Hegel's very first acknowledged publication was, among other things, an attack on Fichte. In 1801, Hegel was still laboring in almost complete obscurity, while Fichte was an international sensation, though already somewhat past the peak of his meteoric career. In the 1801 Differenzschrift, Hegel cut his teeth by criticizing Fichte's already widelycriticised Wissenschaftslehre, and by demonstrating that Schelling's philosophical system was not simply to be equated with it. Fichte himself never bothered to respond to Hegel's criticisms; indeed he never publicly (...) acknowledged their existence. This was not because he was unconcerned with criticisms of his views; quite the contrary. But at the time he had bigger fish to fry. He responded to Jacobi's criticisms, and to Schelling's; he replied in great detail to critical questions raised by Reinhold, and with vituperative intensity to objections raised by skeptics and purportedly loyal Kantians. But Hegel's Differenzschrift was left without a Fichtean rebuttal. This is a pity, both because of the missed opportunity to illuminate by controversy central issues at stake in the post-Kantian period, but also because it made it easier for Hegel simply to reiterate his youthful criticism as if it were the last word. And reiterate it he did: in one form or another Hegel's early criticisms of Fichte reappear at every subsequent stage of his career: in the Phenomenology, in the Science of Logic, in the Encyclopaedia, as the final chapter in Hegel's History of Philosophy, and in countless other minor works and documents from the Nachlass and correspondence. (shrink)

Hegel’s very first acknowledged publication was, among other things, an attack on Fichte.1 In 1801, Hegel was still laboring in almost complete obscurity, while Fichte was an international sensation, though already somewhat past the peak of his meteoric career. In the 1801 Differenzschrift, Hegel cut his teeth by criticizing Fichte’s already widely-criticized Wissenschaftslehre, and by demonstrating that Schelling’s philosophical system was not simply to be equated with it. Fichte himself never bothered to respond to Hegel’s criticisms; indeed he never publicly (...) acknowledged their existence. This was not because he was unconcerned with criticisms of his views; quite the contrary. But at the time he had bigger fish to fry. He responded to Jacobi’s criticisms, and to Schelling’s; he replied in great detail to critical questions raised by Reinhold, and with vituperative intensity to objections raised by skeptics and purportedly loyal Kantians. But Hegel’s Differenzschrift was left without a Fichtean rebuttal. This is a pity, both because of the missed opportunity to illuminate by controversy central issues at stake in the post-Kantian period, but also because it made it easier for Hegel simply to reiterate his youthful criticism as if it were the last word. And reiterate it he did: in one form or another Hegel’s early criticisms of Fichte reappear at every subsequent stage of his career: in the Phenomenology, in the Science of Logic, in the Encyclopaedia, as the final chapter in Hegel’s History of Philosophy, and in countless other minor works and documents from the Nachlass and correspondence. (shrink)

Although Levinas does not specifically articulate an environmental ethic, he certainly has a concept of nature working within his philosophy, a portrait of which can be drawn from the various texts that describe in detail what he believes to be the human, primordial relationship to the elemental. The following essay is an attempt to articulate how Levinas comes to define that relationship, and to imagine what kind of environmental ethic is implied by it. We will see that an important, dichotomous (...) distinction is made between two types of infinity, the “bad infinity” of the sacred and the “good infinity” of the holy. This distinction corresponds to the separated subject’srelationship to the natural world and to the human world. For Levinas, this distinction addresses not only the rationalist vs. empiricist question concerning the relationship between consciousness and the body, a guiding question for modern philosophy from Descartesthrough Husserl, but also the question concerning technology, especially as it is posed by Heidegger and other twentieth century continental philosophers. These two related questions can help guide us to an understanding of how Levinas imagines environmentalimperatives toward both the body’s exclusive relationship to nature, and to the interpersonal relationships between the self and other human beings. We will begin this analysis with Husserl’s answer to the question of consciousness. (shrink)

