Sean Bowden explains the connection between natural numbers and poetical nature in Alain Badiou's Being and Event.

Indeed, it is from this generation of “natural” numbers, all woven from the void in accordance with the axioms of being, that Badiou will establish his concept of “Nature.” Or more precisely, that Badiou understands Nature in this way is the result of the way in which set-theory ontology provides a resolution of the tension, highlighted since the work of Heidegger, between Nature understood poetically as appearance or the poetic coming-to-presence of being (the pre-Platonic poem), and Nature interpreted as Idea, subtracted from all appearance (in the manner of Plato). In other words, within the perspective of a set-theoretical ontology, Badiou will be able to find another arrangement of these two opposed orientations. In short, following Heidegger, he will maintain that Nature is “the stability of maintaining-itself-there” within the opening forth of its immanent coming-to-presence. On the other hand, he will mathematize the Platonic subtraction of being from appearance. Or again, he will develop a concept of Nature as a network of multiples which are interlocking and exhaustive without remainder, but which are also woven entirely from what is subtracted from all presence: the void. The point is, of course, that without reference to the opposing conceptions of Nature belonging to Heidegger and Plato, the assertion that natural or ordinal numbers formalize the being of natural things would appear somewhat arbitrary or as a play on words. Certainly, nothing within set theory itself authorizes such an ontological appropriation of the generation of ordinals.

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