Paul Livingston

In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents.

This forward-thinking collection presents new work that looks beyond the division between the analytic and continental philosophical traditions—one that has long caused dissension, mutual distrust, and institutional barriers to the development of common concerns and problems. Rather than rehearsing the causes of the divide, contributors draw upon the problems, methods, and results of both traditions to show what post-divide philosophical work looks like in practice. Ranging from metaphysics and philosophy of mind to political philosophy and ethics, the papers gathered here bring into mutual dialogue a wide range of recent and contemporary thinkers, and confront leading problems common to both traditions, including methodology, ontology, meaning, truth, values, and personhood. Collectively, these essays show that it is already possible to foresee a future for philosophical thought and practice no longer determined neither as "analytic" nor as "continental," but, instead, as a pluralistic synthesis of what is best in both traditions. The new work assembled here shows how the problems, projects, and ambitions of twentieth-century philosophy are already being taken up and productively transformed to produce new insights, questions, and methods for philosophy today.

Several debates of the last years within the research field of contemporary realism – known under titles such as "New Realism," "Continental Realism," or "Speculative Materialism" – have shown that science is not systematically the ultimate measure of truth and reality. This does not mean that we should abandon the notions of truth or objectivity all together, as has been posited repeatedly within certain currents of twentieth century philosophy. However, within the research field of contemporary realism, the concept of objectivity itself has not been adequately refined. What is objective is supposed to be true outside a subject’s biases, interpretations and opinions, having truth conditions that are met by the way the world is. The volume combines articles of internationally outstanding authors who have published on either Idealism, Epistemic Relativism, or Realism and often locate themselves within one of these divergent schools of thought. As such, the volume focuses on these traditions with the aim of clarifying what the concept objectivity nowadays stands for within contemporary ontology and epistemology beyond the analytic-continental divide. With articles from: Jocelyn Benoist, Ray Brassier, G. Anthony Bruno, Dominik Finkelde, Markus Gabriel, Deborah Goldgaber, Iain Hamilton Grant, Graham Harman, Johannes Hübner, Andrea Kern, Anton F. Koch, Martin Kusch, Paul M. Livingston, Paul Redding, Sebastian Rödl, Dieter Sturma.

This paper considers the kind of illumination that is provided by an analysis of the global logical forms of the structure and relations of worldly facts and events. I argue that such a global logical reflection, as undertaken in representative forms by Wittgenstein and by Nāgārjuna, shows how we can consider the traditional principle of sufficient reason (PSR) as a formally empty principle rather than a metaphysically substantive one. This recognition of the formal emptiness of the PSR does not suggest the nonexistence of the facts and phenomena it is appealed to in explaining, but rather provides for a radical alternative to forms of global appeal to it within the metaphysical tradition (e.g., those made by Spinoza and Parmenides), on which this appeal appears rather to license a conclusion of monism and the inference to a prior, undifferentiated, substantial One, before or behind the world of articulated facts and events itself.

Seit Žižeks ersten auf Englisch veröffentlichten Schriften spielt Alain Badious Denken und dessen Theorie des „Seins und des Ereignisses“ eine entscheidende Rolle: in der Theoretisierung politischer Subjektivität, in der Auslegung einer materialistischen Ontologie und mit Bezug auf die Möglichkeit radikaler politischer Transformation entlang universalistischer Linien. Die Bedeutung Badious für Žižek geht nicht nur auf das gemeinsame Erbe Lacans und die gemeinsame Ablehnung „postmoderner“ und dekonstruktiver Positionen in der philosophischen und kritischen Theorie zurück, sondern auch auf ihr gemeinsames Engagement für eine antikapitalistische Politik der radikalen Gleichheit, der voluntaristischen Transformation und der Wahrheit der kommunistischen Idee.

