Paul Livingston

In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and the Indefinite Dyad provides, in the later Plato, a unitary theoretical formalism accounting, by means of an iterated mixing without synthesis, for the structural origin and genesis of both supersensible Ideas and the sensible particulars which participate in them. As these commentators also argue, this duality furthermore provides a maximally general answer to the problem of temporal becoming that runs through Plato’s corpus: that of the relationship of the flux of sensory experiences to the fixity and order of what is thinkable in itself. Additionally, it provides a basis for understanding some of the famously puzzling claims about forms, numbers, and the principled genesis of both attributed to Plato by Aristotle in the Metaphysics, and plausibly underlies the late Plato’s deep considerations of the structural paradoxes of temporal change and becoming in the Parmenides, the Sophist, and the Philebus. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. These implications of Plato’s duality include not only those of the constitution of specific theoretical domains and problematics, but also implicate the reflexive problematic of the ideal determinants of the form of a unitary theory as such. We argue that the consequences of the underlying duality on the level of content are ultimately such as to raise, on the level of form, the broader reflexive problem of the basis for its own formal or meta-theoretical employment. We conclude by arguing for the decisive and substantive presence of a proper “Platonism” of the Idea in Deleuze, and weighing the potential for a substantive recuperation of Plato’s duality in the context of a dialectical affirmation of what Deleuze recognizes as the “only” ontological proposition that has ever been uttered. This is the proposition of the univocity of Being, whereby “being is said in the same sense, everywhere and always,” but is said (both problematically and decisively) of difference itself.

Some contemporary discussion about the explanation of consciousness substantially recapitulates a decisive debate about reference, knowledge and justification from an earlier stage of the analytic tradition. In particular, I argue that proponents of a recently popular strategy for accounting for an explanatory gap between physical and phenomenal facts – the so-called “phenomenal concept strategy” – face a problem that was originally fiercely debated by Schlick, Carnap, and Neurath. The question that is common to both the older and the contemporary discussion is that of how the presence or presentation of phenomenal experiences can play a role in justifying beliefs or judgments about them. This problem is, moreover, the same as what was classically discussed as the problem of acquaintance. Interestingly, both physicalist and non-physicalist proponents of the phenomenal concept strategy today face this problem. I consider briefly some recent attempts to solve it and conclude that, although it is prima facie very plausible that acquaintance exists, we have, as yet, no good account of it.

Over a period of several decades spanning the origin of the Vienna Circle, Schlick repeatedly attacked Husserl''s phenomenological method for its reliance on the ability to intuitively grasp or see essences. Aside from its significance for phenomenologists, the attack illuminates significant and little-explored tensions in the history of analytic philosophy as well. For after coming under the influence of Wittgenstein, Schlick proposed to replace Husserl''s account of the epistemology of propositions describing the overall structure of experience with his own account based on the structure of language rather than on the intuition of essences. I discuss both philosophers'' accounts of the epistemology of propositions describing the structure of experience. For both philosophers, this epistemology was closely related to the general epistemology of logic; nevertheless, neither philosopher had a completely coherent account of it. Comparison of the two approaches shows that perennial and severe theoretical obstacles stand in the way of giving an epistemology of the structure of experience, a central requirement for both philosophers'' theories. Consideration of these obstacles sheds a new light on the reasons for the historically decisive split between the continental and the analytic traditions, as well as on the subsequent development of the analytic tradition away from the structural description of experience.

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 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.

One difference between Russell’s logical atomism in The Philosophy of Logical Atomism and Wittgenstein’s in the Tractatus is that Russell’s doctrine is explicitly epistemological, whereas Wittgenstein’s is not; another difference is that Wittgenstein gives an a priori argument for the doctrine of logical atomism whereas Russell gives no such argument. I argue that these two differences are instructively connected: Russell’s focus on epistemology prevents him from being able to give a motivated argument for the truth of logical atomism. Furthermore, I argue that this is not just a contingent failure of Russell’s system: no primarily epistemological atomism can avail itself of Wittgenstein’s style of a priori argument for the truth of atomism. An important suggestion of the argument, illuminating with respect to the subsequent history of analytic philosophy, is that Russell’s logical atomism already contains the seeds of verificationism in a nascent form, whereas Wittgenstein’s atomism has no tendency toward verification.

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

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.

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..

