Prolegomena Kant Wrote the Prolegomena

Prolegomena

Kant wrote the Prolegomena as a primer and a "state of the field" essay for any future thinkers on metaphysics. He also wrote it as a "sketch" to the longer, more dense Critique of Pure Reason, which was either ignored or misunderstood upon its release two-year earlier.

First, Kant explains his own progression into this question, which came as a result of reading David Hume's work. David Hume challenging reason, demonstrating "…that it was perfectly impossible for reason to think a priori and by means of concepts a combination involving necessity. We cannot at all see why, in consequence of the existence of one thing, another must necessarily exist, or how the concept of such a combination can arise a priori." (Preamble). Hume believed we attributed causation to what was merely association, our past experience of seeing two things always appearing conjoined together. He concluded that our supposed a priori cognitions were "…nothing but common experiences marked with a false stamp." (Preamble).

Kant agreed with Hume's objection to causal reasoning, but not with his conclusion that a priori cognitions were impossible. Additionally, Kant clarified that Hume did not question whether the concept of cause was useful or necessary, but whether it "…could be thought by reason a priori, and consequently whether it possessed an inner truth, independent of all experience, implying a wider application than merely to the objects of experience." (Preamble). Kant realized that "…the concept of the connection of cause and effect was by no means the only idea by which the understanding thinks the connection of things a priori, but rather that metaphysics consists altogether of such connections. (Preamble).

Kant understood that Hume's objection threw doubt not only causality, but on all metaphysics. For Kant, proving the possibility of a priori cognition would restore the possibility of metaphysical reasoning. It would also allow Kant "…to determine the whole sphere of pure reason completely and from general principles, in its circumference as well as in its contents." (Preamble).

How there can be a priori synthetic propositions.

First, Kant attempts to define metaphysics as a science by distinguishing it from all other sciences. He first focuses on the sources of metaphysical cognition, reasoning that they cannot be empirical. (Sec. 1). However, the same can be said for pure Mathematics. (1). Kant further distinguishes metaphysics by calling it "pure philosophical cognition." (1).

Kant reasons that synthetic judgments must consist of nothing but a priori judgments. Of judgments in general, there are only two kinds: analytic judgments and synthetic judgments. (2a). Analytic judgments are explicative, adding nothing to the content of cognition, while synthetical judgments are expansive, increasing the given cognition. (2a). For example, the statement that "all wives are married" is an analytic judgment because it does not alter our understanding of "wife." The statement that "all wives have neighbors" is a synthetic judgment because it adds something to our understanding of wife which is not actually thought in the general concept of wife. Thus, it "…amplifies our knowledge by adding something to the concept." (2a).

Kant defines analytic judgments as a priori by nature. They can be so because they require only the law of Contradiction for proof. (2b). The "…predicate of an affirmative analytical judgment is already contained in the concept of the subject, of which it cannot be denied without contradiction." (2b). Even when the concepts are empirical, analytic judgments are always a priori. (2b).

Of synthetic judgments, there are a posteriori judgments of empirical origin and a priori judgments of which spring from pure Understanding and Reason. (2c). Empirical judgments are always synthetical because analytical judgments have no need of empirical knowledge because they can be proved by the Law of Contradiction alone. (2c1).

Mathematical judgments are all synthetical. (2c2). A "…synthetical proposition can indeed be comprehended according to the law of contradiction, but only by presupposing another synthetical proposition from which it follows, but never in itself." (2c2). Although most believe that 7+5 must equal12 due to the law of contradiction, the concept of the sum Of 7+5 actually only contains their union in a single number. (2c2). The concept of 12 is not thought of by merely thinking of the combination of 7+5. It can only be found by reference to some concrete image [Anschauung], such as our five fingers. (2c2).

Geometry is sythenthical as well. Some principles used by geometers depend on the law of contradiction, such as a=a or a+b>a, but they are only admitted in mathematics because they can be represented in some visual form. (2c2). We only believe these principles to be analytical judgments because of the duplicity of the expression, e.g. a=a, which makes us believe that the predicate, that "a equals a," is implied in the thought of the concept "a." However, this predicate is only shown to be necessarily contained in the concept "a" indirectly by means of a visualization. (2c2).

Summary

The essential and distinguishing feature of pure mathematical cognition among all other a priori cognitions is, that it cannot at all proceed from concepts, but only by means of the construction of concepts. (4). Thus, they are not analytical judgments, but synthetical judgments. This proves that synthetical knowledge a priori is possible, with Mathematical judgments being a clear example. Kant then seeks to discover how such knowledge is possible in order to deduce the principle which makes all synthetic knowledge a priori possible, including metaphysics.

Kant posited that all mathematical knowledge consists of concepts derived from the intuition of an object. This intuition is not based on the experience of an object, but on the mere form of sensory experience. (7). We can intuit things a priori only through the mere form of sensuous intutition. (10). Mathematical concepts are constructed from a synthesis of intuitions such as the concept of number, which is constructed from the successive addition of units in time. These forms exist in us prior to all of our intuitions of objects. (10). For instance, the boundlessness of infinity cannot be shown from concepts, but only through pure intuition. (12).

How such propositions allow for the possibility of metaphysics while at the same time they set limits to pure reason.

Synthetic knowledge a priori make metaphysical knowledge possible because there is a priori knowledge of nature that precedes all experience. (16). Judgments of experience are empirical judgments that are valid for external objects. They require special pure concepts which have originated in the pure understanding. (18). All judging subjects will agree on their experience of the object. When a perception is subsumed under these pure concepts, it is changed into objective experience. (18).

We cannot immediately and directly know an object as it is apart from the way that it appears. (19). However, if we say that a judgment must be valid for all observers, then we are making a valid statement about an object. (19). Judgments of experience are valid judgments about an object because they necessarily connect everyone's perceptions of the object through the use of a pure concept of the understanding. (19).

A judgment of experience results when a sense perception and a judgment of perception are unified by a concept that makes the judgment necessary and valid for all perceivers. (21a). The senses intuit. The understanding thinks, or judges. Experience is generated when a concept of the understanding is added to a sense perception. (22).

According to Kant, metaphysics is not possible in the sense that the objective reality of metaphysical concepts are confirmed by experience. (40). Metaphysics is only possible, or rather subjectively actual, because its problems occur to everyone as a result of the nature of their reason (40). The concepts of reason are transcendent because they are concerned with the absolute totality of all possible experience, which cannot itself be experienced. (40).

The concepts of reason never appear in experience but the concepts of understanding appear in experience. Thus, only the concepts of understanding can be confirmed or refuted through experience. Kant concludes that these concepts of pure reason, Ideas, are useless for the purpose of understanding nature. Only the concepts of pure understanding, Categories, are useful for understanding nature. As such, Metaphysics is only possible and valid as a science in when it confirms or refutes these concepts of pure understanding.

Limits of Pure Reason

We cannot know things in themselves, or things as they are apart from our subjective experience of them. (40). This is the limit of pure reason. However, this does mean that things in themselves do not exist. Things in themselves may exist and there may be other ways of knowing them, apart from our experience. (57). We must guard against assuming that the limits of our reason are the limits of the possibility of things in themselves. To do this, we must determine the boundary of the use of our reason. In other words, a critique of pure reason must systematically investigate the role of a priori concepts in understanding before metaphysics can become a science instead of mere speculation about the natural world.