Since much of the impetus for Deleuze’s approach to the PSR stems from a critique of representation, I thought it would be good to post a quick summary of this critique. In short, Deleuze argues that for representational modes of thought difference is always mediated by an already presupposed identity, when it is precisely the conditions for the possibility of identity itself that most concerns Deleuze. The mediation of representation by identity occurs in four ways, what Deleuze calls the “fourfold root” (see DR 29): namely, identity, analogy, opposition, and resemblance.
Identity
In representational modes of thought, identity looms largest with respect to the determinable concept, such as the determinable genus, color, etc. From this perspective, determinate differences are understood relative to the identity of this determinable. Representational differences are thus mediated by the identity of an undetermined determinable, and this determinable is undetermined precisely because in itself it lacks determinate content.
To clarify, let us take the determinable color. When I say that the color of my shirt is different from the color of my pants, it is the determinable concept color that remains the same while the determinate instances of this self-same concept are precisely what differ. Among examples of this representational approach in the philosophical tradition, we could turn to Aristotle, Kant, and a host of others who reduce representational differences to the mediating identity of an undetermined concept. For Aristotle, and as Deleuze shows in Difference and Repetition, this undetermined concept is the genus that mediates specific differences; and for Kant it is the noumena that mediates the differences of an indefinite series of representations (Kant’s solution to first antinomy).
Analogy
Moving on to the second of the four roots of representation, the mediating role of identity as analogy figures most prominently within judgments. Since different judgments will usually apply or differentiate between different determinable concepts, the basis for the difference between determinable concepts themselves is understood, Deleuze argues, by analogy.
To offer an example, Wilfred Sellars has argued that every judgment always already inhabits what he calls the space of reasons, and thus every concept is always already inferentially related to other concepts. The judgment that my shirt is purple for instance, is inferentially connected to, and yet different from, other judgments, such as this shirt is colored, it is not yellow, or Jeff’s fashion sense is lacking for who wears purple shirts, etc. All these judgments presuppose, as an analogue, the being or totality of the space of reasons, and it is this space of reasons that makes the different judgments possible. We thus do not learn concepts one at a time, Sellars argues, but we come to learn their place within the already presupposed space of reasons. John McDowell has more recently continued largely in this same Sellarsian tradition and has argued for what he calls a “world-disclosing experience” that provides the basis for differentiating between the propriety of our judgments, in short for differentiating between which judgments do and do not carve at the joints. This “world-disclosing experience” is necessary, McDowell argues, if we are to avoid a “frictionless spinning in a void” which would be the result if the spontaneity of our judgments were to be left unchecked. Robert Brandom, finally, also falls into this tradition, a tradition he rightly traces back to Hegel, and for him the analogue to his inferentialism is the community, or a social holism.
Opposition
For Deleuze, the mediating role of identity with respect to representational differences between predicates in relation to their subjects occurs by way of the opposition of predicates within a subject. The maximal difference, therefore, is opposition in a subject, and it is the identity of the subject that mediates representational differences.
As Aristotle argued, and Hegel much later, the greatest difference would be between predicates of a self-same subject. For Aristotle this subject cannot have opposing predicates predicated of it at one and the same time, and in one and the same way. A subject cannot be both hot and cold, light and heavy, fast and slow, etc. Similarly for Hegel, with his notion of absolute contradiction, it is one and the same Absolute Spirit that resolves the maximal difference between universal and particular, being and becoming. In contemporary philosophy it is the proposition, as it is generally understood, that is the identity that mediates the law of the excluded middle whereby a proposition is either true or the negation of the proposition is true. It is the subject, the proposition in this case, that bears these contrary, opposing predicates and remains one and the same.
Resemblance
The final mediating role of identity in representation occurs with respect to perception, where representational differences are subordinated to the identity of a continuum of resemblance.
The difference between the color of my shirt and the color of my pants, for example, can be subordinated to a continuum of resembling colors. The two colors, as represented separately, are thus abstracted from this continuum and the representational difference between them is in the end mediated by the continuity of resemblance. Even Hume, who one would least suspect of affirming the identity of a continuum, relies upon this presupposed identity. It is this presupposed identity of the continuum that can account for Hume’s discussion, in the appendix to his Treatise, where he notes that although blue and green are different colors—“different simple ideas” as he puts it (T637)—they bear more resemblance to one another than blue and scarlet, and this is a resemblance “without having any circumstance the same.” (ibid.). In other words, one can recognize the resemblance without a third idea or a common component, for if there were a common component the simple ideas would not be simple. The continuity of resemblance is thus a primitive for Hume, and it is the basis for mediating perceptual differences.
In each of these four cases, what is presupposed is a brute fact, whether this be the undetermined concept, a space of reasons, an underlying subject or proposition, or the continuum of resemblance. Deleuze, on the other hand, breaks with a broad swath of twentieth century philosophy and reaffirms the principle of sufficient reason (PSR), and a fundamental consequence of this reaffirmation is the rejection of brute, self-identical facts. Let me briefly recap an important aspect of this history, for it will both help us to situate Deleuze’s project into the context of the contemporary philosophic landscape and it will help to prepare the way for understanding Deleuze’s approach to the problem of individuation.