My aim in this paper is to begin a discussion about how, and to what extent, Martin Heidegger’s thinking about technology offers helpful critical terms for thinking about the nature and global sway of today’s most dominant and prevalent forms of technology, namely the interrelated technologies of information, communication, and (capitalist) commerce. My suggestion will be that Heidegger’s thought does indeed have implications for critical thinking about these technologies, but that in order to see how it does, we may have to deepen and further radicalize some of Heidegger’s suggestions about essence, being, and form. This need for deepening is connected with the way in which these specific technologies themselves depend on the character and structure of language , in that they present themselves as effective means for the manipulation, storage, retrieval and exchange of broadly linguistic, symbolic, and informational material. In fact, in the context of Heidegger’s late thought about technology as well as language, the syntagm “information technology” itself – a term that, as far as I know, Heidegger himself never used – nevertheless points the way, as I shall argue, to a deepening of the Heideggerian inquiry into form which itself can facilitate an improved critical understanding of the implications of these technologies for life around the planet today

Heidegger's treatment of 'machination' in the Beiträge zur Philosophie begins the critique of technological thinking that would centrally characterize his later work. Unlike later discussions of technology, the critique of machination in Beiträge connects its arising to the predominance of 'lived-experience' ( Erlebnis ) as the concealed basis for the possibility of a pre-delineated, rule-based metaphysical understanding of the world. In this essay I explore this connection. The unity of machination and lived-experience becomes intelligible when both are traced to their common root in the primordial Greek attitude of techne , originally a basic attitude of wondering knowledge of nature. But with this common root revealed, the basic connection between machination and lived-experience also emerges as an important development of one of the deepest guiding thoughts of the Western philosophical tradition: the Parmenidean assertion of the sameness of being and thinking. In the Beiträge 's analysis of machination and lived-experience, Heidegger hopes to discover a way of thinking that avoids the Western tradition's constant basic assumption of self-identity, an assumption which culminates in the modern picture of the autonomous, self-identical subject aggressively set over against a pre-delineated world of objects in a relationship of mutual confrontation. In the final section, I investigate an important and illuminating parallel to Heidegger's result: the consideration of the relationship between experience and technological ways of thinking that forms the basis of the late Wittgenstein's famous rule-following considerations.

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.

Investigation and analysis of the history of the concepts employed in contemporary philosophy of mind could significantly change the contemporary debate about the explainability of consciousness. Philosophical investigation of the history of the concept of qualia and the concept of scientific explanation most often presupposed in contemporary discussions of consciousness reveals the origin of both concepts in some of the most interesting philosophical debates of the twentieth century. In particular, a historical investigation of the inheritance of concepts of the elements of experience and the nature of scientific explanation from C. I. Lewis and Rudolf Carnap to contemporary theorists like David Chalmers shows the profound continuity of these concepts throughout the analytic tradition, despite important changes in the dimensions of philosophical relevance and significance that have characterized the emerging debate. I argue that, despite the significant methodological shift from the foundationalist epistemology of the 1920s to today's functionalist explanations of the mind, the problem of explaining consciousness has remained the problem of analysing or describing the logical and relational structure of immediate, given experience. Appreciation of this historical continuity of form recommends a more explicit discussion of the philosophical reasons for the underlying distinction between structure and content, reasons that trace to Lewis and Carnap's influential but seldom-discussed understanding of the relationship between subjectivity, conceived as the realm of private, ineffable contents, and objectivity, understood as public, linguistic expressibility. With this historical background in mind, the contemporary debate about the explanation of consciousness can be re-interpreted as a debate about the relationship between ineffable experience and structurally conceived meaning

Within contemporary analytic philosophy, varieties of “naturalism” have recently attained an almost unchallenged methodological and thematic dominance. As David Papineau wrote in the introduction to his 1993 book Philosophical Naturalism, “nearly everybody nowadays wants to be a naturalist,” although as Papineau also notes, those who aspire to the term also continue to disagree widely about what specific methods or doctrines it implies. My purpose in this paper, however, is not to argue for or against philosophical naturalism on any of the several conceptions current among analytic philosophers, but rather simply to suggest that a closer look at the history of the analytic tradition can offer helpful terms for rethinking what can be meant by applying the categories of “nature” and “culture” within philosophy’s ongoing reflection on the constitutive forms of human life and practice. For, as I shall argue, the central experience of this history – philosophy’s radical encounter with what it envisions as the logical or conceptual structure of everyday language – also repeatedly demonstrates the existence of a fundamental aporia or paradox of origin and practice at the center of the claim of language upon an ordinary human life. The appearance of this paradox has repeatedly determined the results and projects of the analytic tradition, even as analytic philosophers have also reacted to it, on the level of positive theory, in characteristic modes of dismissal, denial, or repression. Besides offering to elicit more clearly what analytic philosophy still offers to show us about our everyday relation to the language that we speak, I shall argue, documenting the existence and effects of this aporia can also yield a clarified sense of the relationship of the analytic tradition itself to the neighboring streams of “continental” philosophy that have also taken up the question of language during the twentieth century.

