A SPECTER IS HAUNTING THE SPECTER OF COMMUNISM. THE SPECTER OF THE NONHUMAN.
Anyway here's more of this essay:
Cantor showed that there is a gap between numbers and sets of numbers.Likewise there is a gap between lifeforms and sets of lifeforms.We can think of these sets as ecosystems, biomes, biosphere—we can think of these sets at any scale, and there is no easy continuity between these sets. An environment is just a certain set of lifeforms.The way one does ecological research is to establish a somewhat arbitrary set—to define a boundary sometimes called a mesocosm, in which one observes lifeforms coming and going, reproducing, struggling. An ecosystem is vague, in the sense that paradoxes called Sorites paradoxes arise when one attempts to define them precisely. How many blades of grass do I have to remove for this meadow not to be a meadow? One—surely not. Two—still a meadow. Three, four, and so on—and the same logic applies until I have only one blade of grass left. I conclude, wrongly,that there is no meadow.These paradoxes plague sets of lifeforms at any scale, and therefore it is strictly impossible to think ecological reality via a meta- physics of presence, namely, a belief that to be a thing, you have to be constantly present.
It is paradoxically much better to think that there is a meadow and there is not a meadow at the same time. We seem to have violated the supposed Law of Noncontradiction, asserted but not proved in Section Gamma of Aristotle’s Metaphysics. There is a meadow, but we can’t point to it directly, because it’s not constantly present. And yet here is the meadow, with the butterflies, the cowslips, the voles. Just as a vole is a set of things that are not voles, so the meadow is a set of things such as voles that are not meadows.
Thus a spectral strangeness that haunts being applies not only to lifeforms—a vole is a not-vole—but also to meadows, ecosystems, biomes and the biosphere. The haunting, withdrawn yet vivid spectrality of things also means that there can be sets of things that are not strictly members of that set, and this violates Russell’s prohibition on the set paradox that arises precisely through thinking Cantor’s transfinite sets.Transfinite sets are as we just saw sets of numbers that contain sets of numbers that are not strictly members of that set.There is an irreducible gap between the set of real numbers and the set of rational numbers—Cantor himself, like Gödel, drove himself crazy trying to find a smooth continuum between the two. This drive to find a continuum is a hangover from the Law of Noncontradiction, which has never been formally proved, but which has been accepted as a precondi- tion for philosophy since Aristotle.