Paul Livingston

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

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.

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..

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

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.

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.

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.