Paul Livingston

Derrida's key concepts or pseudo-concepts of différance, the trace, and the undecidable suggest analogies to some of the most significant results of formal, symbolic logic and metalogic. As early as 1970, Derrida himself pointed out an analogy between his use of ‘undecidable’ and Gödel's incompleteness theorems, which demonstrate the existence, in any sufficiently complex and consistent system, of propositions which cannot be proven or disproven (i.e., decided) within that system itself. More recently, Graham Priest has interpreted différance as an instance of the general metalogical procedure of diagonalisation. In this essay, I consider the extent to which Derrida's key terms and the essential operations of deconstruction can be formalised. I argue that, if formalisation is indeed the technique of writing par excellence, then the formalisation of deconstructive concepts tends to show how the auto-deconstruction of total systems arises from the problematic possibility of writing itself. For instance, since diagonalisation permits the ‘arithmetisation of syntax’ whereby a formal system is able to formulate claims about its own logico-grammatical properties, we can understand its potential to inscribe the undecidable within the systematicity of language as simply one instance of the potential of writing, in figuring itself, to render inscrutable the trace of its own origin.

In this paper, I explore Wittgenstein’s inheritance of one specific strand of Kant’s criticism, in the Critique of Pure Reason, of reason’s inherent pretensions to totality. This exploration reveals new critical possibilities in Wittgenstein’s own philosophical method, challenging existing interpretations of Wittgenstein’s political thought as “conservative” and exhibiting the closeness of its connection to another inheritor of Kant’s critique of totality, the Frankfurt school’s criticism of “identity thinking” and the reification of reason to which it leads. Additionally, it shows how Wittgenstein’s linguistic philosophy offers to challenge and undermine, in a historically novel way, the metaphysical assumptions underlying some of our most characteristic and ubiquitous social practices

If it is reasonable to hope that the current moment in philosophy may ultimately represent one of transition, from the divided remnants of the still enduring "split" between "analytic" and "continental" philosophy to some form (or forms) of twenty-first century philosophy that is no longer recognizably either (or is both), it seems likely as well that the thought and work of Alain Badiou can play a key role in articulating this much needed transition. One of the central innovations of Badiou's work is that it uses the kind of rigorous formalism characteristic of much good analytic philosophy in its attempt to think through some of the main problems of ontology, metaphysics and political theory that have troubled continental philosophers over the course of the twentieth century. Both in Badiou's 1988 magnum opus, Being and Event and its new sequel, Logics of Worlds , the result is a kind of paradoxical formalism of the limits of formalism itself, striking a sometimes uneasy balance between the inveterate tendency of analytic thought to seek formal solutions for theoretical problems of epistemology and metaphysics, and that of continental thought to seek the solution to what are seen as more-than-theoretical problems of social and political praxis in the kinds of liberation that may occur outside the "closed" regime of all that is calculable or tractable by formal systems

After more than a century of its development, philosophers working in the analytic tradition have recently begun to consider its history as an object of philosophical investigation.1 This development, particularly significant in the context of a tradition of inquiry that has often conceived of its own problems as ahistorical, is salutary in that it offers to show what, within the tradition, remains rich and vital for philosophy today, as well as to extract the significant theoretical and doctrinal results that can be considered to have been achieved in its itinerary so far. The appearance of a comprehensive, two-volume consideration of the history of analytic philosophy in the twentieth century, written by one of the tradition’s leading contemporary practitioners, is therefore cause for excitement. And Scott Soames’ two-volume Philosophical Analysis in the Twentieth Century is, by any measure, an impressive work. Running to almost 900 pages, it assembles careful, meticulous and detailed expositions and analyses of the arguments and positions of a wide variety of thinkers within the analytic tradition, evaluating the extent of their insight and suggesting implications for philosophical thought today. The analysis is uniformly lucid and clearly written, offering the student of the analytic tradition an indispensable source of arguments she may want to consider in her own work, as well as, in its own argumentation, a suggestive model of at least one way of doing analytic philosophy. Over the course of his reconstructive and evaluative analysis, Soames considers the views and arguments of early analytic philosophers like Russell and Moore, logical positivists like Ayer and..

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.

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 problem of explaining consciousness remains a problem about the meaning of language: the ordinary language of consciousness in which we define and express our sensations, thoughts, dreams and memories. This book argues that the problem arises from a quest that has taken shape over the twentieth century, and that the analysis of history provides new resources for understanding and resolving it. Paul Livingston traces the development of the characteristic practices of analytic philosophy to problems about the relationship of experience to linguistic meaning, focusing on the theories of such philosophers as Carnap, Schlick, Neurath, Husserl, Ryle, Putnam, Fodor and Wittgenstein. Clearly written and avoiding technicalities, this book will be eagerly sought out by professionals and graduate students in philosophy and cognitive science.

Frege ridiculed the formalist conception of mathematics by saying that the formalists confused the unimportant thing, the sign, with the important, the meaning. Surely, one wishes to say, mathematics does not treat of dashes on a bit of paper. Frege’s idea could be expressed thus: the propositions of mathematics, if they were just complexes of dashes, would be dead and utterly uninteresting, whereas they obviously have a kind of life. And the same, of course, could be said of any proposition: Without a sense, or without the thought, a proposition would be an utterly dead and trivial thing. And further it seems clear that no adding of inorganic signs can make the proposition live. And the conclusion which one draws from this is that what must be added to the dead signs in order to make a live proposition is something immaterial, with properties different from all mere signs. But if we had to name anything which is the life of the sign, we should have to say that it was its use. (Blue Book, p.