A Priori and A Posteriori

The terms "a priori" and "a posteriori" refer primarily to how or on what basis a proposition might be known. A proposition is knowable a priori if it is knowable independently of experience. A proposition is knowable a posteriori if it is knowable on the basis of experience. The a priori/a posteriori distinction is epistemological and should not be confused with the metaphysical distinction between the necessary and the contingent or the semantical or logical distinction between the analytic and the synthetic. Two aspects of the a priori/a posteriori distinction require clarification: the conception of experience on which the distinction turns; and the sense in which a priori knowledge is independent of such experience. The latter gives rise to important questions regarding the positive basis of a priori knowledge.

1. An initial characterization
A priori” and “a posteriori” refer primarily to how, or on what basis, a proposition might be known. In general terms, a proposition is knowable a priori if it is knowable independently of experience, while a proposition knowable a posteriori is knowable on the basis of experience. The distinction between a priori and a posteriori knowledge thus broadly corresponds to the distinction between empirical and nonempirical knowledge.
The a priori/a posteriori distinction is sometimes applied to things other than ways of knowing, for instance, to propositions and arguments. An a priori proposition is one that is knowable a priori and an a priori argument is one the premises of which are a priori propositions. Correspondingly, an a posteriori proposition is knowable a posteriori, while an a posteriori argument is one the premises of which are a posteriori propositions. (An argument is typically regarded as a posteriori if it is comprised of a combination of a priori and a posteriori premises.) The a priori/a posteriori distinction has also been applied to concepts. An a priori concept is one that can be acquired independently of experience, which may – but need not – involve its being innate, while the acquisition of an a posteriori concept requires experience.
The component of knowledge to which the a priori/a posteriori distinction is immediately relevant is that of justification or warrant. (These terms are used synonymously here and refer to the main component of knowledge beyond that of true belief.) To say that a person knows a given proposition a priori is to say that her justification for believing this proposition is independent of experience. According to the traditional view of justification, to be justified in believing something is to have an epistemic reason to support it, a reason for thinking it is true. Thus, to be a priori justified in believing a given proposition is to have a reason for thinking that the proposition is true that does not emerge or derive from experience. By contrast, to be a posteriori justified is to have a reason for thinking that a given proposition is true that does emerge or derive from experience. (See Section 6 below for two accounts of the a priori/a posteriori distinction that do not presuppose this traditional conception of justification.) Examples of a posteriori justification include many ordinary perceptual, memorial, and introspective beliefs, as well as belief in many of the claims of the natural sciences. My belief that it is presently raining, that I administered an exam this morning, that humans tend to dislike pain, that water is H2O, and that dinosaurs existed, are all examples of a posteriori justification. I have good reasons to support each of these claims and these reasons emerge from my own experience or from that of others. These beliefs stand in contrast with the following: all bachelors are unmarried; cubes have six sides; if today is Tuesday then today is not Thursday; red is a color; seven plus five equals twelve. I have good reasons for thinking each of these claims is true, but the reasons do not appear to derive from experience. Rather, I seem able to see or apprehend the truth of these claims just by reflecting on their content.
The description of a priori justification as justification independent of experience is of course entirely negative, for nothing about the positive or actual basis of such justification is revealed. But the examples of a priori justification noted above do suggest a more positive characterization, namely, that a priori justification emerges from pure thought or reason. Once the meaning of the relevant terms is understood, it is evident on the basis of pure thought that if today is Tuesday then today is not Thursday, or when seven is added to five the resulting sum must be twelve. We can thus refine the characterization of a priori justification as follows: one is a priori justified in believing a given proposition if, on the basis of pure thought or reason, one has a reason to think that the proposition is true.
These initial considerations of the a priori/a posteriori distinction suggest a number of important avenues of investigation. For instance, on what kind of experience does a posteriori justification depend? In what sense is a priori justification independent of this kind of experience? And is a more epistemically illuminating account of the positive character of a priori justification available: one that explains how or in virtue of what pure thought or reason might generate epistemic reasons? But before turning to these issues, the a priori/a posteriori distinction must be differentiated from two related distinctions with which it is sometimes confused: analytic/synthetic; and necessary/contingent.

