.

unser Ich nennen.”

44 On the notion of self in Tetens see Thiel 2018, pp. 59–75.

45 “Die Physiologie und Psychologie hat nunmehr so viele Fakta gesammelt, welche diese durchgängige Mitveränderung des Gehirns zu allen Seelenveränderungen offenbar machen, daß solche als außer Zweifel gesetzt angesehen werden kann.”

46 Among the above-mentioned philosophers, Kant has direct knowledge of the works of Wolff, D’Alembert, Darjes and Tetens (Warda 1922).

2.Kant’s pre-critical notion of schema

      Before dealing with the use of the notion of schema in the Critique of Pure Reason, it is important to realise that its use is not limited to Kant’s opus magnum, but it is present in pre-critical (as well as in later) works of Kant, as I will demonstrate in this second chapter.

The literature about the meaning and uses of the term ‘schema’ before the Critique of Pure Reason is very scarce. The Kant-Lexikon ignores the problem, while in the Historisches Wörterbuch der Philosophie from 1992 Stegmeier stresses the presence of the notion in two pre-critical works: the Nova Dilucidatio and the Dissertation from 1770, De mundi sensibilis atque intelligibilis forma et principiis. However, they do not go into the details of Kant’s uses and changes of the meaning of the term. Besides, an interesting paper written by Alba Jiménez Rodriguez from 2016 (Die Projektion des Schematismus in den vorkritischen Schriften Kants: Das Problem der mathematischen Konstruktion), focuses on the anticipation in the pre-critical works of a kind of schematism intended as a constructive process of the imagination similar to that of mathematical⁴⁷ construction. More specifically, Rodriguez points out that Kant’s pre-critical use of ‘schema’ might be related to the Baconian concepts of schematism. As shown in the previous chapter, Bacon’s notion of schema refers to the structure of nature or the ways in which properties are related to each other and ordered in the different substances. According to Rodriguez, the Baconian meaning of ‘schema’ as ←41 | 42→transformation, a building process, has influenced Kant’s notion of schematism, rooted in his account of the mathematical process of construction in his pre-critical works. While Kant does not yet use the terminology of schematism, relevant aspects of the problem of applying pure concepts to experience are already present. In the Inquiry concerning the Distinctness of the Principles of Natural Theology and Morality (Untersuchung über die Deutlichkeit der Grundsätze der natürlichen Theologie und der Moral) from 1764, where the mathematical method is regarded as a way of developing and using rules of construction, in a way similar to the drawing of geometrical figures:

“There are two ways in which one can arrive at a general concept: either by the arbitrary combination of concepts, or by separating out that cognition which has been rendered distinct by means of analysis. Mathematics only ever draws up its definitions in the first way. For example, think arbitrarily of four straight lines bounding a plane surface so that the opposite sides are not parallel to each other. Let this figure be called a trapezium. The concept which I am defining is not given a priori to the definition itself; on the contrary, it only comes into existence as a result of that definition. Whatever the concept of a cone may ordinarily signify, in mathematics the concept is the product of the arbitrary representation of a right-angled triangle which is rotated on one of its sides. In this and in all other cases the definition obviously comes into being as a result of synthesis. The situation is entirely different in the case of philosophical definitions. In philosophy, the concept of a thing is always given, albeit confusedly or in an insufficiently determinate fashion. The concept has to be analysed; the characteristic marks which have been separated out and the concept which has been given have to be compared with each other in all kinds of contexts; and this abstract thought must be rendered complete and determinate.” (AA II, p. 276)⁴⁸←42 | 43→

According to these remarks, the method used in mathematics is synthetic, insofar, as its concepts (for instance a ‘triangle’) are results of their definitions. In contrast, in philosophy concepts are already given but they are unclear and undetermined and therefore need to be analysed⁴⁹. However, in philosophy there is a question that has to be answered using a method similar to a mathematical one: for instance, taking claims such as: “7+5=12”, philosophy has to show how they are related to experience. In order to achieve this task, Kant relies on a method through which objects are constructed following rules of the understanding, which is similar to the mathematical method (Jiménez Rodríguez 2016, p. 440). This is a point which Kant consistently sticks to, as shown in the Critique of Pure Reason and in a footnote contained in the late On a Discovery whereby any New Critique of Pure Reason is to be made Superfluous by an Older One (Über eine Entdeckung, nach der alle neue Kritik der reinen Vernunft durch eine ältere entbehrlich gemacht werden soll):

“Hence it is also requisite for one to make an abstract concept sensible, i.e. display the object that corresponds to it in intuition, since without this the concept would remain (as one says) without sense, i.e. without significance. Mathematics fulfils this requirement by means of the construction of the figure, which is an appearance present to the senses (even though brought about a priori). In the same science, the concept of magnitude seeks its standing and sense in number, but seeks this in turn in the fingers, in the beads of an abacus, or in strokes and points that are placed before the eyes. The concept is always generated a priori, together with the synthetic principles or formulas from such concepts; but their use and relation to supposed objects can in the end be sought nowhere but in experience, the possibility of which (as far as its form concerned) is contained in them a priori.”(KrV A240-B299)⁵⁰←43 | 44→

“In a general sense one may call construction all exhibition of a concept through the (spontaneous) production of a corresponding intuition. If it occurs through mere imagination in accordance with an a priori concept, it is called pure construction (such as must underlie all the demonstrations of the mathematician; hence he can demonstrate by means of a circle which he draws with his stick in the sand, no matter how irregular it may turn out to be, the properties of a circle in general, as perfectly as if it had been etched in copperplate by the greatest artist). If it is carried out on some kind of material, however, it could be called empirical construction. The first can also be called schematic, the second technical construction.” (AA VIII, p. 192)⁵¹

      Besides Jiménez Rodriguez, Young Ahn Kang also remarks on the connection between mathematical construction and schematism:

      “[…] the construction of a concept is an act of providing a concept with objective reality (cf. Entdeckung BA 10–11; Fortschritte A183). In other words, constructability is a semantic rule of mathematical cognition. It makes possible a meaningful use of mathematical concepts on the one hand, and it restricts the valid sphere of mathematical knowledge to the sensible world on the other (Prolegomena § 13 note). The presentation of a concept in intuition (mathematical schematism) provides the concept with ‘sense and meaning’ (Sinn und Bedeutung) (Prolegomena § 8). Thus, construction has the same function as the transcendental schema both in in its realizing and restricting of the pure concepts at the same time (A147/B187).” (Kang 1985, p. 51)

      After these considerations, that stress that there are hints to the problem of schematism in works before the Critique, I now move on to the analysis of the passages ←44 | 45→in which Kant makes use of the term ‘schema’ in his pre-critical writings. In the first part of the chapter I will focus on the metaphysical meaning of ‘schema’ as presented in the New Elucidation, while in the second part I will consider the various meanings of the term in the Dissertation