La escuela como escenario de construcción de la cultura

Theorems 1 and 2 showed the negative property of the determining ground of an objective principle: It must not be matter. The corollary determined

18

With respect to the philosophical analysis I will use the term ‘postulate’ instead of ‘axiom’. The term ‘axiom’ will be reserved for the formal context. This division should make the distinction between the philosophical and logical part of the thesis more clear.

19

In this corollary Kant introduces the term ‘formal law’ as well, though merely as a synonym for ‘objective principle’ and ‘practical law’. Kant deduces the formal character of a practical law officially in the proof of his third theorem. I will therefore postpone the use of this term to the next section.

the only possible origin of such a ground: Pure reason. The aim of Kant’s third theorem is to establish the properties of an objective determining ground positively. This theorem consists of Kant’s derivation of ‘the mere form of a practical principle’ as the objective determining ground of the will. Before the proof of this theorem can be provided, Kant’s general distinction between form and matter must be properly determined.

3.5.1 Form and Matter

The previous sections showed that, in Kant’s practical philosophy, matter is inevitably connected with the objects of the faculty of desire. In the present section the main focus will be on Kant’s notion of form. Consider the following remark by Kant on the distinction between form and matter with respect to concepts in general:

With every concept we are to distinguish matter and form. The matter of the concept is the object, their form universality. [Kan92a, Jäsche Logic - 9:91]

The matter of a concept is that which is concerned with the object. The form of a concept is the concept’s universality. The distinction coincides with Kant’s distinction of the use of a cognition in concreto, with respect to its objects, and its usein abstracto, with respect to its universality: “Every concept can be used universally or particularly (in abstracto or in concreto)” [Kan92a, Jäsche Logic 9:99]. According to Kant,

the expressionsabstractandconcreterelate not to concepts in themselves

- for every concept is an abstract concept - but rather only to their use. And this use can in turn have various degrees. [Kan92a, Jäsche Logic - 9:99]

The distinction between matter and form must therefore be seen as a distinc- tion in usage. That is, a concept can be regarded with respect to its sole matter or mere form, though the concept itself always contains both. With respect to the use of a concept matter and form are therefore mutually exclusive.

Postulate 5. Every practical principle can be regarded with respect to its

mere form and with respect to its matter. If a practical principle is regarded KL with respect to its mere form, then it is not regarded as to its matter. If a practical principle is regarded with respect to its matter, then it is not regarded as to its mere form.

The question is: What in a concept constitutes its form? The following quote shows that the form of a concept is its universality and concerns that which is common to many; to be more precise, it concerns that what is uni- versally represented in the extension of the concept:

For since every concept, as a universally valid representation, contains that which is common to several representations of various things, all these things, which are to this extent contained under it, can be repres- ented through it. [Kan92a, Jäsche Logic - 9:96]

The mere form of a concept represents an abstract rule that determines which objects belong to the extension of that concept and, subsequently, represents what is common to all objects in the concept’s extension. Hence, the form of the concept of a practical principle is an abstract rule that represents what is common to all practical principles in the concept’s extension; that is, its universal structure. Consequently, a practical law regarded as to its mere form must be regarded as to its universal lawgiving structure. The remaining question is: How can the mere form of such a principle be obtained? Kant provides a straightforward answer: “Now, all that remains of a law if one separates from it everything material [...] is the mere form of giving universal law” [Kan96a, 5:27]. The above elaboration provides the following axiom and definition:

Postulate 6. The mere form of a practical principle is obtained by subtract-

ing the principle of all its matter.

Definition3.14. (Mere Form) A practical principle’s mere form is defined

as the principle’s use with respect to its universal structure; that is, with re- spect to what is commonly represented in all practical principles (of that sort). 3.5.2 Theorem III - the Argument

Kant formulates his third theorem as follows:

Theorem3. “If a rational being is to think of his maxims as practical universal

laws, he can think of them only as principles that contain the determining KL ground of the will not by their matter but only by their form.” [Kan96a, 5:27]20

In the above quote, ‘them’ and ‘their’ do not refer to maxims in general, but to ‘maxims regarded as practical universal laws’. This theorem can therefore be seen as a thought-experiment to determine the necessary characteristics of a practical law: ‘If we think of our maxims as practical laws, what should they

20

The occurrence of the word ‘only’ twice in this theorem causes some confusion. Consider the German original: “Lehrsatz III. Wenn ein vernünftiges Wesen sich seine Maximen als praktische allgemeine Gesetze denken soll, so kann es sich dieselbenurals solche Prinzipien denken, die, nicht der Materie, sondern bloßder Form nach, den Bestimmungsgrund des Willens enthalten” [Kan90, 5:27 - bold emphasis my own]. The first ‘only’ corresponds to the German ‘nur’, which implies that the term must be given a strict interpretation; that is, it signifies the determination of a necessary condition (only if). The second ‘only’ is a translation of the German ‘bloß’ which also translated as, for example, ‘merely’. This last ‘only’ functions to highlight that the determining ground at stake must bemere form.

look like?’. That this theorem aims at determining the necessary characteristics of such a principle can be clearly seen through Kant’s use of ‘either ... or’ in the reformulation of the claim at the end of the proof:

Therefore,eithera rational being cannot think of his subjectively prac-

tical principles, that is, his maxims, as being at the same time universal

lawsorhe must assume that their mere form, by which they are fit for

a giving of universal law, of itself and alone makes them practical laws. [Kan96a, 5:27 – bold emphasis my own]

I propose the following reading of the claim: ‘If a rational being thinks of its maxim as a practical law then it must think of this principle as a principle con- taining a determining ground that consists merely of the form of that principle as a law’.21 In the contrapositive this interpretation says, ‘if a rational being does not think of its maxim as a principle containing a determining ground that consists of the mere form of a practical law, then it cannot think of its maxims as practical laws’. In other words, the mere form of a practical law as determining ground of the will is the necessary characteristic of a principle regarded as practical law.

The argument runs as follows: The matter of a principle is always the object of the will. There are two possibilities, this matter can be either (i) the determining ground of the principle or (ii) not (see [Kan96a, 5:27]). In the latter case matter would still be present in the principle, since the will needs something to be determined to (an action), though it would not be the ground on which the will is determined. If a rational being accordingly thinks of its maxim as a practical law, Theorem 1tells us that, if (i) is the case this principle could never be a practical law. Hence, we must conclude that, if a rational being thinks of its maxim as a practical principle, then (ii) must be the case. That is, the determining ground of this principle must be non-matter. The question that rises is: What in this principle, instead of its matter, can constitute its determining ground? The ground must consist of what remains after subtracting everything material from this principle, which is nothing but the mere form of the principle as a law as such: The mere form of giving universal law. Thus, the determining ground of such a principle must be the mere form of this principle as if it would be a universal law. (The structured proof of Theorem 3can be found in the Appendix at A3.)