A priori and a posteriori

Knowledge that does not depend on experience for its justification, and knowledge that does.

Theme: Knowledge, truth and reason
Tradition: Western
Term fixed: 1781

In plain terms

Some things you can work out without looking. That nothing is both entirely red and entirely green. That every bachelor is unmarried. That seven and five make twelve.

Other things require looking. Whether it is raining, how many planets there are, what water is made of.

The distinction is about justification rather than origin. Everyone learns the words bachelor and unmarried from experience, but no further experience is needed to see that the one implies the other. Where the argument gets interesting is whether anything substantial - anything that tells you about the world rather than about your own concepts - can be known in the first way. Kant said yes and built a system on it. The century after him spent a long time finding out that his best example was false.

As a philosopher would put it

The pair is epistemic and cuts across two others it is constantly confused with. Analytic and synthetic is semantic - whether the predicate is contained in the subject. Necessary and contingent is metaphysical - whether it could have been otherwise. Traditionally the three were assumed to coincide.

Kant's synthetic a priori is the claim that some substantive truths are known independently of experience - mathematics and the principles of natural science - and his explanation is that they are conditions of any possible experience rather than reports of it. Euclidean geometry was his showcase.

Two attacks broke the traditional alignment. Quine's Two Dogmas denies the analytic-synthetic distinction and with it any class of truths immune from empirical revision. Kripke separates necessity from apriority in the opposite direction: identities like water and H₂O are necessary and known only empirically, while the length of the standard metre bar could be fixed a priori and is contingent. Both moves leave the two distinctions cross-cutting rather than nested.

Where you meet it

Kant held that Euclidean geometry was synthetic a priori: it tells us something substantive about space, and no experiment could refute it, because space just is the form our sensibility imposes. That the angles of a triangle sum to two right angles was not, on his account, a claim experience could touch.

In the 1820s and 1830s Bolyai, Lobachevsky and Gauss showed that consistent geometries exist in which the parallel postulate fails. Riemann generalised this in 1854 into the mathematics of curved spaces. For eighty years these were regarded as formal curiosities.

Then general relativity made spacetime curvature physical, and in May 1919 Eddington's expeditions photographed stars near the sun during a total eclipse and measured their apparent displacement. The geometry of actual space was settled by photography. Kant's best example of an unrevisable substantive truth turned out to be an empirical hypothesis that was false - which is not a refutation of the whole category, but it is the loss of its most confident instance.

What is actually disputed

Whether there is any a priori knowledge.

Radical empiricism, following Quine, holds that all knowledge is answerable to experience and that the apparently a priori truths are simply the ones held most firmly and revised last - logic included. The reply is that this makes the position self-undermining, since the argument for it is not itself empirical, and that a claim revisable in principle but never in practice is doing exactly what a priori knowledge was supposed to do.

Moderates keep the analytic a priori and deny the synthetic. Kantians reply that mathematics is not plausibly analytic and that its application to the world needs explaining. And even the analytic cases are contested, since Quine's objection was precisely that no clean line between meaning and fact has ever been drawn - a challenge that is fifty years old and has produced more attempts than agreements.

Defined against

Experience The distinction exists precisely to mark what does and does not depend on it for justification

Philosophers

Immanuel Kant The synthetic a priori, and the system built on it
David Hume Relations of ideas against matters of fact, the sharper predecessor
Gottfried Wilhelm Leibniz Truths of reason against truths of fact
Willard Van Orman Quine The denial that any truth is immune from revision
Rudolf Carnap The attempt to save the a priori as analytic

Works

Critique of Pure Reason Where the distinction becomes central
A Treatise of Human Nature The empiricist version of the same split
Monadology Truths of reason and of fact
Language, Truth and Logic The positivist settlement
Naming and Necessity Where apriority and necessity come apart

Schools

German Idealism Where the synthetic a priori is defended
British Empiricism Where it is denied in advance
Vienna Circle Where the a priori is made analytic and empty
Cartesianism Where reason alone delivers substantive truth
Classical Pragmatism Where the whole distinction is treated as a matter of degree

Related concepts

Necessity c. 330 BC · Experience c. 330 BC · Knowledge c. 369 BC · Reason c. 500 BC · Truth c. 330 BC

The Latin terms are scholastic; Kant's 1781 formulation, and his claim that some knowledge is both a priori and substantive, is what made the distinction the central issue in modern epistemology.