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Bloomsbury, ISBN: X. Philosophy Today Vol. Problemi Vol. Translated by Drew S. Burk and Anastazia Golemi. Translated by Judith Dellheim. Translated by Mauricio Rugeles Schoonewolff. Translated by Dennis Schep. Translated by Vesna Madzoski.

Translated by Arlind Qori. Tusk of the Translator The Universal Reach of Popular Uprisings. The Tusk of the Translator. Verso Books. Badiou , Alain. Badiou, Alain, "Reducing the Sophist to Silence. Lacanian Ink 35 Lacanian Ink 34 Fulks, and Peter Bradley. Lacanian Ink 33 Lacanian Ink 32 Badiou, Alain, and John Van Houdt. Editions Lignes, Alain Badiou. Actes Sud, What is Philosophy?

A Lecture by Alain Badiou. Edited by Srdjan Cvjeticanin. Atropos Press, Fayard, Controversies: Politics and Philosophy in our Time. Polity, Translated by Jason Smith. Columbia University Press, Translated by Joseph Litvak. Mathematics of the Transcendental: Ontology and being-there , Badiou, Alain.

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Mathematics of the Transcendental: Ontology and being-there. Translated by A. Bartlett and Alex Ling. Translated by Susan Spitzer.

Flammarion, Confrontation: A Conversation with Aude Lancelin. Polity Press, Badiou and the Philosophers: Interrogating s French Philosophy. Rhapsody For The Theatre. Translated by Bruno Bosteels. Cinema , Badiou, Alain. In Praise of Love , Badiou, Alain. In Praise of Love. Translated by Nicolas Truong and Peter Bush. Serpent's Tail, The Adventure of French Philosophy. Translated and Edited by Bruno Bosteels.

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About Mathematics of the Transcendental

The Rational Kernel of the Hegelian Dialectic. Translated by TzuchienTho. Wittgenstein's Antiphilosophy , Badiou, Alain. Wittgenstein's Antiphilosophy. Eloge De L'Amour.

Alain Badiou

La Relation Enigmatique entre Politique et Philosophie. Germina, Mercier Durand, Le Fini et l'Infini , Badiou, Alain. Le Fini et l'Infini. Bayard, Nous, Previously unpublished in either French or English, Mathematics of the Transcendental provides Badiou's readers with a much-needed complete elaboration of his understanding and use of category theory. The book is vital to understanding the mathematical and logical basis of his theory of appearing as elaborated in Logics of Worlds and other works and is essential reading for his many followers.

Description In Mathematics of the Transcendental, Alain Badiou painstakingly works through the pertinent aspects of category theory, demonstrating their internal logic and veracity, their derivation and distinction from set theory, and the 'thinking of being'. The demand for the unconditioned is essentially a demand for ultimate explanation, and links up with the rational prescription to secure systematic unity and completeness of knowledge.

Reason, in short, is in the business of ultimately accounting for all things. Controversially, Kant does not take it that this demand for the unconditioned is something we can dismiss, nor does he take the interests we have in metaphysics to be merely products of misguided enthusiasm. Although the demand for the unconditioned is inherent in the very nature of our reason, although it is unavoidable and indispensably necessary, Kant nevertheless does not take it to be without problems of a unique sort; for the very same demand that guides our rational scientific inquiries and defines our human reason is also the locus of error that needs to be curbed or prevented.

Reason plays this role by generating principles and interests that incite us to defy the limitations of knowledge already detailed in the Transcendental Analytic. Kant refers to this capacity of reason as one that leads to the specifically transcendent judgments that characterize metaphysics. Kant, however, complicates things somewhat by also stating repeatedly that the illusion that grounds metaphysics roughly, that the unconditioned is already given is unavoidable. Moreover, Kant sometimes suggests that such illusion is somehow necessary for our epistemological projects cf.