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

I explore the decisive connection Frege often draws between the context principle and antipsychologism, arguing that his assertion of this connection occupies a central place within the articulation of his linguistic method. In particular, Frege’s appeal to the context principle in the course of describing the epistemology of arithmetic, I argue, connects his doctrine of the nature of judgment with his defense of the objecthood of numbers, showing how an appeal to the special role of judgment in securing truth can function as a linguistically based account of objectivity that excludes subjectivist psychologism. Expanding and clarifying this appeal, moreover, allows us to understand better the special pragmatic position of the recognition of patterns of use and practice in the process of analyzing meanings. In particular, it emerges that these patterns cannot bear the explanatory weight they have sometimes been taken to bear within an envisaged reductive “theory of meaning.” Rather, their recognition must figure within a practice of analysis that is continuous with, rather than an explanatory reduction of, our ordinary discursive practices, and whose elucidatory resources are not accessible except from within the perspective of those practices

I consider the relationship of Badiou’s schematism of the event to critical thought following the linguistic turn as well as to the mathematical formalisms of set theory. In Being and Event, Badiou uses formal argumentation to support his sweeping rejection of the linguistic turn as well as much of contemporary critical thought. This rejection stems from his interpretation of set theory as barring thought from the 'One-All' of totality; but I argue that, by interpreting it differently, we can understand this implication in a way that is in fact consistent with the critical and linguistic methods Badiou wishes to reject.

The question of the place of what are called “animals” does not seem, at first, obviously to capture the deepest or most important imperative of a deconstructive politics devoted to challenging the constitutive structures of war, mastery, violence and sovereignty in the ‘contemporary scene’ of ‘globalization,’ or what Derrida often described as the ever more problematic and contested “mondialisation” or ‘becoming world’ of the world. And yet, as Derrida said in 1967 with respect to the “question of language” (which is, as I shall argue, at bottom the same question) the question of the life of the simply living (what a longstanding tradition, still operative at the very foundation of contemporary politics, understands as that of the animal) has certainly never been simply one question among others.[1] Indeed, as we shall see, the vanishing trace of an undeterminable “animal” life runs across Derrida’s own text from beginning to end, as it does, in a way that is at once silent, massive, and decisive, across the onto-theologically structured reality of contemporary “global” politics that this text attempts ceaselessly to decipher. This trace or track of a non-human life that crosses this global scene and unsettles its most profoundly orienting axioms cannot in fact be determined as that of “animals,” “an animal” or of “the animal” in general – for as Derrida has ceaselessly reminded us, there is not and has never been any such thing; the first and most essential imperative of a deconstructive reading committed to discerning difference and non-identity is to protest the universalizing gesture of the term or syntagm that, ignoring all of the vast differences of type, function, and characteristic, simply groups and indifferently unites all that is living and not human or plant under a single common term. Yet the deconstructive reading that tracks the trace of a non-human life across the discourses and practices of contemporary politics is nevertheless, as I shall argue, such as to call into question the political, social, theological and metaphysical privilege of the human, everywhere this privilege underlies and supports the axiomatics of what it is to speak or answer, what it is to ask or question, what it can mean to take up the life, community, or identity, of what can perhaps no longer, traversing it, be determined as that of the being that speaks..

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.

In this essay, I explore Alain Badiou’s longstanding project of theorizing political situations and political transformation through the analysis of forms and formalisms. This amounts, I argue, to a politics of form that draws on the thought of Sartre, Althusser, and Lacan, but offers new alternatives for political thought and action today. In particular, Badiou’s rigorous consideration of forms, which draws on mathematics, model theory, set theory, and category theory, allows him to theorize political change in a way that avoids the errors of existing critical approaches. Central to this consideration are Badiou’s theory of what he calls the event, which summons itself into existence by its own naming of itself or auto‐nomination, and his recent theory of the plurality of worlds and their possible transformation in Logics of Worlds. I also discuss Badiou’s recent treatment of the 20th century project of formalization in The Century, arguing that Badiou’s analysis here offers useful terms for the political thought of the present situation

I consider Plato’s argument, in the dialogue Cratylus, against both of two opposed views of the “correctness of names.” The first is a conventionalist view, according to which this relationship is arbitrary, the product of a free inaugural decision made at the moment of the first institution of names. The second is a naturalist view, according to which the correctness of names is initially fixed and subsequently maintained by some kind of natural assignment, rooted in the things themselves. I argue that: 1) Plato’s critical challenge to both views anticipates considerations introduced by Wittgenstein in the Philosophical Investigations ’ consideration of rules and rule-following; 2) Understanding Plato’s appeal to the “form” [ eidos ] of a thing in resolving the problems of both views helps to explicate Wittgenstein’s own appeal to “forms of life” as the “given” ground of linguistic practice; and 3) We should not understand the grounding of language in form-of-life either as a basis in the plural practices of different communities, or as a biological/anthropological basis in the specific nature of the human organism. Rather, it points to an autonomous dimension of form, which articulates the relationship between language and life as it relates to the possibility of truth