Hegel's very first acknowledged publication was, among other things, an attack on Fichte. In 1801, Hegel was still laboring in almost complete obscurity, while Fichte was an international sensation, though already somewhat past the peak of his meteoric career. In the 1801Differenzschrift, Hegel cut his teeth by criticizing Fichte's already widelycriticisedWissenschaftslehre, and by demonstrating that Schelling's philosophical system was not simply to be equated with it. Fichte himself never bothered to respond to Hegel's criticisms; indeed he never publicly acknowledged their (...) existence. This was not because he was unconcerned with criticisms of his views; quite the contrary. But at the time he had bigger fish to fry. He responded to Jacobi's criticisms, and to Schelling's; he replied in great detail to critical questions raised by Reinhold, and with vituperative intensity to objections raised by skeptics and purportedly loyal Kantians. But Hegel'sDifferenzschriftwas left without a Fichtean rebuttal. This is a pity, both because of the missed opportunity to illuminate by controversy central issues at stake in the post-Kantian period, but also because it made it easier for Hegel simply to reiterate his youthful criticism as if it were the last word. And reiterate it he did: in one form or another Hegel's early criticisms of Fichte reappear at every subsequent stage of his career: in thePhenomenology, in theScience of Logic, in theEncyclopaedia, as the final chapter in Hegel'sHistory of Philosophy, and in countless other minor works and documents from theNachlassand correspondence. (shrink)

Articles on Sikh philosophy, tradition, and history.

Perhaps nowhere better than, "On the Names of God," can readers discern Laclau's appreciation of theology, specifically, negative theology, and the radical potencies of political theology. // It is Laclau's close attention to Eckhart and Dionysius in this essay that reveals a core theological strategy to be learned by populist reasons or social logics and applied in politics or democracies to come. // This mode of algorithmically informed negative political theology is not mathematically inert. It aspires to relate a fraction (...) or ratio to a series ... It strains to reduce the decided determinateness of such seriality ever condemned to the naive metaphysics of bad infinity. // It is worth considering that it is the specific 'number' of Dionysius in differential identification with an ineffable god (and, as such, a singular becoming between theology and numbers) that is floating in at least two dimensions [of signification] (be it political Demand on the horizontal dimension or theological Desire on [a] floating dimension) that cannot but *perform the link that relinks* names of god with any political life, populist reason, social justice, or radical democracy straining toward peace. (shrink)

Central to Levinas’ “phenomenological” approach to ethics is his identification of an “infinite signification” in the human face. This insistence on the appearance of an infinitely signifying phenomenon has led many, notably Dominique Janicaud, to decry Levinas’ work as anti-phenomenological: little more than a novel approach to metaphysics. A significant element of the phenomenological revolution, Janicaud insists, referencing Husserl and the early Heidegger for support, is grounded in the recognition that phenomena arise in and are circumscribed by finitude. Any reference (...) to an infinite phenomenon which breaks with apperception, he therefore concludes, necessarily breaks as well with the phenomenological tradition, signaling a reversion to idealism, metaphysics, and ultimately theology. As this paper will argue however, a close reading of Husserl reveals not only the recognition of infinite phenomena; but, more significantly, the possibility that all phenomena are potentially infinite. This means that in many ways Levinas is not only more faithful to Husserl’s project than is often admitted; but moreover, that Levinas’ work serves as a lens through which a hitherto under-emphasized element of Husserl’s work can be examined – an element which challenges the traditional critique of Levinas. What’s more, the possibility of infinite phenomena opened up in Husserl’s work, when read through Levinas’ analysis of the ethical significance of the infinite, creates the possibility of recognizing the potential ethical value of all objects, and not merely one object in particular: the human face. This possibility, as I will show, contributes to further blurring the already ambiguous distinction within Levinas between “good” and “bad” infinities – a blurring which, as I will argue, serves as a powerful heuristic in interpreting certain human pathologies, from obsessive compulsive disorder and certain forms of schizophrenia, to the temptation of evil. In this way, an analysis of the status of the infinite in Husserl and Levinas provides a purely phenomenological ground for exploring issues traditionally seen as the exclusive domain of metaphysics and theology. (shrink)

