Badiou,Priest, and the Hegelian Infinite

Abstract

Hegel’s distinction between the bad and true infinites has provoked contrasting reactions in the works of Alain Badiou and Graham Priest. Badiou claims that Hegel illegitimately attempts to impose a distinction that is only relevant to the qualitative realm onto the quantitative realm. He suggests that Cantor’s mathematical account of infinite multiplicities that are determinate and actual remains an endlessly proliferating bad infinite when placed within Hegel’s faulty schema. In contrast, Priest affirms the Hegelian true infinite, claiming that Cantor’s formal mechanisms of boundary transcendence, such as ‘diagonalization’, are implicit in Hegel’s dialectic. While arguing that a clear dividing line can be drawn here between these two interpretations of the relationship between Hegel and Cantor, this paper also mounts a defence of the Hegelian true infinite by developing Priest’s suggestion that Cantorian diagonalizing functions are prefigured by Hegel’s dialectical overcoming of limits.     

Philosophy as Anti-Religion in the Work of Alain Badiou

The Heideggerian rupture in the history of philosophy in the name of a phenomenological and poetic ontology has provided an opening which many of the key figures in twentieth century continental thought have exploited. However, this opening was marked by Heidegger himself as an ambiguous one, insofar as metaphysics was perhaps integrally ‘onto-theology,’ that is, ultimately continuous with the world-historical capture of the thought of being. This piece argues that the philosophy of Alain Badiou, which departs from the recognition that Heidegger is the ‘last universally recognised philosopher’, provides the means for a radical reconsideration of the philosophy-theology relationship in its specifically Heideggerian form, involving as it does further questions of science and technology, the status of the poem, and the nature of ontological thought as such. We argue that, through the deployment of mathematics as ontology, the Gordian knot of onto-theology and its legion of consequences can be cut, and a new assemblage of many of the key Heideggerian motifs can be put into play: the poem, history, and philosophy itself.

The errant name: Badiou and Deleuze on individuation,causality and infinite modes in Spinoza

Although Alain Badiou dedicates a number of texts to the philosophy of Benedict de Spinoza throughout his work—after all, the author of a systematic philosophy of being more geometrico must be a point of reference for the philosopher who claims that “mathematics = ontology”—the reading offered in Meditation Ten of his key work Being and Event presents the most significant moment of this engagement. Here, Badiou proposes a reading of Spinoza’s ontology that foregrounds a concept that is as central to, and celebrated in, his philosophy as it is strictly excluded by Spinoza: the void. In nuce, Badiou contends that for all of Spinoza’s efforts to offer an ontology of total plenitude, the void returns in his philosophy under the (at first sight) unlikely name of infinite mode. The presence of this errant name in Spinoza’s philosophy bears witness to the failure of his most profound intellectual endeavour. However striking Badiou’s reading of Spinoza, this paper argues that it fails to adequately grasp Spinoza’s metaphysics, particularly with respect to the central concept of modal essence, a concept which does not appear at all in the Badiouian text. By introducing a consideration of this concept, it becomes able to resolve the status of infinite modes, and to account for the move across the notorious finite–infinite divide. Thus the argument turns to the reading of Spinoza offered by Gilles Deleuze for a more thorough-going and nuanced approach, much superior to Badiou’s procrustean critique.

Infinity in Mathematics and Theology

Abstract

“Infinity” and its derivatives are frequently used in mathematics and theology. Do these expressions denote the same thing in those distinct areas of scholarship? In this article the uses of “infinity” in mathematics and its uses in theology are examined and compared. One conclusion is that quite different concepts go under the heading of “infinity.” Although they must not be confused, there are some relations between mathematical and theological senses of infinity.     

Phantom of consistency: Alain Badiou and Kantian transcendental idealism

Immanuel Kant is one of Alain Badiou’s principle philosophical enemies. Kant’s critical philosophy is anathema to Badiou not only because of the latter’s openly aired hatred of the motif of finitude so omnipresent in post-Kantian European intellectual traditions—Badiou blames Kant for inventing this motif—but also because of its idealism. For Badiou-the-materialist, as for any serious philosophical materialist writing in Kant’s wake, transcendental idealism must be dismantled and overcome. In his most recent works (especially 2006’s Logiques des mondes), Badiou attempts to invent a non-Kantian notion of the transcendental, a notion compatible with the basic tenets of materialism. However, from 1988’s Being and Event up through the present, Badiou’s oeuvre contains indications that he hasn’t managed fully to purge the traces of Kantian transcendental idealism that arguably continue to haunt his system—with these traces clustering around a concept Badiou christens “counting-for-one” (compter-pour-un). The result is that, in the end, Kant’s shadow still falls over Badiouian philosophy—this is despite Badiou’s admirable, sophisticated, and instructive attempts to step out from under it—thus calling into question this philosophy’s self-proclaimed status as materialist through and through.

