A Priori and A Posteriori

Nobody has checked every triangle. Nobody has surveyed the bachelors to confirm that none is married. Yet the claims that the angles of a Euclidean triangle sum to two right angles, and that bachelors are unmarried, seem settled in a way that no amount of further looking would improve.

Contrast the claim that water boils at one hundred degrees at sea level. That one was found out, could have been otherwise, and would be revised if the measurements came out differently. The difference between the two kinds of case is old, and the question of whether it marks a real division is one of the places where epistemology and the philosophy of language meet.

The distinction

Three clarifications keep the distinction from collapsing under the first objection anyone raises.

The distinction is epistemological, not psychological. It concerns what justifies a belief, not how anyone came to have it. A mathematician who arrives at a theorem through a dream and then proves it has a priori justification, and the dream is irrelevant.

Experience is required for concept acquisition on any view. You cannot know that bachelors are unmarried without having learned the words, and learning them took experience. The claim is that once the concepts are possessed, no further experience is consulted. Kant put the point by saying that although all our knowledge begins with experience, it does not follow that it all arises out of experience.

The distinction is not the same as necessary versus contingent, and Saul Kripke's 1970 lectures established that they come apart in both directions. That water is H2O is necessary and known a posteriori. That the standard metre bar is one metre long was, on Kripke's analysis, knowable a priori by whoever fixed the reference, and contingent, since the bar might have been longer.

What is supposed to do the justifying

The term is unfortunate, since it suggests hunches. What is meant is closer to intellectual seeing. When you consider whether anything can be red and green all over at once, something happens that is not a hunch and is not an inference from observed cases. You grasp that it cannot be.

Laurence BonJour, having abandoned coherentism, spent the later part of his career defending rational insight as a genuine source of justification, on the grounds that no empiricist account can explain our warrant for the principles of inference that empiricism itself uses. George Bealer's version treats intuitions as a basic evidential source with the same standing as perception.

The standard objection is that the account explains nothing. Saying a proposition is justified by rational intuition, when rational intuition is defined as the state of grasping that it is true, comes close to saying that it is justified because it is obvious. The empiricist wants to know what this faculty is, how it could be reliable about abstract matters that do not interact with us causally, and why its deliverances have so often been wrong. The last point carries real weight. Euclidean geometry seemed rationally evident to competent thinkers for two thousand years and is not true of physical space.

The innateness question

The doctrine has a famous first appearance. In the Meno, Socrates draws geometrical results from an untaught slave boy using only questions, and concludes that the boy is recollecting what his soul knew before birth. The argument is memorable, and the conclusion does not follow: the questions do most of the work, and the demonstration shows that the boy can reason, not that he knew.

Locke's attack in the Essay was decisive against the version he targeted. If there were principles universally assented to, children and the cognitively impaired would assent to them, and they do not. Leibniz's reply in the New Essays was that innate knowledge is dispositional rather than occurrent, present as a tendency that experience triggers, and the image he uses is of veins in a block of marble that dispose it to be split one way rather than another.

The contemporary descendant is not a theory of knowledge but of language. Chomsky's argument from the poverty of the stimulus holds that the linguistic input available to a child radically underdetermines the grammar the child acquires, so that substantial structure must be contributed by the learner. Whether this is innate knowledge in the epistemologist's sense is contested, since an innate constraint on hypothesis formation is not obviously a justified true belief, and Chomsky himself has been careful about the claim.

The argument is the strongest one in the rationalist's hands, and the empiricist has two ways to resist. The first is to deny the first premise and hold that apparent necessities are deeply entrenched empirical generalisations, which is Quine's route and the subject of the next article. The second is to grant the conclusion while draining it of interest, by holding that necessary truths are true by convention or by meaning, so that knowing them requires only knowing the language.

The state of play

Almost nobody now holds the strong rationalist position that substantive truths about the world are knowable by pure reason. Almost nobody holds the strong empiricist position either, because logic and mathematics remain stubborn: the claim that they are empirical generalisations has never been made plausible in detail, and the claim that they are empty of content has its own difficulties.

Where the field has settled, to the extent it has, is on a modest a priori. There is justification that does not rest on experience, it covers logic, mathematics, and conceptual truths, it is defeasible rather than certain, and its epistemology remains unclear. That last clause is not a footnote. A source of justification whose workings nobody can explain is exactly what the empiricist tradition objected to, and calling it modest does not dispose of the objection.

Next

The empiricist's best attempt to explain the a priori away, and Quine's argument that the attempt cannot be stated without going in a circle.