Logic

If we speculate about what Nietzsche meant by “Schopenhauer as Educator” the present interpretation follows.

“His [Kant] object of experience,” of which he is constantly speaking, the proper subject of the categories, is not the representation of perception, nor is it the abstract concept; it is different from both, and yet is both at the same time, and is an utter absurdity and impossibility. 

Schopenhauer, Arthur, E F. J. Payne, and Arthur Schopenhauer. The World As Will and Representation. , n.d.. Print.

Nietzsche follows suit:

The extraordinary courage and wisdom of Kant and Schopenhauer have succeeded in gaining the most difficult victory, the victory over the optimism concealed in the essence of logic, - an optimism that is the basis of our culture. 

The Birth of Tragedy and the Case of Wagner. New York: Vintage, 1967. Print. ℙ 18

My interpretation of Peirce’s categories, from The One Law of Mind, can simply be stated that Second-ness determines First-ness into Third-ness. It is the second-ness of the Immediate Object that is filtered by Space and Time. Space and Time make possible the indexing of this second-ness. Space and Time may be subjective, but they are necessary conditions not only for the mind to have experience of a mind independent object, but also to formulate a representation that can index that experience to a Final interpretant and be shared with a community of inquirers. Don’t forget the Copernican Revolution!

It is illuminating in that Peirce distinguished three types of Sign: icon, index, and symbol. Peirce’s analysis of Kant’s Critique’s concludes with a type of realism that makes consistent the logic between the Intuition and the Concept, defined by Peirce as the Immediate Object and the Dynamic Object. This allows a community of interpreters to use realism as a guide in their investigations that lead to a Final Interpretant. The object of experience can be indexed in some cases, and is more than a mere icon or a symbol that is deconstructed into absurdity.

As Schopenhauer points out, the object of experience is what is in question. Peirce’s Semiotics composes a set of definitions that make possible the consistent reference to the object of experience. The representation and the two types of objects are elements which the mind synthesizes into meaning from experience of an object. Which object you may ask? Both, which is an intimation to Peirce's solution to the Continuum Hypothesis. 

Schopenhauer and Nietzsche seem to be at the level of the Immediate Interpretant, unable to transcend the order of the universe and are thus caught in an eternal return of confusion. Nietzsche may no doubt be an idiot, because he originates deconstruction of experience from the confusion of the work that a sign does. It seems clear he really didn't think there was a solution to Kant's attempt to synthesize the Phenomenon and Noumenon. He is clearly not on the level of Charles Sanders Peirce, who wanted two things in life; to have his name pronounced correctly, and to be known as a logician.

Nietzsche’s philosophy is a political philosophy on the struggle for existence in the presence of pure power. If the world needs unity through revolution, let it be the Copernican Revolution of Kant and Peirce.