In “Violence and Metaphysics” Jacques Derrida suggests that “the only effective position to take in order not to be enveloped by Hegel would seem to be…to consider false-infinity…irreducible.” Inversely, refuting the charge of logocentrism associated with Hegelian true infinity ( wahrhafte Unendlichkeit ) would involve showing that Hegel’s speculative logic does not establish the infinity of being exempt from the negativity of the finite. This paper takes up Derrida’s challenge, and argues that true infinity is crucial (...) to Hegel’s understanding of ideality as a question of normative authority, which does not fall prey to logocentrism. Through an exposition of the dialectic of the finite and the infinite in Hegel’s Science of Logic , I argue that true infinity is not an ontological category that eliminates division, but rather refers to the metalogical standpoint involved in a philosophical account of determinacy. Although fully achieved at the end of the Logic , the metalogical standpoint that Hegel elaborates in the Seinslogik under the banner of the true infinite already clarifies that determinacy is a product of normative authority that is itself precarious. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:For Today, There Will Be a Speech (and a Song) TomorrowErik DoxtaderFor we see that things that are going to be take their start from deliberating and from acting, and equally that there is in general a possibility of being and not being in things that are not always actual. In them, both are open, both being and not being, and so also both becoming and not becoming. And (...) plenty of things are obviously like this.—Aristotle, De Interpretatione, IX*Wish again, four times again Four wishes deep into the well There's a price to pay for a wish to come true Trade a small piece of your life Roots in soil, uprooting the soil Mountain high, high mountain. The wish is only to speak a kind—Bob Mould, “Wishing Well”This is the time Because there is no time—Lou Reed, “There Is No Time” [End Page 311]The potential of rhetorical culture abides. In the subtle last lines of Norms of Rhetorical Culture, Tom Farrell imbued this potential with the aura of a (double) wish: when read with a forgiving spirit, the value of the “classical rhetorical tradition” appears in its capacity to “restore the power and resilience of the wish in the thought and expression of our civic life” (1993, 320). From within the history of our (not) being together, there are rhetorical goods to (be)come.Wishes must be made. Today, if it is not to betray the fact that a “rhetorical culture is something that must be cultivated,” our inheritance of rhetoric's potential is not a matter of fate. Far from given, although perhaps a gift that speaks volumes about our humanity, its appearance hinges on a choice to “uncover and engender new sources of creative reason” and to do so together, with an appreciation that this shared work is “unmistakably of ethical, aesthetic, and normative significance” (Farrell 1993, 11, 3). Confronted with such a task, as Farrell stressed again and again, “The question is how? How are we to find and develop the capacities that warrant and establish rhetorical study?” (1993, 65). And, from a theoretical and practical perspective, how can we struggle meaningfully with “our own nature as rhetorical creatures: an undiminished capacity to engage limitation through imagination, to find moral content in the experience of the other as audience, and wisdom through the collective production and enactment of logos ” (Farrell 1990, 83)? The rhetorical impulse coincides with the exigency of human experience that remains forgotten and yet unforgettable.1Knocking on modernity's door, Tom Farrell was deeply concerned with rhetoric's manifold potential. Over the course of a prolific career, he pursued the matter with passion, rigor, and integrity. He asked his colleagues, his students, and indeed his discipline to question conventional wisdom about the terms and power of rhetorical theory; interested in both everyday and extraordinary rhetorical practices, Farrell's criticism helped a field to see why its work counted as a vocation at the same time that he reached over the academy's walls in order to suggest that so-called mere rhetoric was quite a bit more complicated and much more important than perhaps some cared to admit. That his vision was compelling is evidenced not least by the numerous awards that he received for his work and the ways in which it continues to inform and shape critical thinking about the art of rhetoric.Just over two years after Tom's unfortunate and tremendously saddening death, this issue of Philosophy and Rhetoric pays tribute to his ground breaking work. Yet, as Farrell himself suspected, the risk that unbridled praise is the short road to bad infinity's silence brings the need for something more. Today, a consideration of his thought and writing demands a space [End Page 312] for critical reflection with practical significance, a forum—in Farrell's sense of the term—that affords an opportunity to ask both whether and how we might understand, extend, and indeed challenge Farrell's contention that rhetoric is the “collaborative manner of engaging others through discourse so that contingencies may be resolved, judgments rendered, action produced” (1990, 83). To these ends, this issue of the... (shrink)

