Jon Cogburn has a nice short post on Graham Priest here.
New realists have got to have an honest confrontation with the Kantian problems of totality, and Priest’s characterization of such problems in terms of varieties of Russell’s Paradox is an essential step forward. Russellian paradoxical proofs have two moments: one of Transcendence where a set A is provably not a member of some set B, and one of Closure where A is provably a member of B (with Russell’s paradox A and B are the same set; the problem concerns whether the set of all sets that are not members of themselves is itself a member of itself). This provides a rigorous model of precisely what always goes wrong with transcendental idealism, limiting what can be said or known (Closure) and having to surpass those limits (Transcendence) in order to state or think the initial limitation.
I like Jon’s designation “new realism” and I think that after a short (and hopefully thoughtful) pause it would be great to get back to the conversations about realism (Realism Wars™) when we read Lee Braver’s book.
My own understanding of Kant’s issue of totality is mainly related to my attempts to think what he called Weltbegriff in a couple of passages I referred to earlier, but also his discussion of totality, world, and nature that is, of course, found throughout his corpus. Since Jon’s post is a sort of personal expression of his philosophical agenda, it’s only fair I reveal my own late interests and directions.
It’s becoming increasingly clear to me, and I apologize if you have already discovered it and think it’s so yesteryear, that Kant was a philosopher of nature (what we today would call a philosopher of science) from the very beginning – think Universal Natural History, which by the way already contains the first element of Kant’s famous expression about starry skies and moral law from the second Critique – and as is lately been pointed out by folks like Martin Schönfeld (The Philosophy of the Young Kant), we need to move away from Kant’s own view of his philosophy as really only beginning with 1781 publication of the first Critique (Cassirer is all about this narrative as well, plus Kant did not even want his pre-critical writings included in his collected works). I believe it’s important to take Kant as making an essential turn with critical philosophy, but that it cannot be understood and appreciated without Kant’s so-called pre-critical thought (and, for that matter, post-critical political writings which are ignored sometimes precisely because they are not thought to be part of the “critical philosophy” and its transcendental approach). In any case, this is a very long way of saying this: Kant’s discussion of totality, world and nature in the first Critique are to be read in light of his general interest in science, in cosmology, in mathematics and so forth.
The ideas of world and nature are discussed in the following terms that I find very interesting:
We have two expressions, world and nature, which are sometimes run together. The first signifies the mathematical whole of all appearances and the totality of their synthesis in the great as well as in the small, i.e., in their progress through composition as well as though division. But the very same world is called nature insofar as it is considered as a dynamic whole and one does not look at the aggregation in space or time so as to bring about a quantity, but looks instead at the unity in the existence of appearances. [A418-9/B446-7]
Kant has four “cosmological ideas” that he now labels world-concepts [Weltbegriffe] and then again divides these world-concepts into world-concepts proper that deals with mathematical whole and “transcendent concepts of nature” that deal with dynamic whole.
Since it seemed to me previously that world-concepts can also be considered close to what Kant called “cosmopolitan sense” of philosophy, I wonder if there’s a connection between this theoretical cosmological sense of world-concepts and practical cosmopolitan sense? Or, to return to Jon’s short post, I wonder if our theoretical musing about totality and unity also condition our pratical reflections on world and diversity/unity issue?