Philosophy Pages

    Dictionary    Study Guide  Logic   F A Q s
  History Timeline Philosophers   Locke

Kant: Synthetic A Priori Judgments

The Critical Philosophy

Life and Works
. . Critical Philosophy
. . Analytic / Synthetic
. . Mathematics
. . Natural Science
. . Experience & Reality
. . Phenomena / Noumena
. . Metaphysical Ideas
. . Limits of Reason
. . The Moral Law
. . Categorical Imperative
. . Autonomy of the Will
. . Third Critique
Internet Sources

Next we turn to the philosophy of Immanuel Kant, a watershed figure who forever altered the course of philosophical thinking in the Western tradition. Long after his thorough indoctrination into the quasi-scholastic German appreciation of the metaphysical systems of Leibniz and Wolff, Kant said, it was a careful reading of David Hume that "interrupted my dogmatic slumbers and gave my investigations in the field of speculative philosophy a quite new direction." Having appreciated the full force of such skeptical arguments, Kant supposed that the only adequate response would be a "Copernican Revolution" in philosophy, a recognition that the appearance of the external world depends in some measure upon the position and movement of its observers. This central idea became the basis for his life-long project of developing a critical philosophy that could withstand them.

Kant's aim was to move beyond the traditional dichotomy between rationalism and empiricism. The rationalists had tried to show that we can understand the world by careful use of reason; this guarantees the indubitability of our knowledge but leaves serious questions about its practical content. The empiricists, on the other hand, had argued that all of our knowledge must be firmly grounded in experience; practical content is thus secured, but it turns out that we can be certain of very little. Both approaches have failed, Kant supposed, because both are premised on the same mistaken assumption.

Progress in philosophy, according to Kant, requires that we frame the epistemological problem in an entirely different way. The crucial question is not how we can bring ourselves to understand the world, but how the world comes to be understood by us. Instead of trying, by reason or experience, to make our concepts match the nature of objects, Kant held, we must allow the structure of our concepts shape our experience of objects. This is the purpose of Kant's Critique of Pure Reason (1781, 1787): to show how reason determines the conditions under which experience and knowledge are possible.

Varieties of Judgment

In the Prolegomena to any Future Metaphysic (1783) Kant presented the central themes of the first Critique in a somewhat different manner, starting from instances in which we do appear to have achieved knowledge and asking under what conditions each case becomes possible. So he began by carefully drawing a pair of crucial distinctions among the judgments we do actually make.

The first distinction separates a priori from a posteriori judgments by reference to the origin of our knowledge of them. A priori judgments are based upon reason alone, independently of all sensory experience, and therefore apply with strict universality. A posteriori judgments, on the other hand, must be grounded upon experience and are consequently limited and uncertain in their application to specific cases. Thus, this distinction also marks the difference traditionally noted in logic between necessary and contingent truths.

But Kant also made a less familiar distinction between analytic and synthetic judgments, according to the information conveyed as their content. Analytic judgments are those whose predicates are wholly contained in their subjects; since they add nothing to our concept of the subject, such judgments are purely explicative and can be deduced from the principle of non-contradiction. Synthetic judgments, on the other hand, are those whose predicates are wholly distinct from their subjects, to which they must be shown to relate because of some real connection external to the concepts themselves. Hence, synthetic judgments are genuinely informative but require justification by reference to some outside principle.

Kant supposed that previous philosophers had failed to differentiate properly between these two distinctions. Both Leibniz and Hume had made just one distinction, between matters of fact based on sensory experience and the uninformative truths of pure reason. In fact, Kant held, the two distinctions are not entirely coextensive; we need at least to consider all four of their logically possible combinations:

Unlike his predecessors, Kant maintained that synthetic a priori judgments not only are possible but actually provide the basis for significant portions of human knowledge. In fact, he supposed (pace Hume) that arithmetic and geometry comprise such judgments and that natural science depends on them for its power to explain and predict events. What is more, metaphysics—if it turns out to be possible at all—must rest upon synthetic a priori judgments, since anything else would be either uninformative or unjustifiable. But how are synthetic a priori judgments possible at all? This is the central question Kant sought to answer.


Consider, for example, our knowledge that two plus three is equal to five and that the interior angles of any triangle add up to a straight line. These (and similar) truths of mathematics are synthetic judgments, Kant held, since they contribute significantly to our knowledge of the world; the sum of the interior angles is not contained in the concept of a triangle. Yet, clearly, such truths are known a priori, since they apply with strict and universal necessity to all of the objects of our experience, without having been derived from that experience itself. In these instances, Kant supposed, no one will ask whether or not we have synthetic a priori knowledge; plainly, we do. The question is, how do we come to have such knowledge? If experience does not supply the required connection between the concepts involved, what does?

