Kant’s Critique of Pure Reason: The Principles of Pure Understanding

Contents:

1. The Principle of non-Contradiction
2. Synthetic A Priori Truths Revisited
3. Further Principles
4. The Role of Concepts and the Imagination

In this section, Kant brings us a step closer to completing the picture of how our power of understanding actually works in relation to the everyday objects of cognition. So far, Kant has given us a very general basis for the truth of a priori judgments by supplying us with a table of all the general concepts necessary for the possibility of making a priori judgments (i.e. the Categories) in addition to the perceptual forms of space and time that enter into every act of sensory intuition. He now takes another step toward showing how the mind manages formulate synthetic judgments by giving us a few principles whereby such truths may be recognized.

Toward that end, he is initially concerned to establish the basis for the synthetic a priori truths of mathematics in the first two sections of his sections titled the “Axioms of Intuition” and the “Anticipations of Perception.” He then extends the field of principles to account for a priori judgments that arise in relation to the physical sciences in the two sections that follow, the “Analogies of Experience” and “Postulates of Empirical Thought in General.” This, he proceeds from mathematical to physical principles of synthetic a priori judgement.

Such judgments are the nexus point for Kant between the categories and their relation to our possible experience. It is on the basis of the categories that knowledge generally applicable our experience is constituted, but it is only in relation to experience that may serve to affirm or deny such judgments it can have any objective validity. The working out of such principles exemplifies system-building aspect of the Critique that echoes earlier projects such as Spinoza’s in the Ethics or Leibniz’s in Monadology. For some, the pristine systematicity of the Critique is a source of aesthetic delight and a wonder in its own right.

The Principle of Non-Contradiction

Before entering into his discussion of the principles of synthetic judgments, Kant gives us a general principle of a priori reasoning that applies to both analytic and synthetic judgments. Kant writes that while the principle of non-contradiction (applying to propositions of the form “X both is and is not P”) must be “recognized as being the universal and completely sufficient principle of all analytic knowledge” and therefore appliable as a basic condition of judgments in general [B189], it is no guarantee of the objective truth of synthetic ones. Although both kinds of judgments must adhere to this basic principle of reasoning, there is this difference: synthetic propositions require something more, an agreement between the proposition and the state of affairs to which it refers.

Kant writes in B197 that experience is the one type of knowledge that is “capable of imparting reality to any non-empirical [i.e. a priori] synthesis” and that the basis for truth in relation to such a synthesis is its “agreement with the object.” This type of statement from Kant might lead one to suspect that his understanding of non-analytic, synthetic truth might be similar to what is now referred to as a correspondence theory of truth. Yet, the sort of correspondence he has in mind is not to particular states of affairs, but to the way we reason about the world in relation to our experience the world in a much more general sense. Non-contradiction is the highest principle that makes this possible at all, but the further principle that underlies all axioms of intuition [B202] that “all intuitions are extensive magnitudes” (discussed further in the next section below) provides a clarifying example of what Kant has in mind.

Synthetic A Priori Truths Revisited

Before passing on, it should be made clear what sort of correspondence Kant has in mind and how such judgments might be considered to have a veritable a priori foundation. It a mistake to suppose that Kant’s version of the correspondence theory presupposes any form of realism. What Kant has in mind as a condition of genuinely synthetic a priori truth is an agreement with any possible human experience-with any way that is, that humans experience the world, which as Kant has argued, is always conditioned by the forms of space and time. A further, more specific example is the possibility of a “figure” that does not involve an enclosed space (viz. B65). Such a case would not be possible (a) given that a figure is defined as such (here the principle of contradiction comes into play) and (b) because it is simply impossible to imagine a defined space without it being enclosed.

