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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. [ABSTRACT FROM AUTHOR]

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 ( Being and Event) 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

I consider the sense in which language is "finite" for Wittgenstein, and also some of the implications of this question for Alan Turing's definition of the basic architecture of a universal computing machine, as well as some of the vast technological, social, and political consequences that have followed from it. I shall argue that similar considerations about the relationship between finitude and infinity in symbolism play a decisive role in two of these thinkers' most important results, the "rule-following considerations" for Wittgenstein and the proof of the insolubility of Hilbert's decision problem for Turing. Fortuitously, there is a recorded historical encounter between Wittgenstein and Turing, for Turing participated in Wittgenstein's "lectures" on the foundations of mathematics in Cambridge in 1939; their interactions are documented in the text Wittgenstein's Lectures on the Foundations of Mathematics edited by Cora Diamond.1 Although my aim here is not to adduce biographical details, I think their exchange nevertheless evinces a deep and interesting problem of concern to both. We may put this problem as that of the relationship of language's finite symbolic corpus to (what may seem to be) the infinity of its meaning. [ABSTRACT FROM AUTHOR]

The article discusses on the work of philosophers in the analytic tradition and the consideration of its history as an object of philosophical investigation. It mentions two main results to consider in retelling the course of analytic tradition using the work of Scott Soames on the 20th century philosophical analysis. He talks about the three methodological presupposition.

Analyzes the use-doctrine and the meaning-theory in Ludwig Wittgenstein's book "Tractatus." Examination of the meaningfulness of signs in the Tractatus theory; Relationship between the Tractarian program analysis and the use-doctrine meaningfulness of signs; Precedents of Wittgenstein's program of analysis; Contributions of Wittgenstein to analytical philosophy; Investigations made by Wittgenstein on rule-following and private language.

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. [ABSTRACT FROM AUTHOR]