Kant's answer is that we do it ourselves. Conformity with the truths of mathematics is a precondition that we impose upon every possible object of our experience. Just as Descartes had noted in the Fifth Meditation, the essence of bodies is manifested to us in Euclidean solid geometry, which determines a priori the structure of the spatial world we experience. In order to be perceived by us, any object must be regarded as being uniquely located in space and time, so it is the spatio-temporal framework itself that provides the missing connection between the concept of the triangle and that of the sum of its angles. Space and time, Kant argued in the "Transcendental Aesthetic" of the first Critique, are the "pure forms of sensible intuition" under which we perceive what we do.

Understanding mathematics in this way makes it possible to rise above an old controversy between rationalists and empiricists regarding the very nature of space and time. Leibniz had maintained that space and time are not intrinsic features of the world itself, but merely a product of our minds. Newton, on the other hand, had insisted that space and time are absolute, not merely a set of spatial and temporal relations. Kant now declares that both of them were correct! Space and time are absolute, and they do derive from our minds. As synthetic a priori judgments, the truths of mathematics are both informative and necessary.

This is our first instance of a transcendental argument, Kant's method of reasoning from the fact that we have knowledge of a particular sort to the conclusion that all of the logical presuppositions of such knowledge must be satisfied. We will see additional examples in later lessons, and can defer our assessment of them until then. But notice that there is a price to be paid for the certainty we achieve in this manner. Since mathematics derives from our own sensible intuition, we can be absolutely sure that it must apply to everything we perceive, but for the same reason we can have no assurance that it has anything to do with the way things are apart from our perception of them. Next time, we'll look at Kant's very similar treatment of the synthetic a priori principles upon which our knowledge of natural science depends.

Preconditions for Natural Science

In natural science no less than in mathematics, Kant held, synthetic a priori judgments provide the necessary foundations for human knowledge. The most general laws of nature, like the truths of mathematics, cannot be justified by experience, yet must apply to it universally. In this case, the negative portion of Hume's analysis—his demonstration that matters of fact rest upon an unjustifiable belief that there is a necessary connection between causes and their effects—was entirely correct. But of course Kant's more constructive approach is to offer a transcendental argument from the fact that we do have knowledge of the natural world to the truth of synthetic a priori propositions about the structure of our experience of it.

As we saw last time, applying the concepts of space and time as forms of sensible intuition is necessary condition for any perception. But the possibility of scientific knowledge requires that our experience of the world be not only perceivable but thinkable as well, and Kant held that the general intelligibility of experience entails the satisfaction of two further conditions:

First, it must be possible in principle to arrange and organize the chaos of our many individual sensory images by tracing the connections that hold among them. This Kant called the synthetic unity of the sensory manifold.

Second, it must be possible in principle for a single subject to perform this organization by discovering the connections among perceived images. This is satisfied by what Kant called the transcendental unity of apperception.
Experiential knowledge is thinkable only if there is some regularity in what is known and there is some knower in whom that regularity can be represented. Since we do actually have knowledge of the world as we experience it, Kant held, both of these conditions must in fact obtain.

Deduction of the Categories

Since (as Hume had noted) individual images are perfectly separable as they occur within the sensory manifold, connections between them can be drawn only by the knowing subject, in which the principles of connection are to be found. As in mathematics, so in science the synthetic a priori judgments must derive from the structure of the understanding itself.

Consider, then, the sorts of judgments distinguished by logicians (in Kant's day): each of them has some quantity (applying to all things, some, or only one); some quality (affirmative, negative, or complementary); some relation (absolute, conditional, or alternative); and some modality (problematic, assertoric, or apodeictic). Kant supposed that any intelligible thought can be expressed in judgments of these sorts. But then it follows that any thinkable experience must be understood in these ways, and we are justified in projecting this entire way of thinking outside ourselves, as the inevitable structure of any possible experience.

The result of this "Transcendental Logic" is the schematized table of categories, Kant's summary of the central concepts we employ in thinking about the world, each of which is discussed in a separate section of the Critique:

Axioms of IntuitionAnticipations of Perception
Analogies of ExperiencePostulates of Empirical Thought

Our most fundamental convictions about the natural world derive from these concepts, according to Kant. The most general principles of natural science are not empirical generalizations from what we have experienced, but synthetic a priori judgments about what we could experience, in which these concepts provide the crucial connectives.

. . . . .
History of Philosophy
Previous Next

Creative Commons License
Permissions beyond the scope of this license may be available at

©1997, 2011 Garth Kemerling.
Last modified 12 November 2011.
Questions, comments, and suggestions may be sent to:
the Contact Page.