Cet article discute, à travers le parcours critique d’un récent ouvrage d’Anselm Jappe, la thèse d’une illimitation « narcissique » constitutive de la forme subjective propre aux rapports de production capitalistes contemporains. Montrant que cette perspective est fondée sur une conception monolithique et unilatérale de l’histoire du capital et de ses sujets, ainsi que sur une réduction illégitime de toute forme d’in????inité au « mauvais in????ini » de l’illimitation, nous soutenons la nécessité de penser un infini positif irréductible tant à (...) l’illimitation abstraite de la valorisation qu’aux dispositifs capitalistes qui limitent les puissances d’autodétermination et d’autoactivation des individus.This article critically discusses the thesis, recently developed by Anselm Jappe, of a “narcissistic” illimitation constitutive of the subjective form typical of contemporary capitalist relations of production. By showing that this perspective is grounded on a monolithic and one-sided conception of the history of capital and its subjects, as well as on an illegitimate reduction of every form of infinity to the “bad infinity” of illimitation, we defend the necessity to conceive a positive form of infinity, irreducible to both the abstract illimitation of valorization and the capitalist apparatuses that limit the individual power of self-determination and self-activity. (shrink)

Kierkegaard notwithstanding, Hegel's notion of the "good" and "bad" infinity was not unprecedented. On the contrary, this attempt to invest a "logical" category with ethical significances goes back to the very roots of the Western metaphysical tradition. In the Pythagorean doctrine of limit and the unlimited, limit was the arche of the good; the unlimited of evil. In the Pythagorean concept of number as an ens, limit and the unlimited attained ontological status. And since number constituted the determinate character (...) of all things, the Pythagorean peras and apeiron was a logos doctrine, the rational principle of the universe. Thereby Pythagoreanism marked a great advance over the Ionian materialisms. (shrink)

ZusammenfassungAusgehend von zwei Texten Simone Weils und Charles Baudelaires untersucht der Beitrag die religiöse Signatur der literarischen und politischen Moderne des 19. und 20. Jahrhunderts. Manifest wird sie in einem genuin allegorischen Sprach- und Weltverständnis, das sich gegen die schlechte Unendlichkeit einer techno-wissenschaftlich verdinglichten Welt richtet, die sich jeder Alteritätserfahrung verschließt. Religiöse Begriffe und Figuren sind in der literarischen Moderne nicht je schon uneigentliche Rede, sondern verlangen nach einer vorurteilsfreien Lektüre, die theologische Fragen nicht aus-, sondern miteinschließt. Dafür steht nicht (...) zuletzt auch Walter Benjamins Lektüre Baudelaires ein.On the basis of two texts by Simone Weil and Charles Baudelaire, the article examines the religious signature of literary and political modernity in the 19th and 20th centuries. This signature manifests itself in a genuinely allegorical understanding of language and the world, which is directed against the bad infinity of a techno-scientifically reified worldview insulating itself against any experience of alterity. In literary modernity, religious concepts and figures are not to be categorized a priori as inauthentic speech, but demand an unprejudiced reading that does not exclude theological questions. Walter Benjamin’s reading of Baudelaire bears witness to this. (shrink)

This text was originally delivered as the Marshall Lectures in Cambridge in 1967-1968 and one would expect that Alfred Marshall, the great economist of the liberal tradition, would come off the better in comparison with Karl Marx. The expectation is not disappointed, but in the end Kerr finds both Marshall and Marx equally irrelevant to the problems of the contemporary world. The liberalism and socialism which helped shape the modern world now stand historically exhausted. The formative influence in the world (...) is no longer the struggle between classes or between socialism and capitalism. The struggle now is within one pluralistic world, whose industrial nature embraces the socialist as well as the capitalist sectors. The nature of the struggle is no longer for the possession of property, but for power--power to set the rules, fix the rewards, and influence the style of life. Those who engage in the struggle are not economic classes, but social groups and individuals. There is a challenge to the whole society, but by its very nature it cannot succeed. The challenge comes from the under-class and from the outer-class. All other elements, including the workers, the managers, leaders, white-collar employees and self-employed, make up the inner-class and conduct the struggle for power within the framework of acceptance of the existing social order. The two points to emphasize here are that the under-class and outer-class do not have the combined strength to win out, except with the support of some dominant groups of the inner-class--a fairly hopeless prospect. Secondly, no group can win conclusively, since authority in a highly industrialized society can never be held equally by all, or entirely by one. We can only conclude from Kerr's exposition that mankind is forever stuck with what Hegel called a "bad infinity." Post-capitalism and post-socialism have no place to go and a new "end of history" has been attained. Kerr concludes wistfully that we "can only envy the optimism of Marx and Marshall that surround their views of the evolution of the working class."--H. B. (shrink)

