[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]
Chapter 1: Deleuze and Transcendental Empiricism
Subdivision 4: Deleuze and The Logic of Sense
Recall that judgment is a subsumption in a subject-predicate format, for example, all metals are heavy. What holds subject and predicate together is a synthetic unity that lies outside them, namely, the synthetic unity of apperception. [Metal and heavy are separate concepts. To bring them together requires a consciousness of one and a consciousness of the other to be united. This is made possible by a consciousness of these these consciousnesses that is the same consciousness of a same subject, the a priori unity of apperception, the transcendental ego or the unity of the ‘I think’ that accompanies all mental acts.]
For Kant, in order for a judgment to be made of an object, what is required is for the representations of the object to be synthesized into a judgment; thus, the statement, All metals are heavy requires the subsumption of the representation of 'heaviness' under that of 'metal'. While the judgment itself is based on the reciprocal determination of these terms through the structure of the subordination of the predicate to the subject, the two terms, predicate and subject, are still, in themselves, fully determined. Thus, in order for them to be united, it is necessary that they be held together through a function that remains outside of them. This function, for Kant, is the synthetic unity of apperception, the condition of the possibility of the 'I think,' which remains constant through its application to different elements, thus allowing, through its attachment to these concepts, an element of homogeneity to enter into them, thus overcoming their intrinsic heterogeneity. (35)
Removing the transcendental ego from the process of synthesis therefore will require a new model of the way in which the elements of a representation can exist prior to the subject while retaining the possibility of their synthesis. (35)
[Traditionally philosophy has understood logic in terms of subject-predicate structure of states of affairs.] Without a new logic, philosophy has explained the foundation for the subject-predicate logic of states of affairs either as stemming from a supreme I, which is either a transcendental subject or an absolute being, or as being grounded on something indeterminate, an undifferentiated abyss. “Thus for Kant, the parallelism between the transcendental and empirical is justified through the necessity of a transcendental field, and at the same time the belief that if this field is to be structured, it must be structured analogously to the empirical.” (36) In Kant’s transcendental idealism, there is a finite subject [the transcendental ego?] who determines all possible subject-predicate relations through the table of judgments. But even though the subject is finite, our understanding is synthetic which means it can arrive at all possible subject predicate combinations.
This is for Deleuze merely a variation on the traditional metaphysical concept of God, who as a perfect being contains all possible predicates. In this case, the supreme subject is infinite, so it forms an analytic unity, possibility already being encompassed in its perfection. In this model, the subject-predicate structure of God leads to a parallel structure in states of affairs as their properties are derivative of those of God. (36)
Hence Schopenhauer, for instance, although recognizing the will as existing prior to the categories in an undifferentiated form, only allows it to find coherent expression through the world of representation. Even Nietzsche, in The Birth of Tragedy, requires Dionysus to speak through Apollo. (36)
Deleuze will say of this logic that it is no longer "of the form, but neither is it that of the formless: it is rather that of the pure unformed" (LS, 107). Form and formlessness cover the two traditional options provided by philosophy. The third option represents the Deleuzian alternative: that which is unformed in itself, but which is still determinable. As the unformed will generate the formed, we can see that | there is a fundamental difference in kind between the transcendental and the empirical. (36-37)
In Deleuze’s transcendental philosophy there are particular elements that he calls singularities.
For Deleuze, the actual is the expression of the transcendental field. The first level of actualization of the transcendental field produces the subject-predicate structure, which characterizes states of affairs in general. Here bare individuals and their properties are expressed free from any form of hierarchy. As the transcendental field is constituted by the relations between singularities, it is the case that these singularities present many different sets of possible relations that could be actualized. | actualization of the first level cannot give us an adequate account of consciousness, as it does not contain the materials to create anything like the spontaneity which is an integral quality of consciousness. Instead, we require a second level of actualization. This comes about, according to Deleuze, through the recognition that certain features remain stable throughout different incompossible worlds. While it is possible that the state of affairs obtains in which Adam eats the apple, there is another possible state of affairs in which Adam does not eat the apple. In both of these propositions, there is a determinate subject, Adam, who is individuated by his relations to certain predicates, such as in this case to the predicate of "sinner." These two states of affairs are two possible solutions to the problem of how the set of singularities can be actualized simultaneously. Through this, we can see that the structure Adam itself, aside from its relation to the predicate in question, has a correlate in the transcendental field, to the degree that it is partially independent of the precise state of affairs. It is this fixed point, with its ties to the transcendental field, which forms the ego within the Deleuzian system. This ego that is common to several worlds contains within itself a certain ambiguity, as it is not strictly determined by any particular world. It is this ambiguity, this recognition of other possible ways of being, that provides the feeling of spontaneity that is characteristic of the ego. (37-38)
Through this process of actualization, the two principles that Deleuze claims are responsible for the Kantian system come to light. First, the first stage of actualization produces the principle of 'good sense, ' that is, the principled organization of differences according to subject-predicate structure. It is this principle that, when applied beyond its proper domain, leads to the positing of the subject-predicate structure within the transcendental field. The second, 'common sense,' is the principle of identification. It is this that, when applied to the transcendental field, generates the structures, object = x, and the transcendental unity of apperception. In both these cases, Deleuze claims that it is the illegitimate application of these principles that leads to an erroneous conception of the transcendental field. (38)
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