Theology and Mathematics—Key Themes and Central Historical Figures

This article provides a survey of the history of the dialogue between the disciplines of mathematics and theology. It identifies three principal historical periods—the ancient, the scientific revolution, and modern. It identifies five key themes—the ontological status of mathematics; mathematics as a bridge to a noumenal world; God's relationship to the physical universe and how mathematics is part of this; truth—its nature, how we know it, certitude; and the role of mathematics in culture. The author develops these themes by exploring the thinking of several major historical figures.     

Mathematical determinacy and the transferability of aboutness

Competent speakers of natural languages can borrow reference from one another. You can arrange for your utterances of ‘Kirksville’ to refer to the same thing as my utterances of ‘Kirksville’. We can then talk about the same thing when we discuss Kirksville. In cases like this, you borrow “aboutness” from me by borrowing reference. Now suppose I wish to initiate a line of reasoning applicable to any prime number. I might signal my intention by saying, “Let p be any prime.” In this context, I will be using the term ‘p’ to reason about the primes. Although ‘p’ helps me secure the aboutness of my discourse, it may seem wrong to say that ‘p’ refers to anything. Be that as it may, this paper explores what mathematical discourse would be like if mathematicians were able to borrow freely from one another not just the reference of terms that clearly refer, but, more generally, the sort of aboutness present in a line of reasoning leading up to a universal generalization. The paper also gives reasons for believing that aboutness of this sort really is freely transferable. A key implication will be that the concept “set of natural numbers” suffers from no mathematically significant indeterminacy that can be coherently discussed.     

Religion,Theology and Science: A Reformational Dooyeweerdian Approach

The most discussed (and applied) approaches to the relationship between religion and science seem to be basically four: opposition, independence, dialogue and integration. Only a few authors take into account the reformational approach that finds its roots in the work of Abraham Kuyper, Herman Dooyeweerd and others. This model may be described by the formula “inner reformation.” A historical and systematic introduction to this approach is hereby provided by sketching its understanding of the nature of (and relationships among) science, theology and religion. In the process, the originality and value of this approach to the relationship between religion and science are highlighted.     

Van Inwagen and the Quine-Putnam indispensability argument

In this paper I do two things: (1) I support the claim that there is still some confusion about just what the Quine-Putnam indispensability argument is and the way it employs Quinean meta-ontology and (2) I try to dispel some of this confusion by presenting the argument in a way which reveals its important meta-ontological features, and include these features explicitly as premises. As a means to these ends, I compare Peter van Inwagen’s argument for the existence of properties with Putnam’s presentation of the indispensability argument. Van Inwagen’s argument is a classic exercise in Quinean meta-ontology and yet he claims – despite his argument’s conspicuous similarities to the Quine-Putnam argument – that his own has a substantially different form. I argue, however, that there is no such difference between these two arguments even at a very high level of specificity; I show that there is a detailed generic indispensability argument that captures the single form of both. The arguments are identical in every way except for the kind of objects they argue for – an irrelevant difference for my purposes. Furthermore, Putnam’s and van Inwagen’s presentations make an assumption that is often mistakenly taken to be an important feature of the Quine-Putnam argument. Yet this assumption is only the implicit backdrop against which the argument is typically presented. This last point is brought into sharper relief by the fact that van Inwagen’s list of the four nominalistic responses to his argument is too short. His list is missing an important – and historically popular – fifth option.

The Problem of Patriotism: A Psychoanalytic and Theological Analysis

In this article, I examine patriotism from psychoanalytic and theological perspectives, arguing that it is a deeply problematic form of love and devotion. After providing a brief overview of the discourse vis-à-vis patriotism, I depict the characteristics of a dominant form of patriotism (self-state) in the U.S. Given this, I argue that, while patriotism has a variety of forms, the most prevalent form tends toward tragic consequences and it is this tragic tendency that I depict from psychoanalytic and theological perspectives. From a psychoanalytic perspective, the extant form of patriotism in the U.S. represents a self-state that signifies an idealized, omnipotent, and imaginary identification, which is accompanied by and contingent upon a devaluation of the Other. Moreover, the dominant form of patriotic self-states is secured by weak dissociation, omnipotent thinking and, in most cases, a collapse of the symbolic equation. From a Christian theological perspective, patriotism signifies absolutizing the relative and contingent. This form of idolatry manifests a distortion of reason and will, which contributes to corrupted and corrupting forms of love and devotion.     

Leibniz on Infinite Numbers,Infinite Wholes,and Composite Substances

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz's argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz's rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’ – collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.     

