a dualist because he took thought and extension to be the two basic, logically independent ways of being; but in this sense Spinoza was a dualist, too. If we take seriously his talk of “infinite” attributes, we may call him a pluralist on this point, but certainly not a monist. (c) Of how many substances does an embodied person consist? Descartes (ignoring his views about the divisibility of matter): “Two: an embodied person is made up of a body and a mind, which are distinct substances.” Spinoza: “None: an embodied person is a mode (under two attributes) of the one and only substance, and is not made up of any number of substances.” Those are the questions which come most readily to mind, and none yields a dualist/monist contrast between Descartes and Spinoza. But: (d) Given that A and B are basic, logically independent attributes, what is the smallest number of substances needed to instantiate both A and B? To this Descartes does answer “Two” and Spinoza does answer “One.” I suspect that those who “contrast” Descartes and Spinoza as dualist and monist usually have in mind not the genuine contrast brought out by (d) but rather the fact that Descartes answered “Two” to (b) while Spinoza answered “One” to (a). Still, (d) is important in the thinking of both philosophers and in the philosophy of mind generally. Strawson's chapter, “Persons,” for example, is interesting partly for its Spinozist answer to (d): Strawson does not reduce mental predicates to physical or vice versa, but says that predicates of both kinds may apply to a single thing, namely a person.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:New Essays on the RationalistsSteven NadlerRocco J. Gennaro and Charles Huenemann, editors. New Essays on the Rationalists. Oxford: Oxford University Press, 1999. Pp. xvii + 391. Cloth, $60.00.Here is yet another collection of essays on early modern philosophy. The focus this time is on the Seventeenth century, in particular "the rationalists." What this apparently involves is, as the old-fashioned classification has it, Descartes, Spinoza, and Leibniz. But there (...) is no overall theme to the essays, nothing uniting them besides the fact that almost all are devoted to those three thinkers and the fact that the volume was inspired by a summer seminar run by Jonathan Bennett.What the editors mean by "the rationalists" (besides the extensional definition) is [End Page 437] thinkers "united in the belief that the intellect and human reason are powerful tools in our ability to know about the ultimate nature of mind and matter." What is supposed to separate "the rationalists" from "the empiricists" is "a belief in the power of human reason" (xv). This is a fairly weak claim; and I, for one, am skeptical that such categories are truly useful (or even valid—one would be hard-pressed to find a single issue on which Descartes, Spinoza, and Leibniz all agree and on which those who are usually called "empiricists" unanimously dissent). In the light of so much important and creative work done over the last twenty years in seventeenth-century philosophy, it would have been nice to see a volume devoted to "the rationalists" include at least one sophisticated discussion of the legitimacy and grounds of such a label.The essays in this book are divided into three categories: Matter and Substance; Freedom and Necessity; and Mind and Consciousness. The contributors are a broad mix of scholars: some established and accomplished, others new and up-and-coming. The quality of the work is consistently high. There is a lot of detailed and careful work here, both in the attention to the historical texts and in philosophical analyses. However, not all of the essays are of great scope or interest; in fact, most are not. There is a definite tendency toward the small-scale (but not brevity): a concern with micro-problems (for example, the chapter by Clarence Bonnen and Daniel Flage, "Distinctness," is devoted to the question of what the "distinctness" of an idea is for Descartes) and an emphasis on theses and arguments (such as Geoffrey Gorham's examination of the "similarity condition" for causation in Descartes, "Causation and Similarity in Descartes,"). If there is indeed an "analytical" way of doing history of philosophy, that school is well represented here.And then there are a couple of essays that stand out by transcending this narrowness of focus. The chapters by Catherine Wilson ("The Illusory Nature of Leibniz's System") and Don Garrett ("Teleology in Spinoza and Early Modern Rationalism") are, without question, the boldest and most interesting of the collection. Wilson argues that, in the light of Leibniz's changing and inconsistent views on substance, there really is no metaphysical "system" in his philosophy. Garrett, in what is, to my mind, the best essay in the book (although I think I disagree with him), defends an account of teleology in Spinoza's metaphysics, and then compares Spinoza's views on teleology with those of Aristotle, Descartes, and Leibniz; he concludes that Spinoza not only accepted teleological explanations of particular phenomena, but did so more strongly than anyone else in the modern period. Experts will, of course, disagree with the claims made by Wilson and Garrett; that is what this game is all about. But it is truly refreshing to see scholars such as these taking on large-scale issues.It is worth noting that there is also a nice, indirect dialogue between two of the essays: Charles Huenemann's interesting account of a consistent necessitarianism in Spinoza ("The Necessity of Finite Modes and Geometrical Containment in Spinoza's Metaphysics,") and Edwin Curley and Gregory Walski's argument (in "Spinoza's Necessitarianism Reconsidered,") that, when it comes to the finite modes, Spinoza is not a strong or absolute necessitarian. What is truly unfortunate about the collection, however... (shrink)

Dedekind’s methodology, in his classic booklet on the foundations of arithmetic, has been the topic of some debate. While some authors make it closely analogue to Hilbert’s early axiomatics, others emphasize its idiosyncratic features, most importantly the fact that no axioms are stated and its careful deductive structure apparently rests on definitions alone. In particular, the so-called Dedekind “axioms” of arithmetic are presented by him as “characteristic conditions” in the _definition_ of the complex concept of a _simply infinite_ system. Making (...) sense of Dedekind’s method may be dependent on an analysis of the classical model of deductive science, as presented by authors from the eighteenth and early nineteenth centuries. Studying the modern reconstructions of Euclidean geometry, we show that they did not presuppose deductive independence of the axioms from the definitions. Authors like Wolff elaborated a mathematics _based on definitions_, and the Wolffian model of deductive science shows significant coincidences with Dedekind’s method, despite the great differences in content and approach. Wolff had a conception of definitions as _genetic_, which bears some similarities with Kant’s idea of synthetic definitions: they are understood as positing the content of mathematical concepts and introducing thought objects (_Gedankendinge_) that are the objects of mathematics. The emphasis on the spontaneity of the understanding, which can be found in this philosophical tradition, can also be fruitfully related with Dedekind’s idea of the “free creation” of mathematical objects. (shrink)

Spinoza searched for a language that could help him to create a monistic system of ethics. Latin was in the 17th century a fairly malleable medium of communication. In its philosophical use it was largely a creation of Descartes. Spinoza wanted to use it in a way that would resemble Euclid's treatment of geometry. He needed a language that would clearly and precisely describe the process by which a man could liberate himself from the power of affection that hamper naturaly (...) propensity for social peace and mental equaenimity. He decided to begin by describing nature, which was responsible for man's proclivities and abilities. Consequently he needed a new conception of substance which on the one hand could be definied by some initial axioms, and on the other hand would sufficiently flexible to include various aspects of human thought. It is interesting that when Spinoza had to make a choice between flexibility and content, he resolved to adopt a strict method of reasoning at the cost of the received understanding of substance. It is possible that these linguistic considerations led him to adopt the view that substance is identical with God and as such encompasses all principles of operations of the human mind and premises for the deriving of all fundamental notions popular in his times. (shrink)

‘Substance’ (substantia, zelfstandigheid) is a key term of Spinoza’s philosophy. Like almost all of Spinoza’s philosophical vocabulary, Spinoza did not invent this term, which has a long history that can be traced back at least to Aristotle. Yet, Spinoza radicalized the traditional notion of substance and made a very powerful use of it by demonstrating – or at least attempting to demonstrate -- that there is only one, unique substance -- God (or Nature) -- and that all other things are (...) merely modes or states of God. Some of Spinoza’s readers understood these claims as committing him to the view that only God truly exists, and while this interpretation is not groundless, we will later see that this enticing and bold reading of Spinoza as an ‘acosmist’ comes at the expense of another audacious claim Spinoza advances, i.e., that God/Nature is absolutely and actually infinite. But before we reach this last conclusion, we have a long way to go. So, let me first provide an overview of our plan. In the first section of this paper we will examine Spinoza’s definitions of ‘substance’ and ‘God’ at the opening of his magnum opus, the Ethics. Following a preliminary clarification of these two terms and their relations to the other key terms defined at the beginning of the Ethics, we will briefly address the Aristotelian and Cartesian background of Spinoza’s discussion of substance. In the second section, we will study the properties of the fundamental binary relations pertaining to Spinoza’s substance: inherence, conception, and causation. The third section will be dedicated to a clarification of Spinoza’s claim that God, the unique substance, is absolutely infinite. This essential feature of Spinoza’s substance has been largely neglected in recent Anglo-American scholarship, a neglect which has brought about an unfortunate tendency to domesticate Spinoza’s metaphysics to more contemporary views. The fourth section will study the nature of Spinoza’s monism. It will discuss and criticize the interesting yet controversial views of the eminent Spinoza scholar, Martial Gueroult, about the plurality of substances in the beginning of the Ethics; address Spinoza’s claim in Letter 50 that, strictly speaking, it is improper to describe God as “one”; and, finally, evaluate Spinoza’s kind of monism against the distinction between existence and priority monism recently introduced into the contemporary philosophical literature. The fifth and final section will explain the nature, reality, and manner of existence of modes. We therefore have an ambitious plan; let’s get down to business. (shrink)

The advent of modern science brought deep challenges to traditional religion. Miracles, prophecy, immortal souls, absolute morality - all of these fundamental notions were challenged by the increasingly analytical and skeptical approach of modern scientists. One philosopher, Baruch Spinoza, proposed a new theology, rooted in a close analysis of the Bible, which could fit this new science and provide a sound basis for a social order. "Spinoza's Radical Theology" explains the mechanics and meaning of Spinoza's ideas and how they can (...) inform the questions with which we still struggle today. (shrink)

A square tabular array was introduced by R. C. Punnett in (1907) to visualize systematically and economically the combination of gametes to make genotypes according to Mendel’s theory. This mode of representation evolved and rapidly became standardized as the canonical way of representing like problems in genetics. Its advantages over other contemporary methods are discussed, as are ways in which it evolved to increase its power and efficiency, and responded to changing theoretical perspectives. It provided a natural visual decomposition of (...) a complex problem into a number of inter-related stages. This explains its computational and conceptual power, for one could simply “read off” answers to a wide variety of questions simply from the “right” visual representation of the problem, and represent multiple problems, and multiple layers of problems in the same diagram. I relate it to prior work on the evolution of Weismann diagrams by Griesemer and Wimsatt (What Philosophy of Biology Is, Martinus-Nijhoff, the Hague, 1989), and discuss a crucial change in how it was interpreted that midwifed its success. (shrink)