In this book, Livingston develops the political implications of formal results obtained over the course of the twentieth century in set theory, metalogic, and computational theory. He argues that the results achieved by thinkers such as Cantor, Russell, Godel, Turing, and Cohen, even when they suggest inherent paradoxes and limitations to the structuring capacities of language or symbolic thought, have far-reaching implications for understanding the nature of political communities and their development and transformation. Alain Badiou's analysis of logical-mathematical structures forms the backbone of his comprehensive and provocative theory of ontology, politics, and the possibilities of radical change. Through interpretive readings of Badiou's work as well as the texts of Giorgio Agamben, Jacques Lacan, Jacques Derrida, Gilles Deleuze, and Ludwig Wittgenstein, Livingston develops a formally based taxonomy of critical positions on the nature and structure of political communities. These readings, along with readings of Parmenides and Plato, show how the formal results can transfigure two interrelated and ancient problems of the One and the Many: the problem of the relationship of a Form or Idea to the many of its participants, and the problem of the relationship of a social whole to its many constituents.

The ancient problem of the relationship of the continuous to the discrete, since its discovery by the Greeks, has posed a range of immensely fruitful challenges to both philosophical and mathematical thought, leading to a variety of mathematical and conceptual innovations whose positive development actively continues today. In this brief section introduction, I selectively outline some significant moments at which this problem has provided important historical occasions for concrete mathematical innovation as well as closely linked philosophical insights, before introducing the particular contributions of the section authors to historical and contemporary research and practice into the nature and structure of the continuum, the construction of real numbers, the foundations of analysis, and the logical, set-theoretical, and computational underpinnings of the structure of continuously valued numbers in the most general sense, in both constructive and nonconstructivist contexts.

After more than thirty-five years of debate and discussion, versions of the functionalist theory of mind originating in the work of Hilary Putnam, Jerry Fodor, and David Lewis still remain the most popular positions among philosophers of mind on the nature of mental states and processes. Functionalism has enjoyed such popularity owing, at least in part, to its claim to offer a plausible and compelling description of the nature of the mental that is also consistent with an underlying physicalist or materialist ontology. Yet despite its continued popularity, many philosophers now think that functionalism leaves something out, in particular that functional explanations and analyses fail to account for consciousness, qualia, or phenomenal states of experience or awareness.¹ If the objection is correct, then functionalism fails in its inability..

The paper brings Dummett’s formulation of “realism” into dialogue with Heidegger’s understanding of truth as “unconcealment.” Livingston argues, with references to Frege and Wittgenstein, that the phenomenon of truth can be understood theoretically and analytically as requiring the pre-theoretical appearing and constitution of objects, in experiential, practical, or explicitly linguistic modalities. This approach provides a basis for new logically- and phenomenologically- based accounts of the structure of objectivity within linguistic truth in relation to the appearance and being of objects. Within the context of a development of Heidegger’s idea of ontological difference, this further implies that truth and objectivity must have a logically paradoxical structure. Even if Heidegger does not often say so explicitly, this paradoxical structure of objectivity and truth is centrally involved, as Livingston argues, in his understanding of the “clearing” and the interpretation it allows of beings “as such and as a whole.”

Working through Balaska’s deeply perceptive, elegantly written, and profoundly honest book, Wittgenstein and Lacan at the Limit, a reader steeped in the recent academic literature about either or both of its main figures may come to feel herself placed at what is, itself, a certain kind of limit. The limit I mean is the limit of a familiar type of theoretical discourse about the constitution and structure of language and subjectivity as Wittgenstein and Lacan treat them: it includes the discourses that seek, for instance, to articulate how language and sense are constituted in the Tractatus, and thus what is really meant by “logical form” and “nonsense” there; or those that aim to comprehend the true relationship of our biological nature to language, culture, and the advent of freedom in Lacan; or, again, those that try to find, in either thinker’s works, the precise location of the delicate logical buttonhole that would alone permit us entry, from within everyday language and life, to the absoluteness of an ineffable beyond. These discourses all treat of language and life, but handle these phenomena at arm’s length, theorizing the structure of each and the form of their relationship in such a way as to establish, ultimately, their mutual convertibility to one another, their mutual absorption into a third, more inclusive term, or adduce translations from the dense theoretical matrices of one thinker’s treatment of them to the other’s. Balaska’s book, doing none of these things, rather succeeds in bringing out how an interconnected reading of the Wittgenstein of the Tractatus and Lacan may speak to and inform our response to a certain kind of experience that is characteristic for both thinkers, and typical as well of those moments and occasions of our lives in which we may find ourselves drawn to reflect on what meaning is and how we relate to it.