Algebraic Concepts Characterized / Gilles Deleuze

Gilles Deleuzes’ Key Passage on Quantitability

“However, while it is true that continuousness must be related to Ideas and to their problematic use, this is on condition that it be no longer defined by characteristics borrowed from sensible or even geometric intuition, as it still is when one speaks of the interpolation of intermediaries, of infinite intercalary series or parts which are never the smallest possible. Continuousness truly belongs to the realm of Ideas only to the extent that an ideal cause of continuity is determined. Taken together with its cause, continuity forms the pure element of quantitability, which must be distinguished both from the fixed quantities of intuition [quantum] and from variable quantities in the form of concepts of the understanding [quantitas]. The symbol which expresses it is therefore completely undetermined: dx is strictly nothing in relation to x, as dy is in relation to y. The whole problem, however, lies in the signification of these zeros. Quanta as objects of intuition always have particular values; and even when they are united in a fractional relation, each maintains a value independently of the relation. As a concept of the understanding, quantitas has a general value; generality here referring to an infinity of possible particular values: as many as the variable can assume. However, there must always be a particular value charged with representing the others, and with standing for them: this is the case with the algebraic equation for the circle, x2 +y2 – R2 = 0 hold for
ydy + xdx =0, which signifies ‘the universal of the circumference or of the corresponding function’. The zeros involved in dx and dy express the annihilation of the quantum and the quantitas, of the general as well as the particular, in favour of ‘the universal and its appearance’.”

(Gilles Deleuze, Difference and Repetition, p. 171)

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