continent. 1.1 : 3-13. / 0/ – Introduction I want to propose, as a trajectory into the philosophically weird, an absurd theoretical claim and pursue it, or perhaps more accurately, construct it as I point to it, collecting the ground work behind me like the Perpetual Train from China Mieville's Iron Council which puts down track as it moves reclaiming it along the way. The strange trajectory is the following: Kant's critical philosophy and much of continental philosophy which has followed, (...) has been a defense against horror and madness. Kant's prohibition on speculative metaphysics such as dogmatic metaphysics and transcendental realism, on thinking beyond the imposition of transcendental and moral constraints, has been challenged by numerous figures proceeding him. One of the more interesting critiques of Kant comes from the mad black Deleuzianism of Nick Land stating, “Kant’s critical philosophy is the most elaborate fit of panic in the history of the Earth.” And while Alain Badiou would certainly be opposed to the libidinal investments of Land's Deleuzo-Guattarian thought, he is likewise critical of Kant's normative thought-bureaucracies: Kant is the one author for whom I cannot feel any kinship. Everything in him exasperates me, above all his legalism—always asking Quid Juris? Or ‘Haven’t you crossed the limit?’—combined, as in today’s United States, with a religiosity that is all the more dismal in that it is both omnipresent and vague. The critical machinery he set up has enduringly poisoned philosophy, while giving great succour to the academy, which loves nothing more than to rap the knuckles of the overambitious [….] That is how I understand the truth of Monique David-Menard’s reflections on the properly psychotic origins of Kantianism. I am persuaded that the whole of the critical enterprise is set up to to shield against the tempting symptom represented by the seer Swedenborg, or against ‘diseases of the head’, as Kant puts it. An entire nexus of the limits of reason and philosophy are set up here, namely that the critical philosophy not only defends thought from madness, philosophy from madness, and philosophy from itself, but that philosophy following the advent of the critical enterprise philosophy becomes auto-vampiric; feeding on itself to support the academy. Following Francois Laruelle's non-philosophical indictment of philosophy, we could go one step further and say that philosophy operates on the material of what is philosophizable and not the material of the external world. [1] Beyond this, the Kantian scheme of nestling human thinking between our limited empirical powers and transcendental guarantees of categorical coherence, forms of thinking which stretch beyond either appear illegitimate, thereby liquefying both pre-critical metaphysics and the ravings of the mad in the same critical acid. In rejecting the Kantian apparatus we are left with two entities – an unsure relation of thought to reality where thought is susceptible to internal and external breakdown and a reality with an uncertain sense of stability. These two strands will be pursued, against the sane-seal of post-Kantian philosophy by engaging the work of weird fiction authors H.P. Lovecraft and Thomas Ligotti. The absolute inhumanism of the formers universe will be used to describe a Shoggothic Materialism while the dream worlds of the latter will articulate the mad speculation of a Ventriloquil Idealism. But first we must address the relation of philosophy to madness as well as philosophy to weird fiction. /1/ – Philosophy and Madness There is nothing that the madness of men invents which is not either nature made manifest or nature restored. Michel Foucault. Madness and Civilization. The moment I doubt whether an event that I recall actually took place, I bring the suspicion of madness upon myself: unless I am uncertain as to whether it was not a mere dream. Arthur Schopenhauer. The World as Will and Idea, Vol. 3. Madness is commonly thought of as moving through several well known cultural-historical shifts from madness as a demonic or otherwise theological force, to rationalization, to medicalization psychiatric and otherwise. Foucault's Madness and Civilization is well known for orientating madness as a form of exclusionary social control which operated by demarcating madness from reason. Yet Foucault points to the possibility of madness as the necessity of nature at least prior to the crushing weight of the church. Kant’s philosophy as a response to madness is grounded by his humanizing of madness itself. As Adrian Johnston points out in the early pages of Time Driven pre-Kantian madness meant humans were seized by demonic or angelic forces whereas Kantian madness became one of being too human. Madness becomes internalized, the external demonic forces become flaws of the individual mind. Foucault argues that, while madness is de-demonized it is also dehumanized during the Renaissance, as madmen become creatures neither diabolic nor totally human reduced to the zero degree of humanity. It is immediately clear why for Kant, speculative metaphysics must be curbed – with the problem of internal madness and without the external safeguards of transcendental conditions, there is nothing to formally separate the speculative capacities for metaphysical diagnosis from the mad ramblings of the insane mind – both equally fall outside the realm of practicality and quotidian experience. David-Menard's work is particularly useful in diagnosing the relation of thought and madness in Kant's texts. David-Menard argues that in Kant's relatively unknown “An Essay on the Maladies of the Mind” as well as his later discussion of the Seer of Swedenborg, that Kant formulates madness primarily in terms of sensory upheaval or other hallucinatory theaters. She writes: “madness is an organization of thought. It is made possible by the ambiguity of the normal relation between the imaginary and the perceived, whether this pertains to the order of sensation or to the relations between our ideas” Kant's fascination with the Seer forces Kant between the pincers of “aesthetic reconciliation” – namely melancholic withdrawal – and “a philosophical invention” – namely the critical project. Deleuze and Guattari's schizoanalysis is a combination and reversal of Kant's split, where an aesthetic over engagement with the world entails prolific conceptual invention. Their embrace of madness, however, is of course itself conceptual despite all their rhizomatic maneuvers. Though they move with the energy of madness, Deleuze and Guattari save the capacity of thought from the fangs of insanity by imbuing materiality itself with the capacity for thought. Or, as Ray Brassier puts it, “Deleuze insists, it is necessary to absolutize the immanence of this world in such a way as to dissolve the transcendent disjunction between things as we know them and as they are in themselves”. That is, whereas Kant relied on the faculty of judgment to divide representation from objectivity Deleuze attempts to flatten the whole economy beneath the juggernaut of ontological univocity. Speculation, as a particularly useful form of madness, might fall close to Deleuze and Guattari’s shaping of philosophy into a concept producing machine but is different in that it is potentially self destructive – less reliant on the stability of its own concepts and more adherent to exposing a particular horrifying swath of reality. Speculative madness is always a potential disaster in that it acknowledges little more than its own speculative power with the hope that the gibbering of at least a handful of hysterical brains will be useful. Pre-critical metaphysics amounts to madness, though this may be because the world itself is mad while new attempts at speculative metaphysics, at post-Kantian pre-critical metaphysics, are well aware of our own madness. Without the sobriety of the principle of sufficient reason we have a world of neon madness: “we would have to conceive what our life would be if all the movements of the earth, all the noises of the earth, all the smells, the tastes, all the light – of the earth and elsewhere, came to us in a moment, in an instant – like an atrocious screaming tumult of things”. Speculative thought may be participatory in the screaming tumult of the world or, worse yet, may produce its spectral double. Against theology or reason or simply commonsense, the speculative becomes heretical. Speculation, as the cognitive extension of the horrorific sublime should be met with melancholic detachment. Whereas Kant's theoretical invention, or productivity of thought, is self -sabotaging, since the advent of the critical project is a productivity of thought which then delimits the engine of thought at large either in dogmatic gestures or non-systematizable empirical wondrousness. The former is celebrated by the fiction of Thomas Ligotti whereas the latter is espoused by the tales of H.P. Lovecraft. /2/ – Weird Fiction and Philosophy. Supernatural horror, in all its eerie constructions, enables a reader to taste treats inconsistent with his personal welfare. Thomas Ligotti Songs of a Dead Dreamer. I choose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve,momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which forever imprison us and frustrate our curiosity about the infinite cosmic spaces beyond the radius of our sight and analysis H.P. Lovecraft. “Notes on Writing Weird Fiction” Lovecraft states that his creation of a story is to suspend natural law yet, at the same time, he indexes the tenuousness of such laws, suggesting the vast possibilities of the cosmic. The tension that Lovecraft sets up between his own fictions and the universe or nature is reproduced within his fictions in the common theme of the unreliable narrator; unreliable precisely because they are either mad or what they have witnessed questions the bounds of material reality. In “The Call of Cthulhu” Lovecraft writes: The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age. Despite Lovecraft's invocations of illusion, he is not claiming that his fantastic creations such as the Old Ones are supernatural but, following Joshi, are only ever supernormal. One can immediately see that instead of nullifying realism Lovecraft in fact opens up the real to an unbearable degree. In various letters and non-fictional statements Lovecraft espoused strictly materialist tenets, ones which he borrowed from Hugh Elliot namely the uniformity of law, the denial of teleology and the denial of non-material existence. Lovecraft seeks to explore the possibilities of such a universe by piling horror upon horror until the fragile brain which attempts to grasp it fractures. This may be why philosophy has largely ignored weird fiction – while Deleuze and Guattari mark the turn towards weird fiction and Lovecraft in particular, with the precursors to speculative realism as well as contemporary related thinkers have begun to view Lovecraft as making philosophical contributions. Lovecraft's own relation to philosophy is largely critical while celebrating Nietzsche and Schopenhauer. This relationship of Lovecraft to philosophy and philosophy to Lovecraft is coupled with Lovecraft's habit of mercilessly destroying the philosopher and the figure of the academic more generally in his work, a destruction which is both an epistemological destruction and an ontological destruction. Thomas Ligotti's weird fiction which he has designated as a kind of “confrontational escapism” might be best described in the following quote from one of his shortstories, “The human phenomenon is but the sum of densely coiled layers of illusion each of which winds itself on the supreme insanity. That there are persons of any kind when all there can be is mindless mirrors laughing and screaming as they parade about in an endless dream”. Whereas Lovecraft's weirdness draws predominantly from the abyssal depths of the uncharted universe, Ligotti's existential horror focuses on the awful proliferation of meaningless surfaces that is, the banal and every day function of representation. In an interview, Ligotti states: We don't even know what the world is like except through our sense organs, which are provably inadequate. It's no less the case with our brains. Our whole lives are motored along by forces we cannot know and perceptions that are faulty. We sometimes hear people say that they're not feeling themselves. Well, who or what do they feel like then? This is not to say that Ligotti sees nothing beneath the surface but that there is only darkness or blackness behind it, whether that surface is on the cosmological level or the personal. By addressing the implicit and explicit philosophical issues in Ligotti's work we will see that his nightmarish take on reality is a form of malevolent idealism, an idealism which is grounded in a real, albeit dark and obscure materiality. If Ligotti's horrors ultimately circle around mad perceptions which degrade the subject, it takes aim at the vast majority of the focus of continental philosophy. While Lovecraft's acidic materialism clearly assaults any romantic concept of being from the outside, Ligotti attacks consciousness from the inside: Just a little doubt slipped into the mind, a little trickle of suspicion in the bloodstream, and all those eyes of ours, one by one, open up to the world and see its horror [...] Not even the solar brilliance of a summer day will harbor you from horror. For horror eats the light and digests it into darkness. Clearly, the weird fiction of Lovecraft and Ligotti amount to a anti-anthrocentric onslaught against the ramparts of correlationist continental philosophy. /3/ – Shoggothic Materialism or the Formless Formless protoplasm able to mock and reflect all forms and organs and processes—viscous agglutinations of bubbling cells—rubbery fifteen-foot spheroids infinitely plastic and ductile—slaves of suggestion, builders of cities—more and more sullen, more and more intelligent, more and more amphibious, more and more imitative—Great God! What madness made even those blasphemous Old Ones willing to use and to carve such things? H.P. Lovecraft. “At the Mountains of Madness” On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit. Georges Bataille. “Formless”. The Shoggoths feature most prominently in H.P. Lovecraft's shortstory “At the Mountains of Madness” where they are described in the following manner: It was a terrible, indescribable thing vaster than any subway train – a shapeless congeries of protoplasmic bubbles, faintly self -luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter. The term is a litmus test for materialism itself as the Shoggoth is an amorphous creature. The Shoggoths were living digging machines bio engineered by the Elder Things, and their protoplasmic bodies being formed into various tools by their hypnotic powers. The Shoggoths eventually became self aware and rose up against their masters in an ultimately failed rebellion. After the Elder Ones retreated into the oceans leaving the Shoggoths to roam the frozen wastes of the Antarctic. The onto-genesis of the Shoggoths and their gross materiality, index the horrifyingly deep time of the earth a concept near and dear to Lovecraft's formulation of horror as well as the fear of intelligences far beyond, and far before, the ascent of humankind on earth and elsewhere. The sickly amorphous nature of the Shoggoths invade materialism at large, where while materiality is unmistakably real ie not discursive, psychological, or otherwise overly subjectivist, it questions the relation of materialism to life. As Eugene Thacker writes: The Shoggoths or Elder Things do not even share the same reality with the human beings who encounter them—and yet this encounter takes place, though in a strange no-place that is neither quite that of the phenomenal world of the human subject or the noumenal world of an external reality. Amorphous yet definitively material beings are a constant in Lovecraft's tales. In his tale “The Dream-Quest of Unknown Kadatth” Lovecraft describes Azathoth as, “that shocking final peril which gibbers unmentionably outside the ordered universe,” that, “last amorphous blight of nethermost confusion which blashphemes and bubbles at the centre of all infinity,” who, “gnaws hungrily in inconceivable, unlighted chambers beyond time”. Azathoth's name may have multiple origins but the most striking is the alchemy term azoth which is both a cohesive agent and a acidic creation pointing back to the generative and the decayed. The indistinction of generation and degradation materially mirrors the blur between the natural and the unnatural as well as life and non-life. Lovecraft speaks of the tension between the natural and the unnatural is his short story “The Unnameable.” He writes, “if the psychic emanations of human creatures be grotesque distortions, what coherent representation could express or portray so gibbous and infamous a nebulousity as the spectre of a malign, chaotic perversion, itself a morbid blasphemy against Nature?”. Lovecraft explores exactly the tension outlined at the beginning of this chapter, between life and thought. At the end of his short tale Lovecraft compounds the problem as the unnameable is described as “a gelatin—a slime—yet it had shapes, a thousand shapes of horror beyond all memory”. Deleuze suggests that becoming-animal is operative throughout Lovecraft's work, where narrators feel themselves reeling at their becoming non-human or of being the anomalous or of becoming atomized. Following Eugene Thacker however, it may be far more accurate to say that Lovecraft's tales exhibit not a becoming-animal but a becoming-creature. Where the monstrous breaks the purportedly fixed laws of nature, the creature is far more ontologically ambiguous. The nameless thing is an altogether different horizon for thought. The creature is either less than animal or more than animal – its becoming is too strange for animal categories and indexes the slow march of thought towards the bizarre. This strangeness is, as aways, some indefinite swirling in the category of immanence and becoming. Bataille begins “The Labyrinth” with the assertion that being, to continue to be, is becoming. More becoming means more being hence the assertion that Bataille's barking dog is more than the sponge. This would mean that the Shoggotth is altogether too much being, too much material in the materialism. Bataille suggests that there is an immanence between the eater and the eaten, across the species and never within them. That is, despite the chaotic storm of immanence there must remain some capacity to distinguish the gradients of becoming without reliance upon, or at least total dependence upon, the powers of intellection to parse the universe into recognizable bits, properly digestible factoids. That is, if we undo Deleuze's aforementioned valorization of sense which, for his variation of materialism, performed the work of the transcendental, but refuse to reinstate Kant's transcendental disjunction between thing and appearance, then it must be a quality of becoming-as-being itself which can account for the discernible nature of things by sense. In an interview with Peter Gratton, Jane Bennett formulates the problem thusly: What is this strange systematicity proper to a world of Becoming? What, for example, initiates this congealing that will undo itself? Is it possible to identify phases within this formativity, plateaus of differentiation? If so, do the phases/plateaus follow a temporal sequence? Or, does the process of formation inside Becoming require us to theorize a non-chronological kind of time? I think that your student’s question: “How can we account for something like iterable structures in an assemblage theory?” is exactly the right question. Philosophy has erred too far on the side of the subject in the subject-object relation and has furthermore, lost the very weirdness of the non-human. Beyond this, the madness of thought need not override. /4/ - Ventriloquial Idealism or the Externality of Thought My aim is the opposite of Lovecraft's. He had an appreciation for natural scenery on earth and wanted to reach beyond the visible in the universe. I have no appreciation for natural scenery and want the objective universe to be a reflection of a character. Thomas Ligotti. “Devotees of Decay and Desolation.” Unless life is a dream, nothing makes sense. For as a reality, it is a rank failure [….] Horror is more real than we are. Thomas Ligotti. “Professor Nobody's Little Lectures on Supernatural Horror”. Thomas Ligotti's tales are rife with mannequins, puppets, and other brainless entities which of replace the valorized subject of philosophy – that of the free thinking human being. His tales such as “The Dream of the Manikin” aim to destroy the rootedness of consciousness. James Trafford has connected the anti-egoism of Ligotti to Thomas Metzinger – where the self is at best an illusion and we plead desperately for someone else to acknowledge that we are real. Trafford has stated it thus, “Life is played out as an inescapable puppet show, an endless dream in which the puppets are generally unaware that they are trapped within a mesmeric dance of whose mechanisms they know nothing and over which they have no control”. An absolute materialism, for Ligotti, implies an alienation of the idea which leads to a ventriloquil idealism. As Ligotti notes in an interview, “the fiasco and nightmare of existence, the particular fiasco and nightmare of human existence, the sense that people are puppets of powers they cannot comprehend, etc.” And then further elaborates that,“[a]ssuming that anything has to exist, my perfect world would be one in which everyone has experienced the annulment of his or her ego. That is, our consciousness of ourselves as unique individuals would entirely disappear”. The externality of the idea leads to the unfortunate consequence of consciousness eating at itself through horror which, for Ligotti, is more real than reality and goes beyond horror-as-affect. Beyond this, taking together with the unreality of life and the ventriloquizing of subjectivity, Ligotti's thought becomes an idealism in which thought itself is alien and ultimately horrifying. The role of human thought and the relation of non-relation of horror to thought is not completely clear in Ligotti's The Conspiracy Against the Human Race. Ligotti argues in his The Conspiracy Against the Human Race,that the advent of thought is a mistake of nature and that horror is being in the sense that horror results from knowing too much. Yet, at the same time, Ligotti seems to suggest that thought separates us from nature whereas, for Lovecraft, thought is far less privileged – mind is just another manifestation of the vital principal, it is just another materialization of energy. In his brilliant “Prospects for Post-Copernican Dogmatism” Iain Grant rallies against the negative definition of dogmatism and the transcendental, and suggests that negatively defining both over-focuses on conditions of access and subjectivism at the expense of the real or nature. With Schelling, who is Grant's champion against the subjectivist bastions of both Fichte and Kant, Ligotti's idealism could be taken as a transcendental realism following from an ontological realism. Yet the transcendental status of Ligotti's thought move towards a treatment of the transcendental which may threaten to leave beyond its realist ground. Ligotti states: Belief in the supernatural is only superstition. That said, a sense of the supernatural, as Conrad evidenced in Heart of Darkness, must be admitted if one's inclination is to go to the limits of horror. It is the sense of what should not be- the sense of being ravaged by the impossible. Phenomenally speaking, the super-natural may be regarded as the metaphysical counterpart of insanity, a transcendental correlative of a mind that has been driven mad. Again, Ligotti equates madness with thought, qualifying both as supernatural while remaining less emphatic about the metaphysical dimensions of horror. The question becomes one of how exactly the hallucinatory realm of the ideal relates to the black churning matter of Lovecraft's chaos of elementary particles. In his tale “I Have a Special Plan for This World” Ligotti formulates thus: A: There is no grand scheme of things. B: If there were a grand scheme of things, the fact – the fact – that we are not equipped to perceive it, either by natural or supernatural means, is a nightmarish obscenity. C: The very notion of a grand scheme of things is a nightmarish obscenity. Here Ligotti is not discounting metaphysics but implying that if it does exist the fact that we are phenomenologically ill-equipped to perceive that it is nightmarish. For Ligotti, nightmare and horror occur within the circuit of consciousness whereas for Lovecraft the relation between reality and mind is less productive on the side of mind. It is easier to ascertain how the Kantian philosophy is a defense against the diseases of the head as Kant armors his critical enterprise from too much of the world and too much of the mind. The weird fiction of both Lovecraft and Ligotti demonstrates that there is too much of both feeding into one another in a way that corrodes the Kantian schema throughly, breaking it down into a dead but still ontologically potentiated nigredo. The haunting, terrifying fact of Ligotti's idealism is that the transcendental motion which brought thought to matter, while throughly material and naturalized, brings with it the horror that thought cannot be undone without ending the material that bears it either locally or completely. Thought comes from an elsewhere and an elsewhen being-in-thought. The unthinkable outside thought is as maddening as the unthought engine of thought itself within thought which doesn't exist except for the mind, the rotting décor of the brain. /5/ - Hyperstitional Transcendental Paranoia or Self -Expelled Thought Weird fiction has been given some direct treatment in philosophy in the mad black Deleuzianism of Nick Land. Nick Land along with others in the 1990s created the Cyber Culture Research Unit as well as the research group Hyperstition. The now defunct hyperstitional website, an outgrowth of the Cyber Culture Research Unit, defined hyperstition in the following fourfold: 1-Element of effective culture that makes itself real. 2-Fictional quantity functional as a time-traveling device. 3-Coincidence intensifier. 4-Call to the Old Ones. The distinctively Lovecraftian character of hyperstition is hard to miss as is its Deleuzo-Guattarian roots. In the opening pages of A Thousand Plateaus Deleuze and Guattari write, “We have been criticized for over-quoting literary authors. But when one writes, the only question is which other machine the literary machine can be plugged into”. The indisinction of literature and philosophy mirrors the mess of being and knowing as post-correlationist philosophy, where philosophy tries to make itself real where literature, especially the weird, aims itself at the brain-circuit of horror. The texts of both Lovecraft and Ligotti work through horror as epistemological plasticity meeting with proximity as well as the deep time of Lovecraft and the glacially slow time of paranoia in Ligotti. Against Deleuze, and following Brassier, we cannot allow the time of consciousness, the Bergsonian time of the duree, to override natural time, but instead acknowledge that it is an unfortunate fact of existence as a thinking being. Horror-time, the time of consciousness, with all its punctuated moments and drawn out terrors, cannot compare to the deep time of non-existence both in the unreachable past and the unknown future. The crystalline cogs of Kant's account of experience as the leading light for the possibility of metaphysics must be throughly obliterated. His gloss of experience in Prolegomena to any Future Metaphysics could not be more sterile: Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments which the understanding makes entirely out of sensuous intuitions are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in sensuous intuition [....] Experience consists in the synthetic connection of appearances in consciousness, so far as this connection is necessary. Here it is difficult to dismiss the queasiness that Kant's legalism induces upon sight for both Badiou and David-Menard. Kant's thought becomes, as Foucault says when reflecting on Sade's text in relation to nature, “the savage abolition of itself”. For Badiou, Kant's philosophy simply closes off too much of the outside, freezing the world of thought in an all too limited formalism. Critical philosophy is simply the systematized quarantine on future thinking, on thinking which would threaten the formalism which artificially grants thought its own coherency in the face of madness. Even the becoming-mad of Deleuze, while escaping the rumbling ground, makes grounds for itself, mad grounds but grounds which are thinkable in their affect. The field of effects allows for Deleuze's aesthetic and radical empiricism, in which effects and/or occasions make up the material of the world to be thought as a chaosmosis of simulacra. Given a critique of an empiricism of aesthetics, of the image, it may be difficult to justify an attack on Kantian formalism with the madness of literature, which does not aim to make itself real but which we may attempt to make real. That is, how do Lovecraft's and Ligotti's materials, as materials for philosophy to work on, differ from either the operative formalisms of Kant or the implicitly formalized images of Deleuzian empiricism? It is simply that such texts do not aim to make themselves real, and make claims to the real which are more alien to us than familiar, which is why their horror is immediately more trustworthy. This is the madness which Blanchot discusses in The Infinite Conversation through Cervantes and his knight – the madness of book-life, of the perverse unity of literature and life a discussion which culminates in the discussion of one of the weird's masters, that of Kafka. The text is the knowing of madness, since madness, in its moment of becoming-more-mad, cannot be frozen in place but by the solidifications of externalizing production. This is why Foucault ends his famous study with works of art. Furthermore extilligence, the ability to export the products of our maligned brains, is the companion of the attempts to export, or discover the possibility of intelligences outside of our heads, in order for philosophy to survive the solar catastrophe. To borrow again from Deleuze, writing is inseparable from becoming. The mistake is to believe that madness is reabsorbed by extilligence, by great works, or that it could be exorcised by the expelling of thought into the inorganic or differently organic. Going out of our heads does not guarantee we will no longer mean we cannot still go out of our minds. This is simply because of the outside, of matter, or force, or energy, or thing-in-itself, or Schopenhauerian Will. In Lovecraft’s “The Music of Erich Zahn” an “impoverished student of metaphysics” becomes intrigued by strange viol music coming from above his room. After meeting the musician the student discovers that each night he plays frantic music at a window in order to keep some horridness at bay, some “impenetrable darkness with chaos and pandemonium”. The aesthetic defenses provided by the well trained brain can bear the hex of matter for so long, the specter of unalterability within it which too many minds obliterate, collapsing everything before the thought of thought as thinkable or at least noetically mutable on our own terms. Transcendental paranoia is the concurrent nightmare and promise of Paul Humphrey's work, of being literally out of our minds. It is the gothic counterpart of thinking non-conceptually but also of thinking never belonging to any instance of purportedly solid being. As Bataille stated, “At the boundary of that which escapes cohesion, he who reflects within cohesion realizes there is no longer any room for him” Thought is immaterial only to the degree that it is inhuman, it is a power that tries, always with failure, to ascertain its own genesis. Philosophy, if it can truly return to the great outdoors, if it can leave behind the dead loop of the human skull, must recognize not only the non-priority of human thought, but that thought never belongs to the brain that thinks it, thought comes from somewhere else. To return to the train image from the beginning “a locomotive rolling on the surface of the earth is the image of continuous metamorphosis” this is the problem of thought, and of thinking thought, of being no longer able to isolate thought, with only a thought-formed structure. [1] One of the central tenets of Francois Laruelle's non-philosophy is that philosophy has traditionally operated on material already presupposed as thinkable instead of trying to think the real in itself. Philosophy, according to Laruelle, remains fixated on transcendental synthesis which shatters immanence into an empirical datum and an a prori factum which are then fused by a third thing such as the ego. For a critical account of Laruelle's non-philosophy see Ray Brassier's Nihil Unbound. (shrink)