2. The analytic/synthetic distinction
The analytic/synthetic distinction has been explicated in numerous ways and while some have deemed it fundamentally misguided (e.g., Quine 1961), it is still employed by a number of philosophers today. One standard way of marking the distinction, which has its origin in Kant (1781), turns on the notion of conceptual containment. By this account, a proposition is analytic if the predicate concept of the proposition is contained within the subject concept. The claim that all bachelors are unmarried, for instance, is analytic because the concept of being unmarried is included within the concept of a bachelor. By contrast, in synthetic propositions, the predicate concept “amplifies” or adds to the subject concept. The claim, for example, that the sun is approximately 93 million miles from the earth is synthetic because the concept of being located a certain distance from the earth goes beyond or adds to the concept of the sun itself. A related way of drawing the distinction is to say that a proposition is analytic if its truth depends entirely on the definition of its terms (i.e., it is true by definition), while the truth of a synthetic proposition depends not on mere linguistic convention, but on how the world actually is in some respect. The claim that all bachelors are unmarried is true simply by the definition of “bachelor,” while the truth of the claim about the distance between the earth and the sun depends, not merely on the meaning of the term “sun,” but on what this distance actually is.
Some philosophers have equated the analytic with the a priori and the synthetic with the a posteriori. There is, to be sure, a close connection between the concepts. For instance, if the truth of a certain proposition is, say, strictly a matter of the definition of its terms, knowledge of this proposition is unlikely to require experience (rational reflection alone will likely suffice). On the other hand, if the truth of a proposition depends on how the world actually is in some respect, then knowledge of it would seem to require empirical investigation.
Despite this close connection, the two distinctions are not identical. First, the a priori/a posteriori distinction is epistemological: it concerns how, or on what basis, a proposition might be known or justifiably believed. The analytic/synthetic distinction, by contrast, is logical or semantical: it refers to what makes a given proposition true, or to certain intentional relations that obtain between concepts that constitute a proposition.
It is open to question, moreover, whether the a priori even coincides with the analytic or the a posteriori with the synthetic. First, many philosophers have thought that there are (or at least might be) instances of synthetic a priori justification. Consider, for example, the claim that if something is red all over then it is not green all over. Belief in this claim is apparently justifiable independently of experience. Simply by thinking about what it is for something to be red all over, it is immediately clear that a particular object with this quality cannot, at the same time, have the quality of being green all over. But it also seems clear that the proposition in question is not analytic. Being green all over is not part of the definition of being red all over, nor is it included within the concept of being red all over. If examples like this are to be taken at face value, it is a mistake to think that if a proposition is a priori, it must also be analytic.
Second, belief in certain analytic claims is sometimes justifiable by way of testimony and hence is a posteriori. It is possible (even if atypical) for a person to believe that a cube has six sides because this belief was commended to him by someone he knows to be a highly reliable cognitive agent. Such a belief would be a posteriori since it is presumably by experience that the person has received the testimony of the agent and knows it to be reliable. Thus it is also mistaken to think that if a proposition is a posteriori, it must be synthetic.
Third, there is no principled reason for thinking that every proposition must be knowable. Some analytic and some synthetic propositions may simply be unknowable, at least for cognitive agents like us. We may, for instance, simply be conceptually or constitutionally incapable of grasping the meaning of, or the supporting grounds for, certain propositions. If so, a proposition’s being analytic does not entail that it is a priori, nor does a proposition’s being synthetic entail that it is a posteriori.
This raises the question of the sense in which a claim must be knowable if it is to qualify as either a priori or a posteriori. For whom must such a claim be knowable? Any rational being? Any or most rational human beings? God alone? There may be no entirely nonarbitrary way to provide a very precise answer to this question. Nevertheless, it would seem a mistake to define “knowable” so broadly that a proposition could qualify as either a priori or a posteriori if it were knowable only by a very select group of human beings, or perhaps only by a nonhuman or divine being. And yet, the more narrow the definition of “knowable,” the more likely it is that certain propositions will turn out to be unknowable. “Goldbach’s conjecture” – the claim that every even integer greater than two is the sum of two prime numbers – is sometimes cited as an example of a proposition that may be unknowable by any human being (Kripke 1972).

3. The necessary/contingent distinction
A necessary proposition is one the truth value of which remains constant across all possible worlds. Thus a necessarily true proposition is one that is true in every possible world, and a necessarily false proposition is one that is false in every possible world. By contrast, the truth value of contingent propositions is not fixed across all possible worlds: for any contingent proposition, there is at least one possible world in which it is true and at least one possible world in which it is false.
The necessary/contingent distinction is closely related to the a priori/a posteriori distinction. It is reasonable to expect, for instance, that if a given claim is necessary, it must be knowable only a priori. Sense experience can tell us only about the actual world and hence about what is the case; it can say nothing about what must or must not be the case. Contingent claims, on the other hand, would seem to be knowable only a posteriori, since it is unclear how pure thought or reason could tell us anything about the actual world as compared to other possible worlds.
While closely related, these distinctions are not equivalent. The necessary/contingent distinction is metaphysical: it concerns the modal status of propositions. As such, it is clearly distinct from the a priori/a posteriori distinction, which is epistemological. Therefore, even if the two distinctions were to coincide, they would not be identical.
But there are also reasons for thinking that they do not coincide. Some philosophers have argued that there are contingent a priori truths (Kripke 1972; Kitcher 1980b). An example of such a truth is the proposition that the standard meter bar in Paris is one meter long. This claim appears to be knowable a priori since the bar in question defines the length of a meter. And yet it also seems that there are possible worlds in which this claim would be false (e.g., worlds in which the meter bar is damaged or exposed to extreme heat). Comparable arguments have been offered in defense of the claim that there are necessary a posteriori truths. Take, for example, the proposition that water is H2O (ibid.). It is conceivable that this proposition is true across all possible worlds, that is, that in every possible world, water has the molecular structure H2O. But it also appears that this proposition could only be known by empirical means and hence that it is a posteriori. Philosophers disagree about what to make of cases of this sort, but if the above interpretation of them is correct, a proposition’s being a priori does not guarantee that it is necessary, nor does a proposition’s being a posteriori guarantee that it is contingent.
Finally, on the grounds already discussed, there is no obvious reason to deny that certain necessary and certain contingent claims might be unknowable in the relevant sense. If indeed such propositions exist, then the analytic does not coincide with the necessary, nor the synthetic with the contingent.