The work of Graham Priest and Gilles Deleuze (and Félix Guattari) converge in significant ways on the concept of the nondenumerable.
Turning to Priest first, and to his Beyond the Limits of Thought especially, one finds in this book an interesting history of philosophy, and one with a particular narrative at work; namely, he uncovers numerous contradictions that are encountered as certain unthinkable limits to thought become the subject of thought itself (e.g., primary substance for Aristotle, God for Cusanus, the noumenon for Kant, among other examples). In the history of thought prior to Hegel, according to Priest, these contradictions were largely denied, primarily through a denial of the very limits that gave rise to them. But with Hegel there is an open recognition and affirmation of the contradictory nature of the limits of thought. It is for this reason that Priest claims that the ‘chapter on Hegel [in Beyond the Limits of Thought] is therefore the lynch-pin of the book.’ (7).
In the first paragraph of his Beyond the Limits of Thought, Graham Priest notes that we have long speculated about limits, limits that may be unknown but are known to be there nonetheless. ‘For example,’ Priest claims, ‘we can only guess what the limit time for running a mile is; but we know that there is a limit, set by the velocity of light, if not by many more mundane things.’ For the longest time, the 4-minute mile was thought to be such a limit time. From 1852 to 1954 race times slowly crept down from 4:28 to 4:01.3 by Gunder Hagg in 1945. It was nearly 10 years later when, on May 6, 1954, Roger Bannister ran a time of 3:59.4. Here’s the race, with commentary by Bannister.
Having just finished Graham Priest’s book, in contradiction, a book central to the logical tradition Priest calls dialetheism, I’ve decided to post some thoughts to the blog. Logic is not my area of specialization, nor do I have much to say at the moment about how Priest puts dialetheism to use in reformulating classical logic and semantic theory, but there are some lines of convergence between dialetheism and the metaphysical project I’m engaged in at the moment. Stated baldly, dialetheism accepts that some contradictions are true, or some statements such as the liar’s paradox have two truth values, true and false (hence the term dialetheism); and this position is one I have echoed in various places in my published writings by referring to both/ands, paradoxa, and double articulation. There is a crucial difference, however: whereas I begin my understanding of both/and, paradoxa, and double articulation through a reading of Deleuze, Priest begins with Hegel, and in particular with Hegel’s account of motion. Priest cites Hegel:
[M]otion itself is contradiction’s immediate existence. Something moves not because at one moment of time it is here and at another there, but because at one and the same moment it is here and not here.
A true account of motion, therefore, implies that something both is and is not, or it implies a contradiction. Deleuze, by contrast, rejects Hegelian contradiction because it places difference in subservience to identity, to the identities that constitute the contradictory pair: “α ∧ not-α.” A both/and is thus not a difference subservient to both α and not-α but rather it is the forward-slash, “/”, the “and” between identities that involves a difference deeper than any contradiction – it is the transcendental condition for such contradictions. This is the project Deleuze calls transcendental empiricism and which I detail in my book Deleuze’s Hume.