I argue against a prevailing view that the essence of Godis identical with the attributes. I show that given what Spinoza says in 2d2 – Spinoza'spurported definition of the essence of a thing – the attributes cannot be identical withthe essence of God (whether the essence of God is understood as the distinct attributesor as a totality of indistinct attributes). I argue that while the attributes do notsatisfy the stipulations of 2d2 relative to God, absolutely infinite and eternal power (...) does satisfythose stipulations. Hence, I conclude that absolutely infinite and eternal power is God'sessence and that the attributes are expressions of that power. (shrink)

‘Substance’ (substantia, zelfstandigheid) is a key term of Spinoza’s philosophy. Like almost all of Spinoza’s philosophical vocabulary, Spinoza did not invent this term, which has a long history that can be traced back at least to Aristotle. Yet, Spinoza radicalized the traditional notion of substance and made a very powerful use of it by demonstrating – or at least attempting to demonstrate -- that there is only one, unique substance -- God (or Nature) -- and that all other things are (...) merely modes or states of God. Some of Spinoza’s readers understood these claims as committing him to the view that only God truly exists, and while this interpretation is not groundless, we will later see that this enticing and bold reading of Spinoza as an ‘acosmist’ comes at the expense of another audacious claim Spinoza advances, i.e., that God/Nature is absolutely and actually infinite. But before we reach this last conclusion, we have a long way to go. So, let me first provide an overview of our plan. In the first section of this paper we will examine Spinoza’s definitions of ‘substance’ and ‘God’ at the opening of his magnum opus, the Ethics. Following a preliminary clarification of these two terms and their relations to the other key terms defined at the beginning of the Ethics, we will briefly address the Aristotelian and Cartesian background of Spinoza’s discussion of substance. In the second section, we will study the properties of the fundamental binary relations pertaining to Spinoza’s substance: inherence, conception, and causation. The third section will be dedicated to a clarification of Spinoza’s claim that God, the unique substance, is absolutely infinite. This essential feature of Spinoza’s substance has been largely neglected in recent Anglo-American scholarship, a neglect which has brought about an unfortunate tendency to domesticate Spinoza’s metaphysics to more contemporary views. The fourth section will study the nature of Spinoza’s monism. It will discuss and criticize the interesting yet controversial views of the eminent Spinoza scholar, Martial Gueroult, about the plurality of substances in the beginning of the Ethics; address Spinoza’s claim in Letter 50 that, strictly speaking, it is improper to describe God as “one”; and, finally, evaluate Spinoza’s kind of monism against the distinction between existence and priority monism recently introduced into the contemporary philosophical literature. The fifth and final section will explain the nature, reality, and manner of existence of modes. We therefore have an ambitious plan; let’s get down to business. (shrink)

