The Sense of Finitude and the Finitude of Sense

For Martin Heidegger in Being and Time, human existence (Dasein) is essentially finite in its directedness toward death as a final and unavoidable individuating possibility. In Kant and the Problem of Metaphysics, Heidegger further specifies the finitude of Dasein, following Kant, as the capacity to be affected by external objects, which gives rise to the temporal problem of the relationship between sensibility and understanding. There is also an idea of constitutive finitude that is decisive in analytic philosophy of language, and that this idea can usefully be compared with Heidegger’s. On this conception, language is an essentially finite system of terms and recursively applicable rules capable of infinite application to produce new sentences. One of the most developed applications of this picture is Davidson’s conception of the structure of a “theory of meaning” for a natural language. I argue that certain structural aporias and paradoxes arising from this picture of language in the work of the late Wittgenstein, Cavell, and Turing/Gödel point to a different determination of the relationship of language and sense to the infinite. This points to a constitutive infinity of sense which is nevertheless not the theological or absolute infinite rejected by Heidegger.