Friday, February 11, 2011
Michael Roubach on being and number in Heidegger's thought.
[Heidegger] does not derive the object in general by means of the logical analysis of judgements. Indeed, he does not endorse the idea that logic is prior to ontology, and construes ontological categories as independent of logical categories. The sole connection between the two realms is that the transcendental one, as the absence of multiplicity, is true of every entity, and hence, true of judgments, and judgments are logical objects.

Moreover. Heidegger endorses the centrality of the link between numbers and the object in general, a link that is particularly striking in the definition of number. His characterization of numbers as ordered also reflects an affinity with a fundamental aspect of Dedekind’s conception.

Heidegger, like Hilbert, rejects the reduction of arithmetic to logic. Indeed, while Heidegger’s critique of the reduction of number to set is apparently based on Natorp, Natorp himself based his arguments on Hilbert’s 1904 article '0n the Foundations of Logic and Arithmetic'. In this article, Hilbert uses the general concept of the thing as the starting point from which he goes on to construct arithmetic.

The various influences that have been outlined above come together to paint a complex picture of where Heidegger’s very early thought should be situated relative to the revolutionary developments that had transformed logic and the foundations of mathematics in the preceding years. The young Heidegger was by no means hostile to these developments, and in fact, his own approach places him squarely in one of the two main camps, in the framework of which he seeks a treatment of the thing in general that transcends the mathematical context and can serve as a foundation for all the sciences.

P. 35
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