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What the ideas do not do, according to Kant, is provide the concepts through which we might access objects that could be known through the speculative use of reason. At the heart of that rejection is the view that although reason is unavoidably motivated to seek the unconditioned, its theoretical efforts to achieve it are inevitably sterile. The Dialectic is concerned to undermine three distinct branches of special metaphysics in the philosophical tradition: Rational Psychology, Rational Cosmology and Rational Theology.

This being stated, the Dialectic proceeds systematically to undermine the arguments specific to each of these disciplines—arguments about, for example, the nature of the soul and the world, and the existence of God. Despite the difference in their objects, however, there are a number of problems shared by all the disciplines of special metaphysics.

For this reason alone, the efforts of the metaphysicians are presumptuous, and at the very least, an epistemological modesty precludes the knowledge that is sought. See also Ameriks , Dyck First, Kant offers an account and critique of the ideas of reason specific to each discipline.

In the same way, that is, that the prescription to seek the unconditioned appears to reason as an objective principle, so too, the subjective ideas appear to reason as objects existing in a mind-independent way. As we shall see, Kant unfortunately is not as clear as we might like on this issue.

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Sometimes, he seems to argue that the ideas and principles of reason play a merely heuristic role in guiding and systematizing the knowledge already obtained. Other times, he suggests that these ideas are deeply essential to the project of knowledge acquisition, and that their presupposition is utterly necessary if we are to acquire knowledge. Indeed, it appears to be precisely the rational constraint to move to the ideas of reason that binds us to our metaphysical propensities and which thus demands a critique of the kind offered by Kant.

Alternatively, a most general, formal, principle that would only hold for things in general is taken, by itself alone, to yield knowledge about appearances. Ultimately, Kant will also seek to reveal the very specific formal fallacies that vitiate the metaphysical arguments, to demonstrate that although they have the appearance of soundness the positions in each case are implicitly grounded in, or deploy, dialectical uses of terms and concepts, misapplications of principles, and conflations of appearances with things in themselves.

One historically predominant metaphysical interest has to do with identifying the nature and the constitution of the soul. Partly for practical reasons, partly for theoretical explanation, reason forms the idea of a metaphysically simple being, the soul. The branch of metaphysics devoted to this topic is Rational Psychology.

Rational psychologists, among whom Descartes or Leibniz would serve as apt historical examples, seek to demonstrate, for example, the substantiality, simplicity, and personal identity of the soul. In other words, Kant takes the rational psychologist to slide mistakenly from formal features of our self concept to material or substantive metaphysical claims about an alleged super-sensible object the soul.


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For Descartes, this move is unproblematic: thought is an attribute, and thus presupposes a substance in which it inheres. Kant denies that the metaphysician is entitled to his substantive conclusions on the grounds that the activity of self-consciousness does not yield any object for thought. Nevertheless, reason is guided by its projecting and objectifying propensities. To elucidate the ways in which the rational psychologist is nevertheless seduced into making this slide from formal representations of self consciousness to a metaphysics of the self, Kant examines each of the psychological arguments, maintaining that all such arguments about the soul are dialectical.

Kant suggests that in each of the syllogisms, a term is used in different senses in the major and minor premises. Consider the first paralogism, the argument that allegedly deduces the substantiality of the soul. In the A edition, Kant formulates the argument as follows:. That the representation of which is the absolute subject of our judgments and cannot be employed as determination of any other thing, is substance.

I, as thinking being, am the absolute subject of all my possible judgments and this representation of myself cannot be employed as determination of any other thing. As such, the major premise simply offers the most general definition of substance, and thus expresses the most general rule in accordance with which objects might be able to be thought as substances. Nevertheless, in order to apply the concept of substance in such a way as to determine an object, the category would have to be used empirically. Unfortunately, such an empirical use is precluded by the fact that the alleged object to which it is being applied is not empirical.

This same kind of complaint is lodged against each of the paralogistic syllogisms that characterize Rational Psychology.