The study aims to show that the Kantian distinction of synthetic and analytical resolution of the courts is originally epistemic and not purely logical. Proof of this proposition is done so that in the first step are distinguished two types of synthetic and analytical predicate relation to the subject - logical-semantic and epistemic. Furthermore, the examples demonstrated that Kant was familiar cases in courts, which are found only logico-semantic synthetic or analytic connection of concepts in trials. (...) Consequently, Kant care for them and are therefore not in terms classifiable Critique of Pure Reason, Kant even offers a way to understand its logic and Prolegomena. Based on various Kant notes offered by Article resolution three types of synthetic courts and courts of two kinds of analysis. The final part of the article is devoted to a brief outline of the relationship of epistemic and epistemic-synthetic-analytic courts, because the courts are due to which Kant its resolution synthetic and analytical courts instituted . Shown is both preferred synthesis of ideas before analysis, first, how Kant based his teachings on unum, verum, bonum featured specific tasks analysis concepts. article is supplemented by a short reflection on Kant's definition of the principle of the dispute and by showing a significant difference between Kant and Bolzano definition of analytic courts, whose oversight can lead to misunderstanding the context in which resolution synthetic and analytical courts in Kant belongs. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Spinoza: Une Lecture d'AristoteYitzhak MelamedFrédéric Manzini. Spinoza: Une Lecture d'Aristote. Paris: Presses Universitaires de France, 2009. Pp. 334. Paper, $39.95.The occasion that prompted the current study was the discovery of a tiny typo in the text of Spinoza's Cogitata Metaphysica—the appendix to his 1663 book, Descartes' Principle of Philosophy. As it turned out, this typo, a reference to Book XI instead of Book XII of Aristotle's Metaphysics, was (...) inadvertently reproduced by Spinoza from a contemporary edition of Aristotle's works, allowing Manzini to identify precisely the edition used by Spinoza as the 1548 edition of Aristotle's works printed in Basel by Johannes Oporinus. It also led him to conclude that, contrary to the belief of many, Spinoza read Aristotle's text very closely, and convinced him of the importance of studying the dialogue between the two great philosophers.The book is comprised of three parts, reversing the order of Spinoza's presentation of his philosophy in the Ethics. The first part discusses Spinoza's ethical and political theories—where, the author claims, the influence of Aristotle is most manifest—against the background of the Nicomachean Ethics and the Politics. Here, much attention is given to the notions of the summum bonum and beatitude. The second part discusses Aristotelian and Spinozistic theories of knowledge. In the third and final part, dedicated to metaphysics and first philosophy, the author compares the philosophers' absolutely impersonal conceptions of God, examines their conceptions of substance, and develops a reading of what he calls Spinoza's "ousio-theology" (305).According to Manzini, Aristotle was one of Spinoza's first major philosophical interlocutors, and there is no doubt he is right about this. This conclusion, however, is unsurprising, [End Page 126] since seventeenth-century philosophers, whether devoted Aristotelians or determined anti-Aristotelians, conversed in an Aristotelian philosophical language. Manzini shows that Spinoza engaged directly with Aristotle's text, but also tries to substantiate an even stronger claim by stressing the agreements between the two philosophers.There are two reasons that make it difficult to see Spinoza as being consciously and positively influenced by Aristotle, however. First, Spinoza's dialogue with his philosophical predecessors is, without exception, highly critical and polemical. He does not usually mention philosophers with whom he agrees (e.g. Crescas and Machiavelli). Secondly, several of Spinoza's explicit references to Aristotle are highly critical. Consider, for example, Spinoza's claim, in a letter to Hugo Boxel, that "the authority of Plato, Aristotle, and Socrates carries little weight with me" (Letter 56), or his mockery of the "delusions of the Aristotelians and Platonists" (Theological Political Treatise [TTP], Pref.; cf. ch. 13). Manzini suggests that in these passages Spinoza is not so much addressing Aristotle, but rather using him as a foil to target medieval Aristotelianism (13). Looking closely at the context, my impression is that he is right about the passages in the TTP, but not about the quote from Letter 56. More importantly, the claim that Spinoza uses Aristotle's name as a foil is a double-edged sword that may also serve to undermine Manzini's argument. Throughout the book, Manzini points out interesting and significant similarities between Spinoza's and Aristotle's texts, but to establish direct positive influence one must consider and rule out mediating agents. In the present case there is plenty of evidence that Spinoza read medieval Hebrew Aristotelians closely. Unfortunately, most of the Hebrew authors mentioned by Spinoza were never translated into modern European languages, and there are very few, if any, good studies of Spinoza's dialogue with these texts; in the absence of such translations and studies, some of Manzini's conclusions must remain tentative.Manzini's erudition and analysis of the text are impressive. For example, near the end of his celebrated Letter on the Infinite, Spinoza criticizes "recent Peripatetics" for misunderstanding the ancient method of proving God's existence, citing Crescas's correct formulation of the ancient proof. Manzini rightly points out that the proof Spinoza ascribes to the "recent Peripatetics" was in fact Aristotle's, while the alleged "ancient" proof (which allows for actual infinity and relies on Avicennian... (shrink)

This thesis is directed towards a philosophy of music by attention to conceptions and perceptions of space. I focus on melody and harmony, and do not emphasise rhythm, which, as far as I can tell, concerns time rather than space. I seek a metaphysical account of Western Classical music in the diatonic tradition. More specifically, my interest is in wordless, untitled music, often called 'absolute' music. My aim is to elucidate a spatial approach to the world combined with a curiosity (...) about the nature of the Pythagorean intervals. Thus one question I seek to answer is: What do the Pythagorean intervals import to music? In their original formulation by Pythagoras, and further, by Plato, their import seemed mystical and analogous to a 'harmony of the spheres.' In this spatial approach, the Pythagorean intervals are indicative of infinite depth. The faculty of hearing alone does not ordinarily spatially locate sources. Hearing is ordinarily combined with sight in order to spatially locate a sound. Yet we talk about music as if it were spatially located, that is, as if it were a visible object with a surface and themes or 'objects'. I explore the faculty of vision and consider in what ways the processes of vision might be similar to and distinct from audition. My source for this approach is David Marr's book 'Vision' and his theory of the 2 1/2-dimensional sketch. In a medium in which there is no spatial location, it is important to situate the listener. Newton solved the problem of location by demonstrating the effects of gravity. P. F. Strawson claims that an analogy of distance is required in hearing to situate the listener, that is, a sense of nearer to and further from a source or object that permits a perception of distance. I claim that in music, the key signature and the scalar relations of musical themes provide this analogy of distance. The works of Plato, Aristotle, Descartes, Leibniz, and Newton are studied for their accounts of motion, bodies, and space. From these metaphysicians can be gleaned elements of music that include form, motion, timbre, dynamics, and attraction. By incorporating motion, I aim to show that although we may not know the true nature of space, we can learn from hearing music that space is perceptible in other than three dimensions. (shrink)

The paper, which retains a hypothetical character, argues that Spinoza's propositions referring to God (or involving the use of the name ‘God’, essentially in the Ethics), can be read in a fruitful manner apart from any pre-established hypothesis concerning his own ‘theological preferences’, as definite descriptions of three ‘ideas of God’ which have the same logical status: one (akin to Jewish Monotheism) which identifies the idea of God with the idea of the Law, one (akin to a heretic ‘Socinian’ version (...) of Christianity) which identifies it with the idea of Human Love, and one (akin to a form of Cosmotheism, rather than ‘Pantheism’) which identifies it with Nature. Evidence of this analytic tripartition can be found in the letter of the texts themselves. If accepted (at least as a thought experiment), it would carry three interesting consequences: 1) to renew our understanding of the theory of the ‘three kinds of knowledge’, which have obvious affinities with the three possible ways of understanding the idea of God; 2) to emphasize the critical move associated by Spinoza with each of the three ideas of God (passing from an anthropomorphic legislator to an impersonal command, passing from an imaginary community of similarities to a practical community of singularities, and passing from a teleological and harmonious idea of nature to a causal, even conflictual, idea of its infinite power); 3) to locate the essential ethical and political questions associated with religion on the ‘vectors’ which lead from one idea to another, and represent themselves practical conatus: obedience, utility, order. It is also assumed that such a reading enhances the relevance of Spinoza's philosophy with respect to contemporary debates about religion and secularism. (shrink)

Although the idiom “genesis and structure” is usually associated with the rise of structuralism in the late 1950s and early 1960s, the two notions are arguably among the most persistent methods in the history of modern philosophy. This article outlines the emergence of “genetic epistemology” in the seventeenth century, when the seemingly antithetical character of the conceptual pair was reworked into a productive epistemological theory, especially in Descartes, Hobbes, Spinoza, and Leibniz, who increasingly used diachronic (genetic) narratives to (...) explain the synchronic (structural) features in their theories. Against Cassirer, I argue that it was Descartes rather than Hobbes who first presented structural issues genetically. In Descartes’ natural philosophy, his frequent claims that showing how a thing is produced reveals its true nature foreshadow precisely what Hobbes and Isaac Barrow later describe as causal definitions of geometric figures, in which the process of ideal generation by motion is what constitutes the very essence of a figure. I link this method to the historicizing discourse on origins in the Enlightenment and conclude by suggesting that there is a trace of Platonic idealism in genetic epistemology. (shrink)

In my dissertation I approach the subject of the attributes of God in Spinoza's metaphysics by considering three pivotal and closely linked problems. I discuss the problem of the relation of God to the attributes, the problem of the essence of God, and the problem of the true conception of God. ;I examine three interpretations of God and the attributes in Spinoza: that of Jonathan Bennett, according to which God is the thing that has the attributes and modes as properties, (...) that of Edwin Curley and Alan Donagan, according to which God is the collection of attributes, and that of H. F. Hallett and Steven Parchment, according to which God is the totality of attributes. I examine each stance relative to the three problems. I reveal the weaknesses of each interpretation by making explicit the problems that each interpretation is unable to deal with successfully and by exposing new problems that some of the interpretations create. I then discuss topics in Spinoza that need to be understood in order to arrive at the correct answers to the three problems. For example, I carefully examine 2D2---a definition that commentators on Spinoza generally consider imperative in the discussion of the essence of God. ;I then suggest an interpretation of God and the attributes that is motivated by Spinoza's claim in 1P34 that God's power is God's essence. I claim that an adequate idea of the essence of God is a de re conception of God; and I invoke Michael Della Rocca's account of the opacity of attribute-contexts in order to support my view of de re conceptions of God. I show that, for Spinoza, the essence of a thing is given by the definition of the thing; and I show that 1D6 correlates with his claim in 1P34 that God's power is God's essence. I argue that God's essence is absolutely infinite and eternal power, and that power is what is constituted and expressed by each of the infinite attributes. (shrink)

The following article compares the notion of the absolute in the work of Georg Cantor and in Alain Badiou’s third volume of Being and Event: The Immanence of Truths and proposes an interpretation of mathematical concepts used in the book. By describing the absolute as a universe or a place in line with the mathematical theory of large cardinals, Badiou avoided some of the paradoxes related to Cantor’s notion of the “absolutely infinite” or the set of all that is (...) thinkable in mathematics W: namely the idea that W would be a potential infinity. The article provides an elucidation of the putative criticism of the statement “mathematics is ontology” which Badiou presented at the conference Thinking the Infinite in Prague. It emphasizes the role that philosophical decision plays in the construction of Badiou’s system of mathematical ontology and portrays the relationship between philosophy and mathematics on the basis of an inductive not deductive reasoning. (shrink)

Between the years 1643 and 1649, Princess Elisabeth of Bohemia and René Descartes exchanged fifty-eight letters—thirty-two from Descartes and twenty-six from Elisabeth. Their correspondence contains the only known extant philosophical writings by Elisabeth, revealing her mastery of metaphysics, analytic geometry, and moral philosophy, as well as her keen interest in natural philosophy. The letters are essential reading for anyone interested in Descartes’s philosophy, in particular his account of the human being as a union of mind and body, as well (...) as his ethics. They also provide a unique insight into the character of their authors and the way ideas develop through intellectual collaboration. Philosophers have long been familiar with Descartes’s side of the correspondence. Now Elisabeth’s letters—never before available in translation in their entirety—emerge this volume, adding much-needed context and depth both to Descartes’s ideas and the legacy of the princess. Lisa Shapiro’s annotated edition—which also includes Elisabeth’s correspondence with the Quakers William Penn and Robert Barclay—will be heralded by students of philosophy, feminist theorists, and historians of the early modern period. (shrink)

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates to the (...) nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination. (shrink)