It is commonly assumed that Aristotle denies any real existence to infinity. Nothing is actually infinite. If, in order to resolve Zeno’s paradoxes, Aristotle must talk of infinity, it is only in the sense of a potentiality that can never be actualized. Aristotle’s solution has been both praised for its subtlety and blamed for entailing a limitation of mathematic. His understanding of the infinite as simply indefinite (the “bad infinite” that fails to reach its accomplishment), his conception of (...) the cosmos and even its prime mover as finite (in the sense of autarchic/self-contained) have been contrasted with the subsequent claim of God as ens infinitum (understood as a “positive” infinity). The goal of this essay is to reexamine the major texts (notably De caelo) and to demonstrate that (1) Aristotle’s claim according to which there is no actual infinite concerns only substances, not processes. (2) That Aristotle does not deny an actual infinite as such. (3) That when considering time and God (qua eternal) Aristotle acknowledges an actual infinite. (shrink)

This paper describes a scenario in which a person in his afterlife will with probability 1 spend twice as many days in Heaven as in Hell, but, even though Heaven is as good as Hell is bad, his expected utility for any given day in that afterlife is negative.

Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity -- (...) Axiomatic set theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

Abstract:Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary (...) meta-ontological and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above two (...) schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship – (...) the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (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)

The classical response to Zeno’s paradoxes goes like this: ‘Motion cannot properly be defined within an instant. Only over a period’ (Vlastos.) I show that this ob-jection is exactly what it takes for Zeno to be right. If motion cannot be defined at an instant, even though the object is always moving at that instant, motion cannot be defined at all, for any longer period of time identical in content to that instant. The nonclassical response introduces discontinuity, to evade the (...) paradox of infinite proximity of any point of a distance with any ‘next’. But it introduces the wrong sort of discontinuity because, rather than assuming the discontinuity of motion, as Quantum Theory does, it assumes the discontinuity of space. Due then to the resulting spacetime disorder, though all else is certainly lost, the Tortoise now turns up at least as fast as Achilles and hence not even this much is rescued. Zeno rejects motion because he shows that a moving object must be where it is not. Hence motion, if to occur, must violate the Law of Contradiction (LNC). Applying the concept of quantum discontinuity, I produce an alternative. If an object is to move discontinuously between two boundary points, A and B, what actually obtains is, rather, that it is nowhere at all in-between A and B. And cannot therefore be at two places in-between A and B. And cannot therefore be where it is not. Thus, LNC is conserved. However, in these conditions, the Law of the Excluded Middle (LEM) fails. To mitigate the undesirability of this effect, I show that LEM fails because LNC holds. Thus, the resulting nonbivalent logic, which is also appropriate for quantized transitions of all kinds, will always turn up nonbivalent, because consistent. And this is not too bad, considering. (shrink)

Doctors have always thought, it seems, that the female body is more susceptible to illness than the male. Ancient medicine founded this dogma on the doctrine of elementary qualities, in attributing to woman a cold and humid constitution. As heat is the principal instrument which nature uses to produce the forces of the body and to maintain them, it must be lacking in woman, as is proved by her weakness, the softness of her limbs, her lack of external sexual organs (...) and the crudeness of her menstrual blood. If the Aristotelians and the Galenists diverge, in the Renaissance and in the XVIIth century, about the nature—fertile or not—of the “female seed,” they agree to pledge the female body to illnesses. Such a predisposition is explained by the female constitution: its coldness and its humidity, as well as retaining women's strength badly, contribute to giving them a “soft, slack body, of rare texture,” little suited to letting the body fluids, of which it is full, circulate correctly; their blood, corrupted by humidity, instead of being properly heated like it is in men, accumulates, blocks up the too small blood-vessels and causes all the illnesses of which they are the habitual victims. To this it is necessary to add the pathogenic importance of the womb, “a part of the body so sensitive and so easily upset, that its least indisposition causes an infinity of strange and almost unbearable evils.” The indispositions which affect this part of the body are always in relation to humidity or dryness, that is with “the two excrements” which it receives: sperm and menstrual blood. Whether, insufficiently impregnated by the virile liquor, “it mounts to the liver and other higher parts of the body to suck humidity from them until it becomes moist,” or it retains for an abnormally long time the seed, which decays inside it; or the periods are suppressed, or on the other hand they are produced too often; all womens illnesses are a question of impeded or excessive discharge. (shrink)

