Schopenhauer's criticism of Kant's schemata is part of Schopenhauer's criticism of the Kantian philosophy which was published in 1819. In the appendix to the first volume of his main work, Arthur Schopenhauer attempted to assign the psychological cause of Kant's doctrines of the categories and their schemata. Schopenhauer's analysis holds that Kant misused argument by analogy to connect abstract reasoning to empirical perception; Schopenhauer argues that this comparison is baseless, and that its conclusions are thus invalid.
From pure intuitions to pure concepts
Schopenhauer claimed that Kant had made an important discovery. This was his realization that time and space are known by the human mind (Gemüt) apart from any worldly experience. In fact, they are merely the ways that the mind organizes sensations. Succession is time. Position, shape, and size are space. The pure forms of time and space are the basis of the perceptions that constitute experience of objects in the external world.
According to Schopenhauer's psychological hypothesis, Kant "… aimed at finding for every empirical function of the faculty of knowledge an analogous a priori function … ." Kant's tacit reasoning was similar to the following: "If pure intuition is the foundation of empirical intuition, then pure concepts are the foundation of empirical concepts." From this symmetrical analogy, Kant claimed that the human mind has a pure understanding, just as he had previously claimed that the mind has a pure sensibility. This pure understanding, according to Kant, consists of pure concepts or categories which allow the mind to discursively think about the objects that are intuitively perceived as being arranged in time and space.
Using intuitions to substantiate concepts
Kant wrote that "To demonstrate the reality of our concepts, intuitions are required." Since empirical concepts are derived from perceptions, examples of the intuitive perceptions can be used to verify the concept. Kant asserted that pure concepts, or categories of the understanding, can also be verified by inspecting their intuitions or schemata. "If the concepts are empirical, the intuitions are called examples: if they are pure concepts of the understanding, the intuitions are called schemata." Schopenhauer described the use of examples in the following way:
Thus, since he aimed at finding for every empirical function of the faculty of knowledge an analogous a priori function, he remarked that, between our empirical perceiving and our empirical thinking, carried out in abstract non–perceptible concepts, a connection very frequently, though not always, takes place, since every now and then we attempt to go back from abstract thinking to perceiving. We attempt this, however, merely to convince ourselves that our abstract thinking has not strayed far from the safe ground of perception, and has possibly become somewhat high–flown or even a mere idle display of words, much in the same way as, when walking in the dark, we stretch out our hand every now and then to the wall that guides us. We then go back to perception only tentatively and for a moment, by calling up in imagination a perception corresponding to the concept that occupies us at the moment, a perception which yet can never be quite adequate to the concept, but is a mere representative of it for the time being.— 
Pure concepts and the pure intuitional form of time
Kant preferred to create arrangements in symmetrical, analogous tables or lists. For Kant, the symmetrical analogues of empirical examples are the a priori schemata. But, in the case of pure concepts and their schemata, how could a reference be made to intuitive perceptions? Schopenhauer declares that concepts a priori "… have not sprung from perception, but come to it from within, first to receive a content from it. Therefore they have as yet nothing on which they could look back [for verification]. The only intuition that a priori concepts can be referred to is the pure intuitional form of time, according to Kant. Time, the mind's ability to know succession, is the only content of a pure, a priori concept of the understanding, or category. "The schemata," he wrote, "therefore are nothing but determinations of time a priori according to rules … .".
Kant's use of symmetrical analogy
Schopenhauer's criticism of Kant's schemata was done, according to him, to help solve the mystery of Kant's way of philosophizing. He tried to show that "… after the happy discovery of the two forms of intuition or perception a priori (space and time), Kant attempts, under the guidance of analogy, to demonstrate for every determination of our empirical knowledge an analogue a priori, and this finally extends in the schemata even to a mere psychological fact. Here the apparent depth of thought and the difficulty of the discussion merely serve to conceal from the reader the fact that its content remains an entirely undemonstrable and merely arbitrary assumption."
…here more than anywhere else do the intentional nature of Kant's method of procedure and the resolve, arrived at beforehand, to find what would correspond to the analogy, and what might assist the architectonic symmetry, clearly come to light. … By assuming schemata of the pure (void of content) concepts a priori of the understanding (categories) analogous to the empirical schemata (or representatives of our actual concepts through the imagination), he overlooks the fact that the purpose of such schemata is here entirely wanting. The purpose of the schemata in the case of empirical (actual) thinking is related solely to the material content of such concepts. Since these concepts come from empirical perception, we assist ourselves and see where we are, in the case of abstract thinking, by casting now and then a fleeting, retrospective glance at perception from which the concepts are taken, to assure ourselves our thinking still has real content. This, however, necessarily presupposes the concepts which occupy us spring from perception…. With a priori concepts, which have no content at all, obviously this is of necessity omitted because these have not sprung from perception, but come to it from within, to first receive content from it.— The World as Will and Representation, Volume I, Appendix, p. 450
Empirical concepts are ultimately based on empirical perceptions. Kant, however, tried to claim that, analogously, pure concepts (Categories) also have a basis. This pure basis is supposed to be a kind of pure perception, which he called a schema. But such an empiricist analogy contradicts his previous rationalist assertion that pure concepts (Categories) simply exist in the human mind without having been derived from perceptions. Therefore, they are not based on pure, schematic perceptions.
References to Schopenhauer's discussion
In his 1909 book Kant's Philosophy as Rectified by Schopenhauer, Michael Kelly drew attention to Schopenhauer's discussion of Kant's Schemata. In his Preface, Dr. Kelly justified his book by saying: "…a short exposition of Transcendental Idealism with Schopenhauer's constructive and destructive criticism may be of use to those that cannot make a simultaneous study of Kant and Schopenhauer in the original. To think that the former [Kant] can be understood without the latter [Schopenhauer] is a fatal delusion. If anybody should doubt this, let him try to make out what Kant meant by the ' Schematismus,' and he will soon find it advisable to avail himself of the assistance of a man who is worth ten times more than all the post-Kantian philosophers and professors put together."
In Chapter XI, Kelly provided a condensation of Schopenhauer's explanation of Kant's false analogy between empirical and pure cognitions:
Having sought to find an a priori cognitive faculty corresponding to every empirical [a posteriori] one, Kant remarked that, in order to make sure that we are not leaving the solid ground of perception, we often refer back from the empirical [a posteriori] abstract idea [concept] to the latter [the perception]. The temporary representative of the idea [concept] thus called forth, and which is never fully adequate to it, he calls a 'schema,' in contradistinction to the complete image. He now maintains that, as such a schema stands between the empirical [a posteriori] idea [concept] and the clear sensual perception, so also similar ones stand between the a priori perceptive faculty of the sensibility and the a priori thinking faculty of the pure understanding. To each category, accordingly, corresponds a special schema. But Kant overlooks the fact that, in the case of the empirically [a posteriori] acquired ideas [concepts], we refer back to the perception from which they have obtained their content, whereas the a priori ideas [concepts], which have as yet no content, come to the perception from within [cognition] in order to receive something from it. They have, therefore, nothing to which they can refer back, and the analogy [of the a priori schema] with the empirical [a posteriori] schema falls to the ground.
- Critique of Pure Reason, A22
- The World as Will and Representation, Volume I, Appendix, p. 449
- Critique of Pure Reason, A80
- Critique of Judgment, § 59
- The World as Will and Representation, Volume I, Appendix, p. 450
- Critique of Pure Reason, A145
- The World as Will and Representation, Volume I, Appendix, p. 450 f.