The impossibility of even imagining a defined space without an enclosure follows not only from an analysis of the concepts of a figure, but immediately from the way the transcendental conditions for the possibility of experience in general, space and time, manifest themselves condition our experience itself. We may find Kant arriving at this kind of insight in B56 for example, where he writes that time and space are the “pure forms of all sensible intuition, and so are what make a priori synthetic propositions possible.” It is for this reason that Kant argues against taking time and space to be merely empirical principles and in favor of understanding time, for example, as an “absolute and transcendental reality” in B56 even though there is no direct empirical basis for its existence. While Kant has transcendental concepts that make a priori judgments possible, the reality of synthetic judgments would have no objective validity were they not related to the transcendental conditions of any possible experience, space and time.

Perhaps Kant has somewhere in mind the Cartesian problem of how reality in any genuine sense may be ascertained, the extent to which it is possible to doubt any aspect of our experience as being either real or true. Cartesian skepticism certainly does not take a transcendental turn at any point and so questions about the reality of space and time amount to ascertaining whether our experience may deceive us, whether we may be dreaming at a particular time, for example, because if we may be so deceived, our knowledge may fall short of certainty. In contrast, the Kantian transcendental turn manages to dissolve this line of questioning because it concerns the possibility of any experience whatsoever. Since all experience is conditioned by the “absolute and transcendental” realities of space and time [B56], their reality is assured inasmuch as it is a necessary condition for the possibility of any experience we might have.

Mathematical Principles

The Axioms of Intuition and Anticipations of Perception make up principles underlying a priori mathematical judgments. Briefly stated, the principles they convey are, in order: (a) “All intuitions are extensive magnitudes” and (b) “In all appearances, the real that is an object of sensation has intensive magnitude, that is, a degree.”

What does Kant mean by these two principles that underlie either the axioms we can form about our intuitions (in geometry) or that we can anticipate as occurring in our perception? In the first case, he means simply that anything that appears to us in our perception as an object must have an extension in space, it must in other words, have a spatial magnitude. Because it is extended, its extension requires time. The example Kant gives is drawing a line. If a line is drawn out, its extension requires a time within which it may become extended.

In the second case, what Kant means to indicate by an “intensive magnitude” is our experience that even if an object is extended it must also possess further quantifiable attributes, for example a degree of brightness or an amount of weight (B215). Both sets of principles apply to the Aristotelian category of “quantity” which preceded “quality,” a category Kant defines as including the concepts of reality, negation, and limitation. It may be noticed that there is an ontological precedence in their ordering. An object may have a quality such as being (in reality) yellow only if the object to which it belongs has an extension in space.

The Role of Concepts and the Imagination

Of course, the possibility of a priori true synthetic judgments is based not only upon the transcendental conditions underlying our sensibility, but upon the content of the concepts that enter into our reasoning. Without objectively valid concepts, no synthetic a priori knowledge would be possible, and such concepts must themselves have an a priori validity if they are to be used to form true synthetic a priori propositions. As mentioned above, such concepts must be based upon the categories of our understanding. However, an additional step is required adverted to in the prior discussion of schematism: the synthesis of experience by the imagination as well as its own prior condition, the unity of apperception, the unity of consciousness that makes unity itself a condition for the possibility of our experience (B194).

It is in our imagination that the synthesis necessary to go beyond the mere analysis of concepts in forming judgments arises. What is required for true a priori synthetic propositions is not just a kind of necessity or universality that is taken from experience–indeed, Humean skepticism shut the door on the very possibility of discovering universality and necessity in experience–but one that can be determined to belong to objects prior to experience. As Kant writes in B195, “The possibility of experience is, then, what gives objective reality to all our a priori modes of knowledge.” What Kant wishes to argue is that a priori concepts enter into the possibility of experience as its transcendental conditioning factors. They enter into experience via the synthetic activity of the imagination and are present in the schematism of its objects. It is by means of such a schematizing synthesis that the a priori principles that condition the possibility of our experience in general can become known as such, that is, when they obtain an objective existence in the representations of our experience. Such representations give us the principles that “alone supply the concept which contains the condition, and, as it were the exponent, of a rule in general. What experience gives is the instance which stands under the rule” (B198).