A distinction that has the potential to create confusion is the one that contrasts the a posteriori not with the a priori but with the innate. Since logical problems are easily confused with psychological problems, it is difficult to disentangle the question of the causal origin of concepts and beliefs from the question of their content and justification.

A concept, such as “five,” is said to be innate if a person’s possession of it is causally independent of his experience—e.g., his perception of various groupings of five objects. Similarly, a belief is innate if its acceptance is causally independent of the believer’s experience. It is therefore possible for beliefs to be innate without being a priori: for example, the baby’s belief that its mother’s breast will nourish it is arguably causally independent of his experience, though experience would be necessary to justify it.

Another supposedly identical, but in fact more or less irrelevant, property of concepts and beliefs is that of the universality of their possession or acceptance—that a priori or innate concepts and beliefs must be held by everyone. There may be, in fact, some basis for inferring universality from innateness, since many innate characteristics, such as the fear of loud noises, appear to be common to the whole human species. But there is no inconsistency in the supposition that a concept or belief is innate in one person and learned from experience in another.

Two main kinds of concept have been held to be a priori. First, there are certain formal concepts of logic and of mathematics that reflect the basic structure of discourse: “not,” “and,” “or,” “if,” “all,” “some,” “existence,” “unity,” “number,” “successor,” and “infinity.” Secondly, there are the “categorial” concepts—such as “substance,” “cause,” “mind,” and “God”—which, according to some philosophers, are imposed by the mind upon the raw data of sensation in order to make experiences possible. One might add to these the more specific theoretical concepts of physics, which are sometimes said to apply to entities that are unobservable in principle.

In the long history of debate over the a priori, it was long taken for granted that all a priori propositions are necessarily true—i.e., true by virtue of the meanings of their terms (“analytic”) or true by virtue of the fact that their negations imply a contradiction. Propositions such as “all triangles have three sides,” “all bachelors are unmarried,” and “all red things are coloured” are necessarily true in one or both of these senses. Likewise, it was held that propositions that are contingently true, or true merely by virtue of the way the world happens to be, are a posteriori. “John is a bachelor” and “John’s house is red” are propositions of this type.

In the 1970s, however, the American philosopher Saul Kripke argued to the contrary that some a priori propositions are contingent and some a posteriori propositions are necessary. According to Kripke, the referential properties of “natural kind” terms like heat can be understood by imagining that their referents were fixed, upon their introduction into the language, by means of certain definite descriptions, such as “the cause of sensations of warmth.” In other words, heat was introduced as a name for whatever phenomenon happened to satisfy the description “the cause of sensations of warmth.” Of course, the phenomenon in question is now known to be molecular motion. Thus heat refers to molecular motion, then and now, because molecular motion was the cause of sensations of warmth when the term was introduced. Given this introduction, however, the proposition “heat causes sensations of warmth” must be a priori. Because its introduction stipulated that heat is the phenomenon that causes sensations of warmth, it is knowable independently of experience that heat causes sensations of warmth, even though it is only a contingent matter of fact that it does. On the other hand, the proposition “heat is molecular motion” is a posteriori, because this fact about heat was discovered (and could only be discovered) through empirical scientific investigation. But the proposition is also necessary, according to Kripke, because once the referent of heat has been fixed as molecular motion, there are no imaginable circumstances in which the term could refer to anything else. This conclusion is supported by the intuition that, if it were discovered tomorrow that sensations of warmth in humans are actually caused by something other than molecular motion, one would not say that heat is not molecular motion but rather that sensations of warmth are caused by something other than heat. Kripke proposed a similar analysis of the referential properties of proper names like “Aristotle,” according to which a proposition like “Aristotle was the teacher of Alexander the Great” is contingent but a priori.

Degrees of empiricism

Empiricism, whether concerned with concepts or knowledge, can be held with varying degrees of strength. On this basis, absolute, substantive, and partial empiricisms can be distinguished.