[1][2] The Critique of the Schopenhauerian philosophy is generally seen as offering a position closer to realism than the idealism of Kant and Schopenhauer.
The most famous challenge came from Hume, namely, if all knowledge is derived from experience we have no right to claim things are caused, we can only perceive that they follow after each other.
Schopenhauer called this comprehension of a change in the sense organ having a cause in space, the causal law (German: Kausalitätsgesetz).
Kant however, maintained that there are inborn concepts, categories, and that they are needed to make from “the chaos of appearances”, the manifold given in perception, an objectively valid connection called nature.
[5]: 428 Schopenhauer has shown that only due to the understanding we can know external objects, by moving the sensation in the sense organ outwards.
Kant writes: It was assumed, that the senses deliver not only impressions, but also conjoin them and provide images of objects.
[10]: A120 Since every appearance contains a manifold, and different perceptions are found in the mind scattered and singly, a conjoinment of them is needed, which they cannot have in the senses themselves.
[10]: B129 This synthesis forms the main topic of the Analytic, and it is very important to never lose sight of the concerned issue, that partial-representations delivered by the senses need a mental faculty before appearing as connected in the mind: The synthesis is a blind but indispensable function of the soul, without which we should have no cognition whatever, but of the working of which we are seldom even conscious.
This "absurd" reasoning which Kant had to make, is not needed when we comprehend the activity which brings forth homogenous partial-representations as coming from the same thing-in-itself.
Schopenhauer accepted this characterization of space and time, as did many neo-Kantians: it was frequently praised as one of the greatest events in philosophy.
Time and mathematical space are no longer forms of perception, but are the synthesis of a manifold which sensibility offers in its original receptivity.
However, space and time do not readily lie in us, to bring forth properties such as extension and motion, but are subjective preconditions to cognize them.
where The separation of space as it is observed and proper length seemed to have no meaning before the discovery of relativity: in a time with only Newtonian mechanics it seemed to many as a superfluous distinction.
As a consequence, not realizing why this would be of any importance, contemporaries of Mainländer accused his philosophy of simply being realism contrary to his own claims.
[5]: 468 Although Mainländer considers Schopenhauer's works on art to be brilliant and spirited, they are often based on pure metaphysics.
[5]: 492 Kant and Schopenhauer briefly discuss the sublime character, but only mention characteristics that explain not its essence.
To the first class belong those who still love life, but care no longer about their individual weal as they fight for a higher ideal (the freedom of a nation, social rights, emancipation), in a word, heroes.
To the second class belong those who are convinced of the worthlessness of life, and this conviction has made them immune to all worldly affairs.
[5]: 520 Schopenhauer called Kant's distinction between the empirical and intelligible character "one of the most beautiful and most profound thought products of this great mind".
Mainländer argues that this distinction follows only because of errors in epistemology, since Kant and Schopenhauer believed that all coercion stems from the subject, instead of the things-in-themselves.
[5]: 574 Schopenhauer used this transcendental freedom to legitimize the negation of motives, quietives, which finds its expression in asceticism.