continent. 1.2 (2011): 78-91. This article consists of three parts. First, I will review the major themes of Quentin Meillassoux’s After Finitude . Since some of my readers will have read this book and others not, I will try to strike a balance between clear summary and fresh critique. Second, I discuss an unpublished book by Meillassoux unfamiliar to all readers of this article, except those scant few that may have gone digging in the microfilm archives of the École normale (...) supérieure. The book in question is Meillassoux’s revised doctoral dissertation L’Inexistence divine (or The Divine Inexistence ), with its seemingly bizarre vision of a God who does not yet exist but might exist in the future. Without literally accepting this view, I will claim that it is philosophically interesting in ways that even a hardened sceptic might be able to appreciate. Third and finally, I will speculate on the possible future of Meillassoux’s speculative materialism itself. And here I mean its future development not by Meillassoux, but by those readers who might be inspired by his book. Plato could never have predicted the emergence of Aristotle’s philosophy, despite the obvious debt of the latter to the former. Nor could Descartes have predicted Spinoza and Leibniz, nor Kant the German Idealists, and neither could Husserl in 1901 have foreseen the later emergence of Heidegger. How are the works of interesting philosophers transformed by later thinkers of comparable importance? While it may seem that there are countless ways to do this, I think there are only two basic ways in which this happens: you can radicalize your predecessors, or you can reverse them. I will close this article with a few words about these two methods, and try to imagine how Meillassoux might be radicalized or reversed by some future admirer. My view is that the more important thinkers are, the easier they are to radicalize or reverse. This helps explain why the great philosophers of the West have so often appeared in clusters, succeeding one another at relatively brief intervals during periods of especial ferment. 1. After Finitude After Finitude is unusually short for such an influential book of philosophy: running to just 178 pages in the original French, and an even more compact 128 pages in the English version, despite the introduction of roughly eight pages of new material for the English edition. Rather than summarizing Meillassoux’s book in the order he intended, I will focus on six points that strike me as the pillars of his debut book. Along the way, I will offer a few criticisms as well. The first pillar of the book is Meillassoux’s own term “correlationism.”1 Although he introduces this term as the name for an enemy, it is striking that Meillassoux remains impressed by correlationism much more than his fellow speculative realists are. This continued appreciation for his great enemy influences the shape of his own ontology. Is there a world outside our thinking of it, or does the world consist entirely in being thought? Traditionally, this dispute between realism and idealism has been dismissed in continental philosophy as a “pseudo-problem,” in a strategy pioneered by Husserl and extended by Heidegger. We cannot be realists, since following Kant we have no direct access to things-in-themselves. But neither are we idealists, since the human being is always already outside itself, aiming at objects in intentional experience, deeply engaged with practical implements, or stationed in some particular world-disclosing mood. The centuries-old dispute between realism and idealism is dissolved by saying that we cannot think either real or ideal in isolation from the other. There is neither human without world nor world without human, but only a primordial correlation or rapport between the two. This is what “correlationism” means: philosophy trapped in a permanent meditation on the human-world correlate, trying to find the best model of the correlate: is it language, intentionality, embodiment, or some other form of correlation between human and world? Among other problems, this generates some friction between philosophy and the literal meaning of science. When cosmologists say that the universe originated 13.5 billion years ago, they do not mean “13.5 billion years ago for us ,” but literally 13.5 billion years ago, well before conscious life existed, and thus at a time when there was no such thing as a correlate. Meillassoux also coins the term “ancestrality” (10) for the reality that predated the correlate, and later expands this term to “dia-chronicity,” (112) to refer to events occurring after the extinction of human beings no less than to those occurring before we existed. Up to this point, Meillassoux’s focus on ancestral entities existing prior to consciousness might seem like a straightforward realist who wants to unmask correlationism as just another form of idealism. Yet Meillassoux also admires the correlationist maneuver, which can obviously be traced back to Kant. Unlike a thinker such as Whitehead, Meillassoux feels no nostalgia for the pre-critical realism that came before Kant: “we cannot but be heirs of Kantianism,” he says (29). What impresses Meillassoux about correlationism is something both simple and familiar. If we attempt to think a tree outside thought, this is itself a thought . Any form of realism which thinks it can simply and directly address the world the way it is fails to escape the correlational circle, since the attempt to think something outside of thought is itself nothing other than a thought, and thereby collapses back into the very human-world correlate that it pretends to escape. For Meillassoux this step, suggested by Kant but first refined by the ensuing figures of German Idealism, marks decisive forward progress in the history of philosophy that must not be abolished. Any attempt to break free from the correlate must first acknowledge its mighty intellectual power. Realist though he may seem, Meillassoux’s works are filled with praise of such figures as Fichte and Hegel, not of so-called “naïve realists.” It is also the case that for Meillassoux, not all correlationisms are the same. The second pillar of his book is a distinction between various positions that I have termed “Meillassoux’s Spectrum,” though of course he is never so immodest as to name it after himself. He distinguishes between at least six different possible positions, and perhaps we could add even subtler variations if we wished. But in its simplest form, Meillassoux’s Spectrum allows for just four basic outlooks on the question of realism vs. anti-realism. Three of these are easy to understand, since we have already been discussing them. At one extreme is so-called “naïve realism,” which holds that a world exists outside the mind, and that we can know this world. Meillassoux rejects this naïve realism as having been overthrown by Kant’s critical philosophy. At the other extreme is subjective idealism, in which nothing exists outside the mind. For to think a dog outside thought immediately turns it into a thought, and therefore there cannot be anything outside; the very notion is meaningless. In between these two is what we have called correlationism. And here comes a crucial moment for Meillassoux, since he distinguishes between the two forms of “weak” and “strong” correlationism, and chooses the strong form as the launching pad for his own philosophy. Weak correlationism is easy to explain, since we all know it from the philosophy of Kant. The things-in-themselves can be thought but not known. They certainly must exist, since there cannot be appearances without something that appears. And we can think about them, which idealism holds to be impossible. They are simply unknowable due to the finitude of human thought. Strong correlationism is the new position introduced by Meillassoux (though he sees it at work in numerous twentieth century thinkers), midway between weak correlationism and subjective idealism. The major difference between the three positions is as follows. Weak correlationism says: “The things-in-themselves exist, but we cannot know them.” The subjective idealist says: “This is a contradiction in terms, since when we think the things-in-themselves, we already turn them into thoughts.” But the strong correlationist says: “Just because ‘things-in-themselves’ is a meaningless notion does not mean that they cannot exist. No one has ever traveled to the world-in-itself and come back to make a report on it. Thus, the fact that we cannot think things-in-themselves without contradiction does not prove that they do not exist anyway. There may be things-in-themselves, we simply are not capable of thinking them without contradiction form within the correlational circle.” This step is crucial for Meillassoux, since strong correlationism is the position he attempts to radicalize into his own new standpoint: speculative materialism. As I see it, this step of the argument fails. Strong correlationism cannot avoid collapsing into subjective idealism, since the statements of the strong correlationist are rendered meaningless from within. All three of the other positions in the Spectrum make perfectly good sense even for those who disagree with them. The naïve realist says that things-in-themselves exist and we can know them; the meaning of this statement is clear. The weak correlationist can say that things-in-themselves exist but lie forever beyond our grasp; this too makes perfect sense, even though the German Idealists try to show a contradiction at work here. We can also understand the claim of the subjective idealist that to think anything outside thought turns it into a thought, and that for this reason we cannot think the unthought. The strong correlationist, alone among the four, speaks nonsense . This person says “I cannot think the unthought without turning it into a thought, and yet the unthought might exist anyway.” But notice that the final phrase “the unthought might exist anyway” is fruitless for this purpose. For we have already heard that to think any unthought turns it into a thought. But now the strong correlationist wants to do two incompatible things simultaneously with this unthought. On the one hand, he neutralizes the unthought by showing that it instantly changes into just another thought. But on the other hand, he wants to appeal to the unthought as a haunting residue that might exist outside thought, thereby undercutting the absolute status of the human-world correlate found in idealism. But this is impossible. If you accept the argument that thinking the unthought turns it into a thought, you cannot also add “but maybe there is something outside that prevents this conversion from being absolutely true,” because this “something outside” is immediately converted into nothing but a thought for us. In short, Meillassoux here seems to be offering a kind of Zen koan: his “strong correlationism” is reminiscent of the gateless gate, or the sound of one hand clapping, or the command to punch Hegel in the jaw when meeting him on the road. We cannot at the same time both destroy the realist challenge of the things-in-themselves in order to undercut realism and reintroduce that very realist sense in order to undercut idealism. In a world where everything is instantly converted into thought, we cannot claim that there might be something extra-mental anyway, because this “might be something” is itself converted into a thought by the same rules that condemned dogs, trees, and houses to the idealist prison. This brings us to the third pillar of Meillassoux’s argument, which is the key to all the rest: the necessity of contingency. His strategy is to transform our supposed ignorance of things-in-themselves into an absolute knowledge that they exist without reason, and that the laws of nature can change at any time for no reason at all. In this way the cautious agnosticism of Kantian philosophies is avoided, but so is the collapse of reality into thought as found in German Idealism. Meillassoux does try to prove the existence of things-in-themselves existing outside thought; he simply holds that they must be proven after passing through the rigors of the correlationist challenge, not just arbitrarily decreed to exist in the manner of naïve realism. As he puts it, “Everything could actually collapse: from trees to stars, from stars to laws, from physical laws to logical laws; and this not by virtue of some superior law whereby everything is destined to perish, but by virtue of the absence of any superior law capable of preserving anything, no matter what, from perishing” (53). If idealism thinks that the human-world correlate is absolute, for Meillassoux it is the facticity of the correlate that is absolute. He tries to show this with a nice brief dialogue between five separate characters (55-59) which is covered in detail in my forthcoming book,2 but which I will simplify here for reasons of time. In this simplified version, we first imagine a dogmatic realist arguing with a dogmatic idealist. The realist says that we can know the truth about the things-in-themselves; the idealist counters that we can only the truth about thought, since all statements about reality must be turned into statements concerning our thoughts about reality. Here the correlationist enters and proclaims that both of these positions are equally dogmatic. For although we have access to nothing but thoughts, we cannot be sure that these thoughts are all that exist; there could be a reality outside thought, there is simply no way to know for sure. And this latter position is the one that Meillassoux attempts to transform from an agnostic, skeptical point into an ontological claim about the contingency of everything. Consider it this way. How does the correlationist defeat the idealist? The idealist holds that the existence of anything outside thought is impossible. The correlationist, by contrast, holds that something might exist outside the human-world correlate. But this “something might” has to be an absolute possibility. It cannot mean that “something outside thought might exist for thought ,” because that is what the idealist already says. No, the correlationist must mean that something might exist outside thought quite independently of thought. In other words, the correlationist says that idealism might be wrong, and this means it is absolutely true that idealism might be wrong. Thus, correlationism is no longer just a skeptical position. It holds that all the possibilities of the world are absolute possibilities. We have absolute knowledge that any of the possibilities about the existence or non-existence of things-in-themselves might be true, and this means that correlationism flips into Meillassoux’s own position: speculative materialism. As Meillassoux sees it, there are only two options here. Option A is to absolutize the human-world correlate, which is what the idealist does: there absolutely cannot be anything outside thought. Option B, by contrast, is to absolutize the facticity of the correlate: its character of simply being given to us, without any inherent necessity. The correlationist cannot have it both ways by saying: “there absolutely might be something outside thought, yet maybe this is absolutely impossible.” In other words, once we escape dogmatism we can only be idealists or speculative materialists, not correlationists. The human-world correlate is merely a fact, not an absolute necessity. But this facticity itself cannot be merely factical: it must be absolute. Here Meillassoux coins the French neologism factualité , which has been suitably translated into the English neologism “factiality.” (7, 122-3) Factialty means that for everything that exists, it is absolutely possible that it might be otherwise, not just that we cannot know whether or not it might be otherwise. Just as Kant transformed philosophy into a meditation on the categories governing human finitude, Meillassoux wishes to turn philosophy into a meditation on the necessary conditions of factiality, which he calls “figures”—a new technical term for him. (80) One such figure is that the law of non-contradiction must be true, and for an unusual reason. Since everything is proven to be contingent, nothing that exists can be contradictory, for whatever is contradictory has no opposite into which it might be transformed, and thus contingency would be impossible.3 Another such figure is that there must be something rather than nothing: for since contingency exists, something must exist in order to be contingent. It is a daring high-wire act, one that sacrifices realism to the correlational circle in order to rebuild it from out of its own ashes. Some might conclude that the lack of reason in things is a byproduct of the ignorance of finite humans, Meillassoux is making precisely the opposite point. For in fact, the doctrine of finitude usually leads directly to belief in a hidden reason. The fact that it lies beyond human comprehension merely increases our belief in this arbitrarily chosen concealed ground. By defending anew the concept of absolute knowledge Meillassoux evacuates the world of everything hidden. The reason for things having no reason is not that the reason is hidden, but that no reason exists. Thus, even while insisting on the necessity of non-contradiction, he rejects the other Leibnizian principle: sufficient reason. Everything simply is what it is, in purely immanent form, without deeply hidden causes. Or as Meillassoux puts it: “There is nothing beneath or beyond the manifest gratuitousness of the given—nothing but the limitless and lawless power of its destruction, emergence, or persistence” (63).The world is a “hyper-chaos”(64). But this is not the same thing as flux. For the chaos of the world is such that stability might occur just as easily as constant, turbulent change. Let’s now digress a bit, and return to the question of ancestrality, which Meillassoux transforms later in the book into “dia-chronicity.” Correlationism holds that all talk of a world outside the correlate is immediately recuperated by the correlate. The phrase “13.5 billion years ago” becomes “13.5 billion years ago for us ,” and the phrase “the universe following the extinction of humans” becomes “the universe following the extinction of humans for humans .” But notice that whether we talk about the world before or after humans, in both cases it is time that is used to challenge the correlate. Meillassoux has no interest in challenges that might be posed by space. For example, what about a vase in a lonely country house that topples to the floor and smashes when no one is there to watch it? Isn’t this also a challenge to correlationism, no less than the Big Bang or the heat death of the universe long after humans have vanished? In an eight-page supplement to the English translation of After Finitude ,4 possibly in response to my own 2007 review of the French original,5 Meillassoux bluntly denies that space is of any relevance to the question. Spatial distance is a merely harmless challenge to the human-world correlate. After all, even though no one is there in the lonely country house to witness the shattering of the vase, we can say that had there been an observer , that observer would have witnessed the toppling and destruction of the vase. For this event still occurs in a world in which the human-world correlate already exists, whereas the diachronicity of events both before and after the existence of humans makes it impossible to say that had there been an observer they would have witnessed the Big Bang occurring in such and such a fashion. However, it seems to me that Meillassoux merely asserts that the temporal simultaneity of our existence with that of the vase in the lonely country house is enough to render it harmless. It is true that the house does not exist prior to the correlate, but nonetheless it exists outside the correlate, and that is enough to make the same challenge. It is difficult to see why the “had there been an observer” maneuver succeeds in the case of a vase in the countryside in April 2011 but fails in the case of the Big Bang. This is not just a matter of nitpicking Meillassoux’s argumentative style: the fact that he bases his argument on time has at least two important consequences for his position. For in the first place, even though Meillassoux insists that the laws of nature are absolutely contingent, this turns out to be true only in a temporal sense. That is to say, it is a paradoxical feature of Meillassoux’s philosophy that he does allow for the existence of laws of nature, and simply believes that they can change at any moment without reason. Within any given moment, laws of nature do exist. He never suggests that different parts of the universe can have different laws at the same time, nor does he have any interest in the laws of part/whole composition that take place within any given instant. Could it be the case that rather than being made of gold atoms, a small chunk of gold could be made of silver atoms, cotton, horses, or that this same small piece of gold could be made of gigantic vaults filled with even more gold? These are not topics that draw Meillassoux’s attention, since he is focused solely on how the laws of nature might change or endure from one moment to the next . Another implication for Meillassoux’s system is that his concept of things-in-themselves turns out to be to be inadequate. For when he proves that things-in-themselves can exist without humans, this turns out to be true only in a temporal sense as well. Namely, things-in-themselves existed ten billion years ago, and they will continue to exist after all humans have succeeded in exterminating themselves. However, being able to exist before our births and after our deaths is just one small part of what it means to be a thing-in-itself. The more important part is that even if a thing is sitting on a table right now, in front of me, even if I stroke it lovingly or press my face up against it directly, I am still dealing only with a phenomenal version of the thing; the thing-in-itself continues to withdraw from all access. Yet no such thing is acknowledged by Meillassoux. For him finitude is a disaster, and absolute knowledge is in fact possible. Meillassoux’s thing-in-itself exists in independence only of the human lifespan , not of human knowledge. The fifth pillar of Meillassoux’s argument is his use of Cantor’s transfinite mathematics to show that even if the laws of nature are contingent, they need not be unstable, and thus we cannot use the apparent stability of nature to disprove his metaphysics of absolute contingency. What Cantor showed is that there are different sizes of infinity, and that all these infinities cannot be totalized in a single infinite number of infinities. Meillassoux sees this as crucial, since it allows him to discredit any “probabilistic” argument against his theory. The probabilistic argument (as defended quite clearly by Jean-René Vernes)6 would say this: given that the laws of nature seem so stable, it it is extremely improbable that there is no hidden reason for their remaining so stable. As Meillassoux sees it, probability is of value only when we can index an accessible total of cases. These can even be infinite: for example, there are an infinite number of points where a rope can break when stretched tight, but this does not stop us from calculating probabilities for various sections of the rope to break. By contrast, there is no way to sum up the number of possible laws of nature. For here there is no way to totalize; we cannot stand outside of nature and calculate the possible number of laws so as to determine the probabilities that any one of them might change. Therefore, although we can speak of probability when dealing with intraworldly events such as elections, horse races, and coin-flips, we cannot use the words “probable” or “improbable” when describing alterations at the level of nature as a whole. Rather than commenting on the validity of this argument and its use of Cantor, let me simply note that it once again creates a dualistic ontology. We already saw that Meillassoux treats time differently from space. In analogous fashion, he now treats the level of world differently from that of intraworldly events. The emergence of worlds is purely contingent and virtual and governed by no probability at all, while events within the world necessarily follow laws (even if these laws can change at any moment without reason), and thus their probabilities can be calculated. It is a strategy deeply reminiscent of Badiou’s (2005) own dualism between the normal “state of the situation” and the rare and intermittent “event.” The sixth and final pillar of Meillassoux’s book can be dealt with briefly, since we have already touched on it elsewhere. It comes at the very beginning of the book, when Meillassoux says that we must revive the distinction between primary and secondary qualities, and that the primary qualities are the ones that can be mathematized. He admits that he has not yet published a proof of this idea, though in fact it is already known as one of his primary doctrines. And here we encounter the familiar problem with Meillassoux’s inadequate conception of things-in-themselves. “Primary qualities” refers to those qualities that a thing has independently of its relations with us or anything else. But if the primary qualities can be mathematized, this means that they are not entirely independent of us, since our knowledge can get right to the bottom of them. The mathematized qualities of things are independent of us only in Meillassoux’s sense that they will still have those qualities even when all humans are dead. But to repeat, autonomy from the human lifespan is not the same as autonomy from human access. Here once more Meillassoux is concerned only with independence from the human-world correlate across time, not in any given instant. 