[Editor's Note: Thanks to new blogger David Crohn for this glimpse into one aspect of Nietzsche's relationship with his idol.]
In ep. 84 PEL touches briefly on Nietzsche's criticism of Schopenhauer—or rather, the ways Schopenhauer's readers have, according to Nietzsche, accepted the weakest aspects of his philosophy first (aphorism 99). Nietzsche was a great admirer of Schopenhauer, however, not least because they shared a rejection of the Kantian thing-in-itself.
Briefly, Kant's epistemology treats the senses, as well as the concepts of time and space and causality, as the conditions that make experience possible. These conditions limit our access to the objects of experience, however, so that things as they actually are, without the shape, size, duration, etc. that these conditions give them, cannot be perceived and are therefore unknowable. Kant is agnostic about the real nature of things-in-themselves (noumena), instead focusing on the way things appears to us (phenomena).
Post-Kantian philosophy has wrestled with the concept ever since. Many of his contemporaries (including Hegel) rejected the notion, seeing it as an empirically unverifiable and unnecessary addition—clutter in an already overstuffed ontology. In The Gay Science, 120 years later, Nietzsche continues the Kant-bashing, calling it a "very ridiculous thing" obtained "by stealth" (his italics). And in the Preface, Nietzsche seems to imply that the phenomenon/noumenon distinction is not just superfluous but entirely irrelevant to the point of doing philosophy. The Greeks, he writes, "knew how to live" because they "adored appearance...forms, tones, words... the whole Olympus of appearance. Those Greeks were superficial—out of profundity.” This is a characteristic take on Aristotelian metaphysics, in which a thing is a substance plus its attributes. Nietzsche celebrates the Greeks for their close attention to surface, whose actual texture of forms and tones and words need not be somehow subordinate to what a thing actually is.
Schopenhauer, on the other hand, lived in roughly the same time and milieu as Kant, and was moved to engage Kantian epistemology directly, critiquing it in his 1813 doctoral dissertation (later published as On the Fourfold Root of the Principle of Sufficient Reason) and refining his critique even further in his magnum opus, The World As Will and Representation (first published 1818). Schopenhauer acknowledges a distinction between what is and how it is experienced, but like Nietzsche refuses to posit this distinction as constituting an unbridgeable epistemic gap. Rather, the object can be perceived in two different, mutually dependent ways, "neither of which causes the other" (Stanford Encyclopedia on Schopenhauer). Things encountered by the senses are "representations" of “Will," broadly understood as the will to life itself rather than any individual will. Furthermore, Schopenhauer’s Will was a key influence on Nietzsche’s Will to Power, which is a more consciously felt, primordial urge toward creation and procreation, creative endeavor, and the whole range of possibilities hinted at by the subtitle of his Twilight of the Idols, which promises to teach the reader “How to philosophize with a hammer."