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... d effect, but all the propositions of arithmetic and geometry, are synthetic. In all these propositions, no analysis of the subject will reveal the predicate. He gives the example 7 + 5 = 12. He points out that 7 and 5 have to be put together to give 12; the idea of 12 is not contained in them, nor even in the idea of adding them together (Prolegomena 2). From his proposition that all mathematics are synthetical, Kant explains how the ideas of space and time are also a priori forms of sensibility.
Geometry is based upon the pure intuition of space. Arithmetic accomplishes its concept of number by the successive addition of units in time; and pure mechanics especially cannot attain its concepts of motion without employing the representation of time. Both representations, however, are only intuitions; for if we omit from the empirical intuitions of bodies and their alterations (motion) everything empirical, or belonging to sensation, space and time still remain, which are therefore pure intuitions that lie a priori at the basis of the empirical (Prolegomena 10). Kant speculates about how Humes thinking would have been different had he recognized that mathematical judgments are not only a priori but synthetic. The good company into which metaphysics would thus have been brought would have saved it from the danger of a contemptuous ill-treatment, for the thrust intended for it must have reached mathematics, which was not and could not have been Humes intention.
Thus that acute man would have been led into considerations which must needs be similar to those that now occupy us, but which would have gained inestimably by his inimitably elegant style (Prolegomena 4). For Kant, in order to develop experience, we must first make a priori synthesis which yield concepts of the understanding, including causality. It is this very type of synthesis, necessary for the cognition of sensations, that makes experience possible. Causality is valid because of the minds organization of intuitions according to necessary laws, under which the connection is objectively valid and thus becomes experience (Prolegomena 20). Kant's solution applies only to perceptions of the phenomenal realm. He maintains that although one cannot form rationally the concept of one thing causing another, I therefore easily comprehend the concept of cause as a concept necessarily belonging to the mere form of experience, and its possibility as a synthetic unification of perceptions in a consciousness in general (Prolegomena 29).
Kant attempts to remove Humes doubt by discussing the way the mind organizes its intuitions. Subjectively the mind senses things in a certain order, which it then rearranges according to a priori concepts of the understanding, so that the order in objective time obeys necessary laws. For this rearrangement to be valid in objective time, the mind develops a set of universal laws which relate the connection of intuitions in objective time. These laws determine what experience is possible: If the empirical determination in relative time is to be objectively valid (i. e. , experience), these universal laws contain the necessity of the determination of existence in time generally. Experience gives to empirical judgments universal validity, and for that purpose requires a pure and a priori unity of the understanding (Prolegomena 26).
Causality is an example of such an a priori unity. Kant goes on to state explicitly that the concept of cause is a concept firmly established a priori, or before all experience, and have their undoubted objective value, though only with regard to experience (Prolegomena 27). Kant states that Hume justly maintains that we cannot comprehend by reason the possibility of causality, that is, of the reference of the existence of one thing to the existence of another which is necessitated by the former... But I am very far from holding these concepts to be derived merely from experience, and the necessity represented in them to be imaginary and a mere illusion produced in us by long habit. On the contrary, I have amply shown that they and the principles derived from them are firmly established a priori before all experience and have their undoubted objective value, though only with regard to experience (Prolegomena 27). The explanation thus far cannot stand alone because although it explains how the a priori basis of cause is possible, it lacks a description of exactly why and how the specific a priori synthesis is made.
Kant admits that although he cannot comprehend the concept of a necessary connection in either noumenal things or even appearances, we have yet a concept of such a connection of representations in our understanding and in judgments generally (Prolegomena 28). He claims that a valid cognition of an object in representations depends on the minds a priori synthesis of concepts of the understanding. Kant gives three examples of such concepts, relationships, and connections of the understanding: the relationship of subject to predicate, the relationship of ground to subsequent, and parts of a whole. He says that necessarily the only way the human mind can organize its understanding of the phenomenal world is by making judgments which include one of these concepts.
He says... the question is not how things in themselves but how the empirical cognition of things is determined, as regards the above moments of judgments in general, that is, how things, as objects of experience, can and must be subsumed under these concepts of the understanding. And then it is clear that I completely comprehend, not only the possibility, but also the necessity, of subsuming all appearances under these concepts, that is, of using them as principles of the possibility of experience (Prolegomena 28). Thus, cause is a principle of the possibility of experience, an a priori synthesis necessary for the organization of intuitions into a coherent understanding of the phenomenal world. Kant, in order to clarify the theoretical explanation of a priori logic, explains in 29 exactly how the mind might proceed in a specific example.
The mind sees the sun shining, an object illuminated by the sun, and senses that the object is growing warm. Constant conjunction and temporal succession, two of the three conditions for the validity of the concept of cause, have been satisfied. The mind makes a hypothetical judgment, merely a subjective connection of perceptions (Prolegomena 29), that the light of the sun causes the heat in the object. The empirical rule of relation that one event always followed another in the past is made, with the hypothetical judgment, into a universal law. The mind makes this leap in the initial process of organizing the intuitions. The judgment of the intuitions, in order to qualify as experience, is taken with universal validity and places upon the intuitions from an objective standpoint the necessary connection that illuminates the concept of cause.
Thus for Kant, in order to develop experience, we must first make a priori synthesis which yield concepts of the understanding, including causality. He maintains that although one cannot form rationally the concept of one thing causing another, I therefore easily comprehend the concept of cause as a concept necessarily belonging to the mere form of experience, and its possibility as a synthetic unification of perceptions in a consciousness in general (Prolegomena 29). In the Prolegomena, Kant solves both the problem of cause and the problem of induction. He does not try to find a corresponding sense impression for cause in experience, as Hume does. He does not need experience to find Humes foundation for the human minds necessity for the concept of cause. A priori concepts of the understanding, such as causation, are both possible and necessary for experience; they are not derived from experience, but experience is derived from them (Prolegomena 30).
Bibliography: Hume, David. An Enquiry Concerning Human Understanding. Hackett Publishing Company, Indianapolis, 1993. Hume, David. A Treatise if Human Nature. Oxford University Press, Oxford, 1978.
Kant, Immanuel. Prolegomena to Any Future Metaphysics. http
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