What is the synthetic a priori?

Immanuel Kant, answered from the texts and cited to the page.

Immanuel Kant answers

The question cuts to the very heart of what the Critique of Pure Reason — that investigation into the conditions of possibility of all human knowledge — was written to answer. Begin with the distinction itself. In any judgment where a predicate is connected to a subject, the connection runs in one of two ways: either the predicate is already contained, however covertly, within the concept of the subject, or it lies entirely outside that concept while standing in genuine connection with it.1

The first kind I call analytic — it merely unpacks what was already thought, adding nothing to the concept, only making explicit what confusion had concealed.2 The second kind is synthetic: it genuinely augments, adding to the subject a predicate that no analysis of the concept alone could ever have yielded.3 Now, most synthetic judgments draw their warrant from experience.

When I say that all bodies are heavy, the predicate heavy is not contained in the bare concept of body; I must go outside the concept and look to what experience teaches me about bodies encountered in the world.4 Such judgments are synthetic, but they are a posteriori — contingent, dependent on what nature happens to show us, incapable of the strict universality and necessity that genuine knowledge requires.

The synthetic a priori is the third kind, and it is the philosophically explosive one. These are judgments that genuinely augment our concepts — they are not mere unpacking — yet they carry with them necessity and universality that no accumulation of experience could ever confer.5 Consider the causal principle: everything that happens has a cause.

The concept of cause lies entirely outside the concept of something that happens; no analysis of the latter will produce the former. Yet the principle commands with absolute necessity and universality — not merely "in all cases we have observed," but necessarily, for any possible experience whatsoever.6 Experience cannot ground this, for experience gives only contingency; and yet the judgment is not analytic, for no dissection of the concept of an event yields causality.

What, then, is the unknown ground — the X, as I put it — upon which the understanding rests when it connects these two concepts necessarily?7 Mathematics furnishes the clearest cases. It might seem that 7 + 5 = 12 is analytic, following from the concepts of seven and five by the law of contradiction alone. But closer examination shows that the concept of their sum contains only their union in a single number, without specifying which number that is; twelve is by no means already thought in the mere combination of seven and five, and no analysis of those concepts, however patient, will extract it.8

To reach twelve, one must go beyond the concepts and call upon Anschauung (intuition) — counting on fingers, marking points, proceeding through the successive addition of units in some concrete image.9 The judgment genuinely amplifies our knowledge; it is synthetic. Yet it carries apodictic necessity; it is a priori. The same holds for geometry: that a straight line is the shortest path between two points is not contained in the concept of straightness, which specifies only quality, not quantity — Anschauung must again come to the aid of the synthesis.10

The whole aim of speculative knowledge a priori depends on such judgments.11 Analytic judgments are indispensable for achieving the clarity of concepts that rigorous inquiry demands, but they yield no real acquisition — they tell us only what we already implicitly knew.12 Synthetic a priori judgments alone extend our knowledge while doing so with the necessity and universality that distinguish science from mere empirical report.

The Critique asks: how are they possible? That question, once clearly posed, transforms the entire landscape of metaphysics.

Sources

  1. In all judgements wherein the relation of a subject to the predicate is cogitated...this relation is possible in two different ways. Either the predicate B belongs to the subject A, as somewhat which is contained (though covertly) in the conception A; or the predicate B lies completely out of the conception A, although it stands in connection with it.
    Critique of Pure Reason, p. 11
  2. the former add in the predicate nothing to the conception of the subject, but only analyse it into its constituent conceptions, which were thought already in the subject, although in a confused manner
    Critique of Pure Reason, p. 11
  3. the latter add to our conceptions of the subject a predicate which was not contained in it, and which no analysis could ever have discovered therein
    Critique of Pure Reason, p. 11
  4. it is experience upon which rests the possibility of the synthesis of the predicate of weight with the conception of body, because both conceptions, although the one is not contained in the other, still belong to one another (only contingently, however), as parts of a whole, namely, of experience
    Critique of Pure Reason, p. 11
  5. all proper mathematical judgments are a priori, and not empirical, because they carry with them necessity, which cannot be obtained from experience
    Prolegomena to Any Future Metaphysics, p. 11
  6. the principle adduced annexes the two representations, cause and effect, to the representation existence, not only with universality, which experience cannot give, but also with the expression of necessity, therefore completely à priori and from pure conceptions
    Critique of Pure Reason, p. 11
  7. what is here the unknown = X, upon which the understanding rests when it believes it has found, out of the conception A a foreign predicate B, which it nevertheless considers to be connected with it?
    Critique of Pure Reason, p. 11
  8. the concept of the sum of 7 + 5 contains merely their union in a single number, without its being at all thought what the particular number is that unites them. The concept of twelve is by no means thought by merely thinking of the combination of seven and five
    Prolegomena to Any Future Metaphysics, p. 11
  9. We must go beyond these concepts, by calling to our aid some concrete image (Anschauung), i.e., either our five fingers, or five points...and we must add successively the units of the five, given in some concrete image (Anschauung), to the concept of seven.
    Prolegomena to Any Future Metaphysics, p. 11
  10. That a straight line is the shortest path between two points, is a synthetical proposition. For my concept of straight contains nothing of quantity, but only a quality...Here, too, visualisation (Anschauung) must come to aid us.
    Prolegomena to Any Future Metaphysics, p. 11
  11. Upon such synthetical, that is augmentative propositions, depends the whole aim of our speculative knowledge à priori
    Critique of Pure Reason, p. 11
  12. although analytical judgements are indeed highly important and necessary, they are so, only to arrive at that clearness of conceptions which is requisite for a sure and extended synthesis, and this alone is a real acquisition
    Critique of Pure Reason, p. 11