A Question Concerning Schopenhauer’s Conception of the Principium Individuationis

“Basically, Schopenhauer holds that the multiplicity that we see is something constructed by our cognition. My question is this: Fair enough—multiplicity as we experience it is a product of our cognition. But how can we rule out that in the “Thing-in-itself” there’s some non-cognitive process that individuates things?”

This is an interesting question. I’ll try to clarify Schopenhauer’s (sometimes inconsistent) views on the issue and provide what I think would be his answer to your question.

For Schopenhauer, all “oneness” and “manyness,” “unity” and “multiplicity,” are features made possible by the principium individuations; and this, Schopenhauer maintained, was Space-Time. Thus, the categories or determinations of “oneness” and “manyness,” “unity” and “multiplicity,” all, in some way or another, invoke Space-Time. Now, Space-Time, as Schopenhauer points out, has its being (i.e., “realizes” or “manifests” itself) in and through its “operations” as spatio-temporal relations (or spatio-temporal “relatings”) holding good of, and within, Substance (i.e., “matter” and its affections—or “causality”). Thus, the principium individuationis has its being only through Substance. Indeed, this principle has no being apart from its manifestation, and this manifestation just is the differentiating of Substance.

  

Schopenhauer held to an idiosyncratic form of an empiricist criterion of meaning—which explains why he believed that the predicates of “oneness” and “manyness,” “unity” and “multiplicity,” could only be sensibly ascribed to Substance (i.e., “matter”).

 

Now, Schopenhauer maintained that Substance (i.e., “matter”) is a function (or correlate) of the Understanding—just as much as the Understanding is a function (or correlate) of Substance. This correlativity entails that Space-Time (i.e., the principium individuationis) is inextricably tied to the Understanding: the two stand and fall together, and the predicates of “oneness” and “manyness,” “unity” and “multiplicity,” cannot be sensibly ascribed to anything that was not itself a mode or modification of matter—the sensible correlative of the Understanding (i.e., cognition). 

Furthermore, since Schopenhauer reserves the features of “oneness” and “manyness,” “unity” and “multiplicity,” for Substance (which itself has no being apart from Space-Time), he would reject the notion that “The Will” or “Thing-in-itself” is a “One” or a “Unity.” Indeed, Schopenhauer mentions (in some place, I can’t remember where exactly) that “oneness” or “unity” cannot be predicated of “The Will” or “Thing-in-itself” in any but a metaphorical sense. “The Will” or “Thing-in-itself” is the ground of “oneness” and “manyness,” “unity” and “multiplicity.” If anything, “The Will” or “Thing-in-itself” ought to be grasped as a “one-in-many” and as a “unity-in-multiplicity” (expressions which Schopenhauer would likely find objectionable because of its “Hegelian” tones).