2. L’Inexistence divine In 1997, the same year in which he turned thirty years old, Meillassoux earned his doctorate at the École normale supériuere with a brazen dissertation entitled L’Inexistence divine ( The Divine Inexistence ). The work was substantially revised in 2003. But even then, with typical fastidiousness, Meillassoux decided that the work was not yet ready for press. It has now been scrapped in favor of some future, multi-volume work bearing the same title. While writing my book on Meillassoux for Edinburgh University Press, I was permitted to translate excerpts from this unpublished work for use as an appendix in my own book; in total, the appendix contains approximately twenty percent of Meillassoux’s 2003 manuscript, the first time any of it will be published in any language. Nonetheless, a portion of the argument was already tested in the article “Spectral Dilemma,” published in English in the journal Collapse (2008: 261-75). There the philosophical motives for the virtual God are already made clear. What troubles us most are early deaths, brutal deaths, deaths of especial injustice– the sorts of deaths in which the brutal twentieth century was so abundant. And here, neither the atheist nor the believer can help us. The atheist can offer nothing but a sad and cynical resignation when reflecting on the victims of these terrible crimes. The believer does little better, being unable to explain how God could have allowed such things to happen, due to the famous intractability of the problem of evil. The solution offered to this dilemma by Meillassoux is bold, and all the more so given that he emerges from such a deeply Leftist, materialist, and unreligious background. His solution is that God does not yet exist, and therefore is not blameworthy for these catastrophes. Given that everything is contingent in Meillassoux’s philosophy, this God and divine justice might never exist, but they can at least exist as an object of hope. Let’s begin by jumping to the end of L’Inexistence divine , where the alternatives are laid out so nicely. There are four basic attitudes that humans can have towards God, Meillassoux says. First, we can believe in God because he exists. This is the classical theist attitude, rejected for the simple reason that it would be amoral and blasphemous to believe in a God who allows children to be eaten by dogs, to use Dostoevsky’s example. Second, we can disbelieve in God because he does not exist: the classical atheist attitude. But this leads to sadness, cynicism, and a sneering contempt for the greatness of human capacity. The third option, rather more complex, is to disbelieve in God because he does exist: in other words, to exist in rebellion against God as the one who must be blamed for the evils of the earth. The examples here might range from Lucifer himself, to the more human figure of Captain Ahab in Melville’s Moby-Dick , to Werner Herzog’s even more recent catchphrase, “Every man for himself, and God against all.” That leaves only the fourth option: believing in God because he does not exist. Meillassoux closes his book by saying that the fourth option has now been tried (namely, in the course of his own book), and that now that all four have been specified, we must choose. The first reaction to this theory of the inexistent God will be laughter. Few readers will ever be literally convinced by it, and probably none will immediately be convinced by it. But if we ask ourselves why we laugh, the answer is because it sounds so improbable that an inexistent God might suddenly emerge and resurrect the dead. It obviously sounds more like a gullible theology than a rigorous piece of philosophical work. Yet two things need to be kept in mind. First, Meillassoux’s theories are hardly more unlikely than those of great philosophers of the past such as Plato, Plotinus, Avicenna, Malebranche, Spinoza, Leibniz, Nietzsche, or Whitehead. We read the great philosophers not because their systems are plausible in commonsense terms that can be measured by the laws of probability. Instead, we read them precisely because they shatter the existing framework of common sense and open up new window on the universe. Second, and even more importantly, Meillassoux has already rejected probability as a valid measuring stick in philosophy. Or rather, he accepts probability in the intra-worldly realm (where it is linked with potentiality), and rejects it at the level of the world itself (where potentiality is replaced with what he calls virtuality). The virtual God can appear at any moment for no reason at all, just as any other new configuration of laws of nature can appear: in a manner that the laws of probability cannot calculate. Responding to those who might ridicule the idea of a sudden emergence of God and a resurrection of the dead, Meillassoux cites Pascal, who asserts that the resurrection of the dead would be far less incredible than the fact that we were born in the first place. This shifts philosophy onto new ground. Rather than concerning ourselves with what is likely to happen in the world as we know it, we focus instead on the most important things that could happen. For this reason, the expected objection that a virtual God is no more likely to appear than a virtual unicorn or a virtual flying spaghetti monster misses the point. Unicorns and spaghetti monsters could also appear, just like any other non-contradictory thing. But these would just be novel bizarre entities among others, not the heralds of completely new worlds. For Meillassoux, the emergence of matter, life, and thought have been the three truly amazing advents of the world so far, each of them dependent on the advent(s) preceding them. As he sees it, there can be no greater intraworldly entity than the human beings who already exist, since nothing in the world is better than the absolute knowledge of which humans alone are capable. This means that the next great advent must be something that perfects human beings rather than superseding them. And this can only be the world of justice, in which the dead are resurrected and their horrible deaths partially cancelled (Meillassoux never considers the possibility of a God who would literally erase the pre-divine past so that it never happened at all). The only immortality worth having is an immortality of this life, not an existence in some ill-defined afterworld. Human existence, he holds, must always be governed by a “symbol” that gives us the “immanent and comprehensible inscription of values in a world.” And just as cosmic history made the three great contingent leaps of matter, life, and thought, with a leap to justice as the only one still to come, a similar structure occurs within human culture and its symbols, which consist so far of the cosmological, naturalistic, and historical symbols, with a “factial” symbol still to come. We can review each of these symbols briefly. The cosmological symbol refers to the ancient dualism between the terrestrial and celestial spheres. Here below everything is conflict, corruption, and decay; but in the heavens nothing is perishable, all movement is circular, and everything is arranged in mutual harmony. This symbol is ended by modern physics when Galileo discovers such blemishes as sunspots and craters on the moon, and when Newton integrates both celestial and terrestrial movement into a single gravitational law. Next comes the naturalistic or romantic symbol, in which perfection comes not from the sky but from nature itself. The world is filled with pretty flowers (Meillassoux claims that the ancients never discussed the beauty of flowers until Plotinus in the third century) and with living creatures naturally moved by pity, at least until society corrupts them. This symbol collapses in the face of reality as we know it, since pity is no more common than war, corruption, and violence. This brings us to the historical symbol, which only now is passing away. Bad things may happen, but history has an inner logic of its own, such that everything works out in the end. The ultimate form of the historical symbol is the economic symbol, whether in a Marxist or neo-liberal form. Just as the Marxist holds that the inner economic logic of the capitalists will inexorably lead them to self-destruction, the neo-liberal assumes that the sum total of individual selfish actions will lead, in the long run, to the greatest possible good. We worship the economy and let it guide history for us, just as the ancients worshipped celestial bodies and held them to be free from blemish. The final remaining symbol is the factial symbol, which Meillassoux hopes will now emerge. Factiality, we recall, is his term for the absolute contingency of everything that exists. Once we have grasped this absolute contingency, we are free to expect the dramatic advent of the coming fourth World: the world of justice, inaugurated by a virtual God and even mediated by a messianic human figure. There is the added feature, however, that this messiah must abandon all claims to special status once the messianic realm of justice is achieved. The messianic figure will then be no more special than any person on the street, since a reign of human equality will have arisen. Although this focus on human being might seem like a return to standard humanism, Meillassoux holds that human pre-eminence has never truly been maintained. Previously, humans have been treated as special only because they contemplate the Good, because they resemble their omnipotent creator, or because they happen to be the temporary victors in a cruel Darwinian death-match between millions of living species. For Meillassoux, by contrast, humans have value because they know the eternal. But it is not the eternal that is important, since this merely represents the blind, anonymous contingency of each thing. What is important is not knowledge of the eternal , but knowledge of the eternal. We should not admire Prometheus for stealing fire from the gods; Prometheus is simply as bad as all the gods, no matter how much he increased our power. Feuerbach and Marx were wrong to say that God is a projection of the human essence, since for Meillassoux the usual concept of God represents the degradation of the human essence. If the traditional God was allowed to inflict plagues and tsunamis on the human race, the Promethean human of the twentieth century simply assumes the right to inflict death camps and atomic fireballs instead. In this respect, we have simply begun to imitate the degradation of humanity that was formerly invested in an omnipotent and arbitrary God. In response to charges that absolute contingency might lead to political quietism, Meillassoux counters that the World of justice would mean nothing unless we had already hoped for it beforehand. A World of justice that came along at random would merely be an improved third World of thought: indeed, a perfect one. But it would have satisfied no craving, and would therefore have no redemptive power. For this reason, we must actively hope for the fourth World of justice for such a fourth World ever to arise. Not only justice, but beauty is dependent on such hope: for Meillassoux, who is here somewhat dependent on Kant, beauty means an accord between our human symbolization and the actual world, which could never be present in a World of the blessed any more than justice could. And just as a messianic figure is needed to incarnate our hope and then abandon power once the World of justice is realized, it is the figure of the child whose fragile contingency shows us a dignity and a demand for justice beyond all power. 3. Meillassoux Radicalized or Reversed Given the promising reception of Meillassoux’s first book, it would not be groundless to engage in early speculation about what it might take to earn him a place in the history of philosophy. Maybe this will never happen—who knows?—but quite possibly it will: his lucid argumentative methods and sheer philosophical imagination at least make him a good candidate to be read well into the future, especially following further elaboration in print of his mature system. Philosophy is often practiced as thought it were nothing more than the amassing of “knockdown arguments.” But this is no more insightful than saying that good architecture is the amassing of steal beams. It is true that poorly constructed building cannot stand for long, but sound construction is merely the first, indispensable step in building. In fact, I am inclined to say that what really makes a philosopher important is not being right, but being wrong . I mean this in a very specific sense. I once heard the interesting remark about twentieth century culture that “you have to remember that the sixties really happened in the seventies.” That is to say, it was in the 1970’s rather than the more honored 1960’s that civil rights, free love, long hair, and the rock and roll drug culture really took root. With respect to the history of philosophy, we might just as easily say: “you have to remember that Plato really happened in Aristotle,” that “Kant really happened in Hegel” or “Hume really happened in Kant,” or that “Husserl’s phenomenology first achieved its truth in Heidegger.” One becomes an important philosopher not by being right, but by attracting rebellious admirers who tell you that you are wrong , even as their own careers silently orbit around your own. To recruit faithful disciples may be comforting and flattering, but the greatest thinkers have generally had to experience refutation at the hands of their most talented heirs. For this reason, I would propose that we size up the magnitude of living thinkers not by deciding how many times they are right and wrong, but by asking instead: who would take the trouble to refute this author? For this reason I do not ask: “Is Meillassoux right?”, since I do not believe in the virtual God myself, nor am I convinced by any important aspect of Meillassoux’s philosophy. Instead, I ask if there are interesting ways to overturn him. Only by being overturned, by no longer remaining a contemporary, does one become a classic. Let’s begin with a simple model of refutation, which can be refined further at a later date once the basic point is established. One kind of refutation simply consists in saying: “This author is a complete idiot.” The refuter now walks away in celebration, and no link between the present and the future is built; all is reduced to rubble. But this sort of mediocre triumphalism is generally practiced by those who achieve little of their own, and is not especially interesting. Much more interesting is the sort of refutation that does not take its target to be a complete idiot. I would like to suggest that there are just two basic ways in which this can be done: radicalization and reversal . It has not escaped my notice that this is a fairly good match for the Deleuzian distinction between irony and humor. Whereas irony critiques and adopts the opposite principle of what it attacks, humor accepts what it confronts but pushes it into highly exaggerated form. The ironist is like the worker who sows chaos by rebeling and contradicting the boss, while the humorist is like the worker who follows orders to an absurdly literal degree, with equally chaotic results. Let’s start with a few examples. In Aristotle’s treatment of Plato, and Heidegger’s of Husserl, we find reversal. Plato’s eidei are transformed by Aristotle into mere secondary substances, and the individual worldly things despised by Plato become what is primary. For Husserl what is primary is whatever is present to consciousness, while for Heidegger this is precisely what is secondary, since the primary stuff of the world withdraws from any form of presence at all. As for radicalization, it is most easily found in the transformation of Kant by German Idealism: “Kant was right to wall off the things-in-themselves from human access, and simply should have realized that the thought of the Ding an sich is also a thought, and thereby the noumena are just special cases of the phenomena,” with much following from this discovery. It would also be easy to read Spinoza as a radicalizer of Descartes, and Berkeley and Hume as radicalized versions of Locke. Perhaps the distinction is now sufficiently clear. Admiring refutations are not those that say “Professor X is an idiot,” which is merely the flip side of the eager disciple’s fruitless “Professor X got everything right.” Instead, it will be some variant of one of the following two options: “Professor X is important, but got it backwards,” or “Professor X is important, but didn’t push things far enough.” In the history of philosophy these two latter cases have often been painful in purely human terms: Aristotle expresses sadness at refuting Plato, Kant is openly annoyed at Fichte, and Husserl feels betrayed and used by Heidegger. Rude handling from later figures almost seems to be the sine qua non of being a great philosopher. Now, it has already been claimed that Meillassoux is an emerging philosopher of the first importance, and by no less a figure than Alain Badiou: “It would be no exaggeration to say that Quentin Meillassoux has opened up a new path in the history of philosophy…” (Preface, vii). But rather than taking Badiou’s word for it, or rejecting his word, we might experiment by asking how Meillassoux could be radicalized or reversed. Are there interesting ways of doing this that might launch whole new schools of philosophy, unexpected or even condemned by Meillassoux himself? While no one can see the future, the present is poor when it is not riddled with virtual futures. The relation between philosophers and their predecessors and successors is always somewhat complicated, of course. But generally there is one central divergence at stake, which might be taken as the key to all the others. On this basis we could say that new thinkers primarily radicalize or primarily reverse the main ideas of their chief philosophical forerunner. There may be specific historical conditions and perhaps even personality traits connected with these two types, but this question can be left aside for now. More important for us is that radicalizers will generally be followed by reversers, and vice versa. Consider the textbook example of a reversal in the history of philosophy: Kant’s Copernican Revolution, which inverts the so-called dogmatic tradition that addresses the world itself, and makes the world revolve instead around the conditions by which it is known. While it is not completely impossible that Kant’s successors might have re-reversed this principle back into a new and stronger dogmatic realism, conditions were premature for such a move. Anyone doing this too early would likely have been an angry anti-Kantian reactionary rather than an original thinker in command of a genuinely new realist principle. The far more likely outcome is the one that actually happened: Kant’s reversal of his predecessors was viewed as incomplete, or as retaining lamentable bits of the traditional view, which despite his admirable breakthrough he was unable to shake off. This was the view of German Idealism, anyway. In similar fashion, Spinoza could also be viewed as a radicalizer of Descartes, who is equally accused of preserving various Scholastic dogmas in an otherwise radical project of philosophical reversal. The point is this: reversals in the history of thought tend to be followed soon thereafter by radicalizations of those reversals. The same may hold true in reverse: radicalizations might generally be followed by reversals, given that it is not always possible to be more radical than the radicals have already been. Consider the case of Husserl, who radicalizes Brentano’s early vagueness about what lies beyond immanent objectivity, and Twardowski’s assertion that there must be an external object lying outside the intentional content, by collapsing everything into the intentional sphere: there is no difference between the Berlin in my consciousness and the actual Berlin that is home to millions of people. It is difficult to see how one could be even more radical than Husserl’s idealist turn here. And thus the road is paved to Heidegger’s reversal of classical phenomenology, in which the key point is what lies deeper than any presence to consciousness: the Sein whose power and obscurity cannot be made exhaustively present, but only sends itself in historical epochs. In similar fashion we might also read Leibniz as a reverser of Spinoza’s radicalization, retrieving a strong sense of individual substance and a certain validity of what the Scholastics had said. Returning to Meillassoux, we might ask which kind of philosopher he is: a radicalizer or a reverser? At present, Meillassoux looks to me like a radicalizer (though for now his future remains shrouded in mist). He takes the correlationist tradition, which allows us to speak only of the relation between human and world, and tries to raise it into an even more extreme claim about the absolute contingency of everything. But whereas German Idealism did this by trying to collapse the distinction between thought and world entirely into the “thought” side, Meillassoux does it by trying to shift the non-absolute contingency of the thought-world correlate from epistemology to ontology. It is no longer a question of the inability of human knowledge to know what lies outside the correlate, but the inability of reality itself to be rooted in any definite laws. Furthermore, if we look at the various features of Meillassoux’s philosophy identified earlier tonight, all but one are already so radical that there is no obvious way to push them further. The one exception would be his claim that the world as a whole can change for no reason at any moment, coupled with the inconsistent claim that within a given world there are laws of nature that everything must follow. If gravitational attraction between all masses is a current law in our world, then for Meillassoux there can be no exceptions to this law for as long as it remains in force. A toppled vase will fall to the floor every time for sure,unless there is a cosmic change by which the laws of nature as a whole have altered. (This is reminiscent of the late medieval distinction between the absolute and ordained power of God, according to which God has the power to set or change the laws of nature, but not to contravene those laws locally once they are set.) On this point, to radicalize Meillassoux would simply be to say: there are no laws of nature even in the local sense. Everything that happens, even in the world here and now, is purely contingent and not governed by even a trace of law. And while this would be a more consistent development of Meillassoux’s thoughts on contingency, it is difficult to see how it could lead to a new philosophy. Instead, the admiring successors of Meillassoux are more likely to reverse one of his already sufficiently radical points. At least four candidates come to mind: *First, we have seen that Meillassoux thinks correlationism is challenged by a time before or after consciousness, but not by a space lying outside it. Perhaps this could be reversed into saying that spatial exteriority is the really crucial point. The arguments on this point are perhaps the least convincing in After Finitude (and do not even occur in the original French edition), and therefore it might be a candidate for the “blind spot” of which no philosopher is ever free. *Second, Meillassoux uses Cantor to claim that the contingency of laws of nature would not entail that they are unstable. A successor of Meillassoux might claim that it does make them unstable, and celebrate this fact. This person would then have to explain why common sense seems to encounter a relatively stable world despite its truly rampant instability. Whereas Meillassoux’s problem is to show how stability might exist despite contingency, this successor’s problem would be slightly different: to show why actual, full-blown instability might have the appearance of stability. *Third, Meillassoux claims that the primary qualities of things are those that can be mathematized. He might be reversed by a successor who says the opposite: the mathematizable qualities are the secondary ones, and the primary ones are those that elude symbolic formulation. While this is a perfectly valid possible objection to Meillassoux, it is one that is made in advance by some of his predecessors and is still made by some of his peers, making it less interesting for futurology than some of his other points. *Fourth and finally, whereas Meillassoux claims that God does not exist but might exist in the future, a successor might argue even more bizarrely that God has always existed but might vanish in the future. Let’s arbitrarily select the first of these possibilities, and imagine briefly where it might lead, if pursued in the future by admiring detractors. Meillassoux comes from the circle of Badiou, and some of Badiou’s most ardent admirers are found in Latin America. So, let’s imagine that towards mid-century some ingenious reversers of Meillassoux emerge in that portion of the Spanish-speaking world. Just for fun, let’s call them Castro and Chávez. And in order to avoid any confusion with the present-day politicians of those names, we will stipulate that Meillassoux’s great successors are both women. The philosopher Castro (we will suppose she comes from Peru) reverses Meillassoux’s argument that the ancestral or diachronic are what most threaten the human-world correlate. Instead, she claims that the diachronic does not threaten the correlate at all, and that we must instead look at space as what ruins the correlate and demands a strange new realism. What would such a philosophy look like? In order to determine this, we might ask what price Meillassoux pays for doing it the opposite way. As I see it, he pays in two separate ways. One is that laws of nature for him are contingent over time . The laws of nature apply to the universe as a whole at any given moment, and would be changed globally if they are ever changed at all. The second price he pays is that Meillassoux has no mereology , or theory of parts and wholes. Everything for him is on the level of the given, or immanent in experience, with the sole proviso that the laws governing this immanence might change without notice at any given moment. In reversing Meillassoux, Castro makes the following claims in the preface to her stunning debut book of 2045, The Cosmos and its Neighborhoods , rapidly translated from Spanish into all the languages of the world: Despite his brilliant analysis of the contingency of laws of nature over time, Meillassoux gets two important assumptions wrong. First, he allows for only one set of contingent laws to govern nature as a whole. Second, he allows laws to govern only the world that is immanent in experience, and thereby fails to explore the contingency among part-whole relations. In this book I will argue, first, that the laws of nature vary in any given instant between one region of the universe and the next; and second, that the world is made up of layers of parts and wholes that are also contingent with respect to one another. Those are the words of Castro. This may sound like a hopeless free-for-all of chaos, yet the book somehow succeeds in drawing some compelling deductions about how laws must vary from one place or level in the world to the next. Trapped in the limited horizon of 2011, and not yet inspired by the heavily balkanized political and technological situation of 2050 that somehow lends additional credence to Castro’s vision, we can only vaguely grasp what such a philosophy might look like. After this reversal of Meillassoux by Castro, the usual pattern leads us to expect a radicalization by Chávez, a young Argentine student of Castro. How could the already strange theories of Castro be radicalized? Perhaps as follows, in a disturbing new book entitled The Implosion of the Neighborhoods , which argues as follows: Castro was right to shift the Meillassouxian framework of contingency from time to space. However, in this respect she retained a surprisingly traditional opposition between the two. In this book I will show that time and space collapse into one another. This may sound too much like the discredited four-dimensional block universe of twentieth century physics and philosophy. However, the four-dimensional universe is a model biased in favor of space, merely adding an extra dimension to the commonsense spatial continuum while stipulating that the serial passage of time is an illusion. In this book I will argue instead for a one-dimensional space-time modeled after our experience of time, in which there is no simultaneous co-existence at all between different parts of the universe, or ‘neighborhoods’ as my esteemed teacher Castro has called them. Instead, the various portions of the universe link to one another by succession rather than by coexistence. Buenos Aires, New York, and Amsterdam do not exist simultaneously in the same landscape, but one after the other in the mind of some observer, and this observer can only be an observer much larger than any human. Against Meillassoux’s notion of a virtual God that does not exist now but might exist in the future, I will argue for an actual God that surveys the universe in sequence, thereby generating the illusion of spatial diversity and even the illusion of individual minds located within that diversity. Once this divine observer dies, the universe as a whole must perish. Again, these ideas are so bizarre that we of 2011 can barely comprehend them, just as Aristotle would have had a difficult time grasping the theories of Descartes. We could then perhaps imagine a further reversal of this theory, emanating from the intellectually resurgent Philippines of the twenty-second century. The Filipino School might argue that the universe is already dead, given the collapse of its spatial richness into the serial observations of a flimsy and mortal God. The virtual universe does not yet exist, but might exist in fully spatial form in the future, and this would require the death of God and the resulting liberation of God’s succession of images as independent, spatially situated realities. With a bit of sharpening, we might be able to make all of these imaginary thinkers more intuitively clear. Along with the history of philosophy, there might arise a new discipline generating imaginary futures for philosophy. The richness of Meillassoux’s system comes not from the fact that he is plausibly right about so many things, but because his philosophy offers such a treasury of bold statements ripe for being radicalized or reversed. He is a rich target for many still-unborn intellectual heirs, and this is what gives him the chance to be an important figure. NOTES 1. Quentin Meillassoux, After Finitude . Trans. R Brassier. (London: Continuum, 2008.) Page 5. The word “correlationism” does not appear in his doctoral thesis. As Meillassoux informed me in an email of February 8, 2011, he first coined this term in 2003 or 2004, while editing for publication a lecture he had given at the École normale supérieure on a day devoted to the theme of “Philosophy and Mathematics,” an event including Alain Badiou as one of the participants. 2. Graham Harman, Quentin Meillassoux: Philosophy in the Making . (Edinburgh: Edinburgh University Press, forthcoming 2011). 3. In an email of December 6, 2010, Meillassoux clarifies that in After Finitude he only deduces the impossibility of a “universal contradiction,” not of a determinate contradiction. In the same email he suggests that he can also prove the latter, though the proof is somewhat lengthier than the one found in After Finitude . 4. After Finitude (18-26), in the passage falling between the two sets of triple asterisks. These pages were sent by Meillassoux to translator Ray Brassier (in French) during the translation process, and do not appear in the original French version of the book. 5. Graham Harman, “Quentin Meillassoux: A New French Philosopher.” Philosophy Today 51.1 (2007): Pages 104-117. The passage where I raise the question of space can be found in the first column of page 107. 6. Vernes is first cited on p. 95 of After Finitude . See Jean-René Vernes, Critique de la raison aléatoire, ou Descartes contra Kant . (Paris: Aubier, 1982).  . (shrink)