Finishing the Story: Aging,Spirituality, and the Work of Culture

ABSTRACT

Society projects its death anxiety onto old age and the aging, who are isolated from generative human contact, with no conversation expected. Any shared, common language atrophies. Broken connection becomes a cultural expectation. Society and the aging lose sight of developmental tasks appropriate to old age. We do not seek or foster last careers devoted to finishing the human story, to completing a sense of meaning about life. Such a last career would raise questions about soul-making and invite awe and wonder at life and death. But no one is called to do such work today, so unfinished cultural business accumulates. We should anoint or commission the aging for their last career because of its significance for them and for culture. When the aging take up such last careers and find themselves immediately confronted with the task of life review, they may discover opportunities for repenting, mythologizing, and sacralizing. The work of culture gets done, and gifts to the future are offered by the aging. The broken circle of conversation is closed, re-connections are made, and human communities, including the worlds of the living and the dead, are made whole.     

The Relatively Infinite Value of the Environment

Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have infinite value, then decision theory prescribes indifference. Second, there is a problem of swamping probabilities: an act with a small but positive probability of saving an endangered species appears to be on par with an act that has a high probability of achieving this outcome, since both have infinite expected value. Our paper shows that a relative (rather than absolute) concept of infinite value can be meaningfully defined, and provides a good model for securing the priority of the natural environment while avoiding the failures noted by sceptics about infinite value. Our claim is not that the relative infinity utility model gets every detail correct, but rather that it provides a rigorous philosophical framework for thinking about decisions affecting the environment.     

Trinity,Filioque and Semantic Ascent

It is difficult to reconcile claims about the Father's role as the progenitor of Trinitarian Persons with commitment to the equality of the persons, a problem that is especially acute for Social Trinitarians. I propose a metatheological account of the doctrine of the Trinity that facilitates the reconciliation of these two claims. On the proposed account, ‘Father’ is systematically ambiguous. Within economic contexts, those which characterize God's relation to the world, ‘Father’ refers to the First Person of the Trinity; within theological contexts, which purport to describe intra-Trinitarian relations, it refers to the Trinity in toto-thus in holding that the Son and Holy Spirit proceed from the Father we affirm that the Trinity is the source and unifying principle of Trinitarian Persons. While this account is solves a nagging problem for Social Trinitarians it is theologically minimalist to the extent that it is compatible with both Social Trinitarianism and Latin Trinitarianism, and with heterodox Modalist and Tri-theist doctrines as well. Its only theological cost is incompatibility with the Filioque Clause, the doctrine that the Holy Spirit proceeds from both the Father and the Son—and arguably that may be a benefit.

Oppy,infinity, and the neoclassical concept of God

In this article I concentrate on three issues. First, Graham Oppy’s treatment of the relationship between the concept of infinity and Zeno’s paradoxes lay bare several porblems that must be dealt with if the concept of infinity is to do any intellectual work in philosophy of religion. Here I will expand on some insightful remarks by Oppy in an effort ot adequately respond to these problems. Second, I will do the same regarding Oppy’s treatment of Kant’s first antinomy in the first critique, which deals in part with the question of whether the world had a beginning in time or if time extends infinitely into the past. And third, my examination of these two issues will inform what I have to say regarding a key topic in philosophy of religion: the question regarding the proper relationship between the infinite and the finite in the concept of God.     

Charting the Road of Inquiry: Deleuze's Humean Pragmatics and the Challenge of Badiou

This essay responds to Badiou's charge that Deleuze fails to set forth a philosophy that is “beyond Gategorical oppositions.” It is argued that this criticism of Deleuze is founded upon a misreading of the Deleuzean distinction between the virtual and the actual, a reading that carries forward Badiou's misreading of Spinoza and, hence, of Deleuze's Spinozism. With this corrected, we show how the virtual‐actual distinction operates within the experimental philosophy, or pragmatics, that Deleuze, and later Deleuze and Guattari, sets forth. It is this pragmatics that is precisely the philosophy of difference that is beyond categorical oppositions. Through a comparison of Deleuzean pragmatics with the work of Hume and Peirce, we are able to respond to Badiou's further criticism that Deleuze's philosophy fails to understand the conditions for creativity in thought and culture. This criticism is itself resolved once one corrects for Badiou's misreading of Deleuze's virtual‐actual distinction.     

The catechism of the citizen: politics,law and religion in,after, with and against Rousseau

As a way of thinking through the bleakness of the political present through which we are all too precipitously moving, this essay attempts to demonstrate the interconnections between three concepts: politics, law and religion. By way of a detailed reading of Rousseau, I try to show how any conception of legitimate politics and law requires a conception of religion at its base and as its basis. In my view, this is highly problematic and in the conclusion an argument is presented for a politics of the supreme fiction, which attempts to show how poetry might take the place of religion.

Disturbing Politics: Neo‐Paulinism and the Scrambling of Religious and Secular Identities

Abstract : One of the most remarkable characteristics of recent cultural theory is its obsession with the early Christian apostle Paul. With this interest in Paul as contemporary cultural theory, a panoply of modern identities find themselves obsolesced, scrambled, or otherwise useless. This essay attempts to find new points of orientation within those scrambled identities that have appeared with this new Paul, and the essay does so by exploring the idea that we are now repeating a Pauline moment of kairos, that apocalyptic moment in which meaningful transformation of the world may occur.