In this insightful study, Bockja Kim evaluates J.N. Findlay's philosophy of religion in order to determine whether it provides a basis for the positive construction of moral philosophy. In this effort, Kim relies heavily on Hegel's distinction between bad and true infinity to interpret Findlay's philosophical thought. Kim argues that the significance of Findlay's moral philosophy lies in its attempt to construct a method for positive moral reflection by redressing the extreme negative philosophies of transcendentalism and existentialism. Findlay's philosophy (...) thus effectively counters the negativity of moral skepticism and mysticism, both of which tend to neglect moral philosophy and ethics. In addition, Kim explores how Findlay's philosophy may promote inter-faith dialogue between religious traditions of the East and West. Philosophers and religious scholars with interests in Christianity and Buddhism will find this thought-provoking work enlightening. (shrink)

This article is a presentation of the problem of human nature in Dostoevsky's writings. Its author does not agree that the great Russian thinker would give his assent to any of the two opposing ideas: neither that man is good by nature nor that his fate from the moment of birth is tragic. Dostoevsky has proved that freedom constitutes the core of human being. When this freedom is used in a wrong way man becomes bad, and if it is used (...) according to Jesus Christ teachings, he may attain righteousness due to His Grace. In such circumstances, there is no space for any predetermination. Man is free, if he wants to be free. He has got free will. He is always responsible for everything he has done. Dostoevsky uses the term n a t u r e in two different meanings. The first one is essential and refers to the notion of freedom. Consequently, Dostoevsky claims, human nature is beyond full cognition. The second meaning of the term nature refers to the attributes of a particular nation. The differences between nations are further evidence of freedom, which manifests in an infinity of ways. Nature understood as such can be changed and comprehended. The change requires much effort over a long period of time but can by achieved. To capture the full picture of the problem of human nature in Dostoevsky's ultimately it works, both meanings of the above notion should be the taken into consideration. (shrink)

This paper develops transfinite extensions of transitivity and acyclicity in the context of population ethics. They are used to argue that it is better to add good lives, worse to add bad lives, and equally good to add neutral lives, where a life's value is understood as personal value. These conclusions rule out a number of theories of population ethics, feed into an argument for the repugnant conclusion, and allow us to reduce different-number comparisons to same-number ones. Challenges to these (...) arguments are addressed, including the issue of comparing existence and non-existence in terms of personal value, the possibility of minimal quanta of time and life, and the meaningfulness of measuring closeness between outcomes with different population sizes. An asymmetry is uncovered between transfinite cycles of worseness and betterness, supporting a version of the weak procreative asymmetry. Transfinite transitivity principles are also favourably compared to the better-known principles of continuity. (shrink)

This book challenges the view that bad beliefs - beliefs that blatantly conflict with easily available evidence - can largely be explained by widespread irrationality, instead arguing that ordinary people are rational agents whose beliefs are the result of their rational response to the evidence they're presented with.

It is widely accepted that consent is a normative power. For instance, consent can make an impermissible act permissible. In the words of Heidi Hurd, it “turns a trespass into a dinner party... an invasion of privacy into an intimate moment.” In this chapter, I argue against the assumption that consent has such robust powers for moral transformation. In particular, I argue that there is a wide range of sex that harms or wrongs victims despite being consensual. Moreover, these cases (...) are not limited to those where con- sent is vitiated by background conditions. I start by calling this category of consensual sex Bad Sex. I then distinguish subspecies of this category, including psychological pressure, social coercion, and epistemically unsafe sex. I end by responding to an objection on which we should treat at least some subspecies of Bad Sex as rape. Though this alternative proposal is often motivated by ameliorative and strategic considerations, I argue that such considerations actually count against collapsing the categories of Bad Sex and rape. (shrink)

A philosophical exploration of the origin and limits of the modern world.