My essay focuses on the relation between consciousness and reality. I argue, following Georg Cantor, that consciousness is a potential infinite driven by care to invest itself in the world historically. As human beings develop an authentic sense of self they are driven by good faith to postulate an Absolute infinite, which, following Spinoza, we may call God. Thus God, as the Absolute infinite, constitutes our reality, which I characterize as implicate information explicating itself through time. To live authentically is (...) to recognize the nature of God and commit to Him through faith. Faith means to understand one’s self as a potentially infinite consciousness attempting to authentically participate in, and understand, the Absolute of God. (shrink)

Spinoza teaches that the nature of things expresses itself in two ways: in motion and in the world of bodies, on the one hand, and in the intellect with its world of ideas, on the other. Physical bodies are in perpetual motion – arising, changing, disappearing; since the human body also participates in these processes, they are perceived by senses. Spinoza calls the knowledge of sensual properties and duration of the existence of bodies “imagination”. The human mind processes images of (...) bodies with the help of a special kind of abstractions, the “beings of reason”, and then it forms, on the basis of “general concepts”, adequate ideas about the “inner essences” of things, their “order and connec­tion”, i.e. about the causes for the existence of things and their causal relations. Scientific definitions, formulae and models represent these causes and relations in a perfectly pure form – “under a species of eternity”. The article shows how Spinoza delineates the limits of human cognition: they are set by the nature of mind as the idea of the body (man con­sists of two modes of substance – the living body and its idea/mind in the infinite intel­lect). The wider the scope of the body’s activity, the more our mind knows about the world and about itself. The last section of the article describes the relationship of rea­son to virtue, logic to ethics, and characterises the way of life “according to the guidance of reason”. Social life appears to Spinoza as a battle of “passions”, the passive affects of solidarity and enmity. Society cannot live according to the guidance of reason, but our minds can find a form of government that minimises the damage caused by the “blind af­fects” of the rulers and the crowd: Spinoza considered democracy to be the “completely absolute state”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in Greek mathematics (...) not only reintroduced these limits with greater force but also instigated two different forms of coping with the unthinkable in Western philosophy, mathematics, and science. As Arkady Plotnitsky sets forth, in response to the incommensurability crisis in the ancient Greek intellectual world, there appeared two different attitudes toward the alogon, that is, the unthinkable or irrational. Plato and his followers sought to overcome the unthinkable, of which the incommensurables in mathematics are only an example, through philosophy. In contrast, the Pythagoreans continued to hold on to mathematics as the primary means of knowing the world, but put a larger emphasis on geometry. Plotnitsky [End Page 359] claims that by not putting aside the primacy of mathematics, the Pythagorean shift from arithmetic to geometry established in Western thought a certain tolerance toward the unthinkable within the realm of the thinkable, “a possibility of the alogon in the logos.” Until modern times this remained no more than a possibility. However, in modern mathematics and mathematical physics Plotnitsky identifies a certain fulfillment of this potential, a “radical Pythagorean mathematics.” In his comprehensive and thought-provoking study, Plotnitsky recounts the development of such radical modern Pythagoreanism, not only to tell its history but also to suggest that the unthinkable is a condition of possibility for thought, and that a proper recognition of this role it plays is crucial for the advancement of mathematical thinking and thinking in general.Plotnitsky begins by portraying in broad strokes the two defining characteristics of radical Pythagorean mathematics: the presence of the unthinkable within mathematical thought itself, and the interplay of algebra and geometry. Relying on an extensive knowledge of the history of modern mathematics and physics, in the first two chapters of the book Plotnitsky gradually demonstrates the key role that the alogon plays in some theories of modern mathematical thought, such as Gödel’s incompleteness theorems and quantum mechanics. He also presents and clarifies his own conception of the history of Western thought as a creative process of concept-forming. By creating rather than discovering concepts, great mathematicians break new ground for thinking. The book as a whole argues in length for these two main theses.In chapter 3, the author addresses the thought of Bernhard Riemann to make the case that Riemann’s mathematical thought puts an emphasis on creative conceptual thinking and is not defined merely by calculations or logic. Such thinking is problem-posing rather than axiomatic. Riemann’s central innovation in this respect is the concept of manifold (Mannigfaltigkeit), which enabled him to think anew space and geometry in a radical non-Euclidean fashion, implying an infinite number of possible geometries. Plotnitsky argues—borrowing Deleuze and Guattari’s terminology—that this opened up a “plane of immanence,” which is to say that Riemann created a concept-generating movement of thought. However, we cannot grasp the generation of concepts in modern mathematics without giving proper attention to the interplay of algebra and geometry that defines it. Chapter 4 demonstrates this interweaving of the two fields by recounting the history of the idea of the curve in modernity, from the analytic geometry and calculus of Fermat and Descartes to its modification in the concept of a Riemann surface, up to its more recent developments in the algebraic geometry of Weil and Grothendieck. It gives a historical account of the algebraization of the curve that at the same time brings into relief the irreducible geometrical aspect, continuity, of all modern mathematical conceptualizations of the curve.The next two chapters provide further case studies. Chapter 5 expands and solidifies the argument of chapter 2. It discusses three examples of mathematical practice, each displayed by a pair of important [End Page 360] mathematicians: Abel and Galois, Lobachevsky and Riemann, Weil and Grothendieck. Each case... (shrink)

