the nondenumerable

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).

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Spinoza, appetites, and inferentialism

Appetite, as Spinoza makes clear, is nothing but our striving to persevere in our being, and this striving, “as related to the mind and body together, it is called appetite” (3P9S). As related to our body, therefore, our appetite is the striving to persevere in a given proportion of motion and rest. Spinoza refers to this striving as the “actual essence of the thing” (3P7), as opposed to the formal essence of the thing which is “the essence of each thing insofar as it exists and produces an effect, having no regard to its duration” (4Preface). The formal essence, or our proportion of motion and rest, is independent of its duration in the face of external objects, objects which could, if they caused our body to lose this proportion, kill the body (Note Spinoza’s claim, in the Short Treatise (I/53): ‘…if other bodies act on ours with such force that the proportion of motion and rest cannot remain 1 to 3 [for example], that is death, and a destruction of the soul…’). The formal essence of the body is the idea of the body as comprehended under the attribute of extension, in contrast to the actual essence of the body that has durational existence. Understood in the context of other bodies, that is actually rather than formally, our striving to maintain the proportion of motion and rest is a striving in the face of external differences (that is, other objects). One of the functions or effects of our appetites, therefore, is to select against excessive differences, to filter and navigate relations in order to ‘maintain the proportion of motion and rest’. Such a selection process is simply part and parcel of the striving to persevere in one’s own being with its proportion of motion and rest. God, on the other hand, as absolutely indeterminate, self-caused substance is the infinite enjoyment of existing that is the affirmation of all differences, or as what Deleuze refers to in Spinoza’s Ethics as the ‘logic of purely affirmative difference and without negation.’ Since God is not absolutely indeterminate substance in potentia, but in actu, and because God does not have to select against difference (i.e., there is nothing lacking in God), God is the most perfect being. Finite and determinate beings, however, must select against difference if they are to persevere in their being. This is its appetite, its proper goal and end. At the same time, however, it is not clear what differences we must select against, or how much we can endure and still persevere in our being in the face of differences.  It is not known in advance what a body can do. Consequently, through processes of experimentation and learned association we can become more perfect; that is, the more difference we do not have to select against, the more perfect we become; and it is in this light that Spinoza argues, in 3P12, for the existence of ideas that “aid the body’s power of acting.” By arguing for the effectiveness of such ideas, Spinoza is not being inconsistent with his earlier claims that the “decisions of the mind are nothing but the appetites.” To the contrary, the decisions of the mind which aid the body’s acting by selecting against difference, or by reducing difference to a common, known form, is nothing but the appetite itself, or our striving to persevere in our being.

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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.

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