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories (...) of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes. (shrink)

Bowin begins with an apparent paradox about Aristotelian infinity: Aristotle clearly says that infinity exists only potentially and not actually. However, Aristotle appears to say two different things about the nature of that potential existence. On the one hand, he seems to say that the potentiality is like that of a process that might occur but isn't right now. Aristotle uses the Olympics as an example: they might be occurring, but they aren't just now. On the other hand, (...) Aristotle says that infinity "exists in actuality as a process that is now occurring" (234). Bowin makes clear that Aristotle doesn't explicitly solve this problem, so we are left to work out the best reading we can. His proposed solution is that "infinity must be...a per se accident...of number and magnitude" (250). (Bryn Mawr Classical Review 2008.07.47). (shrink)

Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination (...) of three central figures in the period: Locke, Descartes, and Leibniz. (shrink)

Bad Language is the first textbook on an emerging area in the study of language: non-idealized language use, the linguistic behaviour of people who exploit language for malign purposes. This lively, accessible introduction offers theoretical frameworks for thinking about such topics as lies and bullshit, slurs and insults, coercion and silencing.

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of (...) infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism. (shrink)

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature (...) of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason. (shrink)

Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.

The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds (...) to set-theory or intuitionist approach to the foundation of mathematics and to Peano or Heyting arithmetic. Quantum mechanics can be reformulated in terms of information introducing the concept and quantity of quantum information. A qubit can be equivalently interpreted as that generalization of “bit” where the choice is among an infinite set or series of alternatives. The complex Hilbert space can be represented as both series of qubits and value of quantum information. The complex Hilbert space is that generalization of Peano arithmetic where any natural number is substituted by a qubit. “Negation”, “choice”, and “infinity” can be inherently linked to each other both in the foundation of mathematics and quantum mechanics by the meditation of “information” and “quantum information”. (shrink)

Levy (2021 Levy, N. (2021). Bad beliefs: Why they happen to good people. Oxford University Press.[Crossref], [Google Scholar]) argues that bad beliefs predominately stem from automatic (albeit rational) updating in response to testimonial evidence. To counteract such beliefs, then, we should focus on ridding our epistemic environments of misleading testimony. This paper responds as follows. First, I argue that the suite of automatic processes related to bad beliefs extends well beyond the deference-based processes that Levy identifies. Second, I push back (...) against Levy’s claim that bad beliefs stem from wholly rational processes, suggesting that, in many cases, such processes are better characterized as arational. Finally, I note that Levy is too quick to dismiss the role that individuals can play in cleaning up their own epistemic environments, and I suggest one route through which this is possible. (shrink)

In this paper I present a novel supertask in a Newtonian universe that destroys and creates infinite masses and energies, showing thereby that we can have infinite indeterminism. Previous supertasks have managed only to destroy or create finite masses and energies, thereby giving cases of only finite indeterminism. In the Nothing from Infinity paradox we will see an infinitude of finite masses and an infinitude of energy disappear entirely, and do so despite the conservation of energy in all collisions. (...) I then show how this leads to the Infinity from Nothing paradox, in which we have the spontaneous eruption of infinite mass and energy out of nothing. I conclude by showing how our supertask models at least something of an old conundrum, the question of what happens when the immovable object meets the irresistible force. (shrink)

When Derrida translated and commented on Husserl’s manuscript The Origin of Geometry in 1962, he gave a central place to what Husserl called the Idea “in the Kantian sense”. This article reflects on the use and function of this Idea in Derrida’s reading of Husserl. It critically interrogates the relationship between the Idea in the Kantian sense and mathematical ideality, as well as the use of this Idea in the interpretation of the Thing (Ding) and the stream of experience (Erlebnisstrom). (...) In the centre of the discussion stands what Derrida calls “pure thinking”, on which he tries to ground the Idea in the Kantian sense. (shrink)