This chapter provides an overview of Thomas Hobbes's materialistic philosophy of mathematics. Hobbes's mathematical ontology rejects the seventeenth century's received view of the subject and his proposed first principles departed quite significantly from the tradition. Hobbes's understanding of geometry as a generalized science of material bodies puts him at odds with the traditional notion that the objects of geometrical investigation are radically distinct from the realm of material things. Hobbes's methodology holds that demonstrative knowledge must be based on definitions that (...) identify the causes of things. Hobbes was quite hostile to the algebraic methods characteristic of Descartes's analytic geometry, and he found fault with some presentations of the “method of indivisibles” that is an important precursor to the calculus. Hobbes approved of Bonaventura Cavalieri's method while dismissing John Wallis's approach as incoherent. The chapter investigates Hobbes's controversy with Wallis. Any discussion of Hobbes's mathematics takes place against the background of his controversy with Wallis. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.2 (2001) 294-295 [Access article in PDF] Schouls, Peter A. Descartes and the Possibility of Science. Ithaca: Cornell University Press, 2000. Pp. x + 171. Cloth, $35.00. There are at least three ways to write the history of philosophy. Truly historical historians of philosophy emphasize the context and development of ideas, concentrating on the intellectual, social, and personal factors that affect the way (...) philosophers have thought about their subject. Analytic philosophers take a critical approach, considering the logic and merit of the arguments of philosophers who have lived in the past almost as if they are engaging in contemporary debates. Another group of philosophers use the ideas of historical figures to support their own philosophical agendas. Peter Schouls' new book on Descartes falls into this third category.Schouls' aim is to present Descartes' philosophy as the origin of modernity. What he means is that "Descartes believed that the world and humanity exist in a relationship which makes it possible for humanity to improve its state through manipulating the world. This manipulation is by means of developing and applying science." Schouls interprets Descartes' notion of progress as leading to "increases in freedom from the drudgery of labor, from the suffering of illness, and from the anxiety of interpersonal and international quarrels,"(ix) arguing that mind-body dualism is necessary for humanity to accomplish these lofty goals.Schouls asks what conditions are needed for humans to develop the science that is a necessary condition for the kinds of progress Descartes sought (and Schouls clearly endorses). Human progress depends on the possibility of science. Descartes founded his science on the pure metaphysics developed in The Meditations. These metaphysical foundations provided the framework for his claim that the human mind can acquire certain knowledge of the world. Central to Descartes' method, Schouls argues, is the view that the imagination must be incorporeal. If this view can be justified, it is a significant departure from the views of most seventeenth-century philosophers who thought that the imagination is a corporeal organ that translates and transmits mechanical impulses to the incorporeal soul. Schouls argues that because the subject-matter of science, especially geometry, involves imagining relationships apart from empirical [End Page 294] experience, it is necessary that the imagination must be incorporeal. Consequently, mind-body dualism is a necessary condition for the kind of science and progress that Descartes sought.There are flaws in this book, some having to do with Schouls' argument and some having to do with its lack of historical context. The two problems are inextricably linked. Schouls reads Descartes without due consideration of historical context. The book's bibliography reveals no primary sources other than the writings of Descartes. Descartes did not write in an intellectual vacuum. He worked within a community of philosophers, and that community provided both the background and audience for his own thoughts. Ignoring this seventeenth-century context causes Schouls to misread the significance of some of Descartes' ideas. For example, he writes that Descartes' philosophy was condemned in both Protestant and Catholic venues "in part because of its assertion of the limitlessness of human freedom" (4). In fact, Descartes' philosophy was banned because he attempted to give a mechanical explanation of the Eucharist. On a related point, Schouls' drive to present Descartes as the origin of modernity causes him to sideline important issues such as the role of theology in Descartes' thought.Similarly, the lack of historical context leads to errors of interpretation. As Alan Gabbey and others have recently demonstrated, terms like "mechanics" and "science" meant something different in the seventeenth century from what they mean today. Even the terms a priori and a posteriori had different meanings in early modern thought. Schouls expresses some mystification about Descartes' use of the term "a priori" in the second Meditiation. This mystification would vanish if he had taken into account early modern usage according to which a priori means reasoning from the one, true cause to an effect rather than acquiring knowledge of the world independently of experience.Schouls' argument sometimes loses... (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. Moreover, Cantor envisioned his transfinite set theory (Mengenlehre) as providing the analytical methods and techniques necessary for a comprehensive, organic, non-reductive description of nature, a Naturphilosophie. Thus Cantor’s novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinity and infinite character of organic life forms is appreciated, and is in some sense a mirror or symbol of the divine. The doctrine of symbolism and their different approach to the laws of logic present in both the work of Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

Kant's theory of space includes the idea that straight lines and planes can be defined in Euclidean geometry by a concept which nowadays has been revived in the field of fractal geometry: the concept of self-similarity. Absolute self-similarity of straight lines and planes distinguishes Euclidean space from any other geometrical space. Einstein missed this fact in his attempt to refute Kant's theory of space in his article ‘Geometrie und Erfahrung’. Following Hilbert and Schlick he took it for granted, mistakenly, that (...) purely geometrical definitions of the concepts of straight line and plane are not feasible, except as “implicit definitions”. Therefore Einstein's criticism is not persuasive. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting (...) with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

This book investigates the relation between mathematics and philosophy in Kant with special focus on the doctrine of the magnitudes. Without doubt, Moretto, who is himself both a mathematician and a philosopher, achieves final results on this matter, because not only does he provide an immanent interpretation of all parts of Kant’s systematic construction of magnitudes, he also provides a detailed history of Kant’s development. Kant gave courses on mathematics during the first eight years of his teaching at Königsberg and (...) warmly recommended the study of mathematics to his most gifted disciples. He himself expressed a profound admiration for it. He wrote in The Only Possible Argument in Support of a Demonstration of the Existence of God that infinitesimal analysis, or, as he calls it, “higher geometry... in its account of the affinities between various species of curved lines,” reveals many of “the harmonious relations which inhere in the properties of space in general.... All these relations, in addition to exercising the understanding by means of our intellectual comprehension of them, also arouse the emotions, and they do in a manner similar to or even more sublime than that the contingent beauties of nature stir our feelings”. In On the Form and Principles of the Sensible and Intelligible World, Kant wrote that pure mathematics “provides us with a cognition which is in the highest degree true, and, at the same time, it provides us with a paradigm of the highest kind of evidence in other cases”. Besides, the mathematician-philosophers of the Leibniz-Wolff school, J. A. Eberhard, J. C. Schwab, J. G. E. Maaß at Halle, and A. G. Kästner at Göttingen, were among the very first to move critiques against the Critique of Pure Reason by focusing on the problem of the foundation of mathematics. They defended Leibniz against Kant, which prompted Kant to start a mathematical school of his own at Königsberg, and J. Schultz, J. G. K. C. Kiesewetter, and C. G. Zimmermann were Kant’s most notable defenders. Finally, one should not forget that it was in order to introduce a completely new set of ideas concerning the philosophy of mathematics that Kant laid out not only the distinction between analytical and synthetical judgments, but also the whole of the transcendental aesthetics. In fact, Kant proposed giving foundation to rational absolute numbers by means of synthetical a priori judgments; he also considered all arithmetical judgments as synthetical a priori; and by dedicating two antinomies to infinite series he suggested analogies to the representation of infinite series of irrational numbers. (shrink)

Samuel Shirley's translations of Baruch Spinoza's Principles of Cartesian Philosophy and Metaphysical Thoughts along with commentary, introduction, and analytic tables.

The aim of this paper is to shed light on our understanding of large scale properties of infinite strings. We say that one string $\alpha $ has weaker large scale geometry than that of $\beta $ if there is color preserving bi-Lipschitz map from $\alpha $ into $\beta $ with small distortion. This definition allows us to define a partially ordered set of large scale geometries on the classes of all infinite strings. This partial order compares large scale geometries of (...) infinite strings. As such, it presents an algebraic tool for classification of global patterns. We study properties of this partial order. We prove, for instance, that this partial order has a greatest element and also possess infinite chains and antichains. We also investigate the sets of large scale geometries of strings accepted by finite state machines such as Büchi automata. We provide an algorithm that describes large scale geometries of strings accepted by Büchi automata. This connects the work with the complexity theory. We also prove that the quasi-isometry problem is a $\Sigma _2^0$ -complete set, thus providing a bridge with computability theory. Finally, we build algebraic structures that are invariants of large scale geometries. We invoke asymptotic cones, a key concept in geometric group theory, defined via model-theoretic notion of ultra-product. Partly, we study asymptotic cones of algorithmically random strings, thus connecting the topic with algorithmic randomness. (shrink)