B ix-x, ¶ 4

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[¶4] Insofar as there is to be reason in these sciences, something in them must be cognized a priori, and this cognition can relate to its object in either of two ways, either merely determining the object and its concept (which must be given from elsewhere), or else also making the object actual. The former is theoretical, the latter practical cognition of reason. In both the pure part, the part in which reason determines its object wholly a priori, must be expounded all by itself, however much or little it may contain, and that part that comes from other sources must not be mixed up with it; for it is bad economy to spend blindly whatever comes in without being able later, when the economy comes to a standstill, to distinguish the part of the revenue that can cover the expenses from the part that must be cut.

Summary

Sciences always have a priori cognitions which either determine what an object is or actualize them (bring them into existence). Sciences that determine are theoretical while those that actualize are practical. Our task is to present the pure (a priori) parts of these rational cognitions without anything from experience mixed in.

Commentary

Contemporary readers often think of science as an empirical endeavor and so they wonder if Kant's insistence on a priori cognitions regard antiquated notions of sciences. An understanding of what is entailed by these a priori cognitions can help the reader understand how these apply now just as much as then.

Every object we encounter empirically (in experience) is singular or, if considered as one among a given group or class, a particular; we do not - and cannot - encounter universal objects per se, but we can think about objects in a universal manner. A concept is already required to encounter a particular because it is considered one among others, but through universal judgments we consider objects further than we can ever experience them. If sciences were completely empirical they would be restricted to considering individuals or, at best, the particulars we encounter. However, our sciences deal with the universal (e.g., concerning all of nature) and so they cannot be completely empirical.

As we experience the world we form empirical concepts with which we can talk about objects we have not yet encountered. For example, from the concept I form of a human I can imagine to myself some human I have never met, or anticipate things about humans that I may meet in the future. Here I have begun to employ my concept to guide my thoughts intentionally rather than reactively in response to whatever I happen to experience. Despite my concept of human being empirical, I still employ this concept a priori whenever I am using it to guide or orient myself outside of experience.

The technique of learning from experience by using concepts to frame our experience is observation. Observations are distinguished from mere perceptions precisely due to the guidance of a priori cognitions (e.g., theories, hypotheses). Through observation we can determine if a notion we have developed of nature in universal terms is violated by any particular occurrence by comparing the consequences of the theory we hold (a priori) and the results of an experiment which should express those consequences of the theory.

From the above we can note something about metaphysics: there are no experiences possible for the objects of metaphysics (i.e., soul, World, and God) and so there is nothing like an observation of these, and so no experimentation. With no way to test theories there is no way to decide among them except logically, and Kant has discussed (in the previous passage) how logic cannot be used to extend our knowledge except negatively, so the only way of eliminating metaphysical theories through general logic is to find a contradiction. In metaphysics, a priori cognitions are certainly being used, but not in the service of guiding us in experience, but completely detached from experience. Kant will determine that these kinds of a priori cognitions are not legitimate.

A final note here of some interest. Kant will employ this understanding of the sciences in modeling his view of our own faculties. A chief characteristic of a priori cognitions is that they are the result of something which we introduce, and so it is with the synthetic a priori judgments which frame our very experience: the coherence of experience is possible because we introduce this element. This topic will be considered further as we proceed.

Questions

How does mathematics avoid the same fate as metaphysics?

Mathematics may seem to be in a similar situation as metaphysics for where can we find a perfect circle in experience? However, Kant doesn't have any concern with mathematics as its concepts are constructed by us and tested also in constructs of our own. There will be more on this topic later.

How does this impact Kant's own proposed science: critique of pure reason?

Kant realizes that he must guide his investigation with concepts in advance; the discussions of pure forms of intuition (i.e., space and time) and pure concepts (i.e., categories), which will be presented in the earlier part of the text, are important primarily because they are necessary to guide critical investigations.

Terminology

theretical (theoretische), practical (praktische), cognitions (Erkentnis), object (object or Gegenstand)