a priori
(from “what is before”) is a Latin term which denotes an epistemological distinction regarding independence from sense experiences when determining how a proposition may be known.  
This is contrasted with a posteriori (from “what is after”) propositions which do require justification by sense experiences. An a posteriori proposition is justified by empirical observations from which certain conclusions may subsequently be drawn. “It is raining outside my office.” is a statement known only a posteriori.


A priori propositions are derived or justified independently of sensory experience. Contemporary, but not incontrovertible, examples of a priori statements have included: “All bachelors are unmarried.” “3 + 3 = 6.”  The reasons for believing an a priori proposition can be determined by pure thought and reason and by simple reflection on its content.


However, the difference between a priori and a posteriori is not as apparent as the provisional definitions and examples might suggest. Major controversies remain. Historically, the question is how to define the concept of “experience” upon which the putative distinction is founded and whether or in what sense knowledge can exist independently of all experience. The latter issue raises important questions regarding the positive, that is, actual, basis of a priori knowledge. While the question remains complicated, it must be stated that an adequate definition of experience must be comprehensive enough to include introspection and memory, yet sufficiently narrow that reputed occurrences of a priori justification can indeed be said to be independent of experience. (Baehr 2006)


Identical propositions may be known a posteriori by one person, but a priori by another. For example, one person may work out a simple mathematical problem in her head, but a second person arrives at the answer by using his calculator. In either case, both will come to believe that, let’s say, 71+54 = 125. The first person’s knowledge is a priori, whereas the second person’s knowledge is a posteriori. In speaking of the first person's knowledge, it might be stated, “that's a priori for her.” In other words, can be known a priori does not mean must be known a priori.  (Kripke, 1980)


But, does experience have any part in justifying mathematical belief? Is it possible to revise mathematical knowledge? Troublesome knowledge must be justified in a way other than by empirical observations, i.e., by the a priori. [Devitt 2005] There is thus some impetus for abandoning the thesis that all knowledge is justified by experience, or a posteriori. Some knowledge, it would appear, is a priori. Yet there the idea of the a priori is ambiguous at best and questions remain: What is it for a belief to be justified a priori? What is the nature of this non-empirical method of justification? Without satisfactory answers the a priori remains shadowy. (Devitt 2005) 


The philosophical heritage of the term a priori may be traced to Aristotle’s Posterior Analytics. For Aristotle, that upon which proof, or the necessity, of truth is based must be prior to and better known than that which is to be proved. The proof of a proposition is a priori if its truth is based on, or concluded from, something prior to it in the sense of being its cause. Aristotle’s starting point is the object perceived or the process of the perception.

Now 'prior' and 'better known' are ambiguous terms, for there is a difference between what is prior and better known in the order of being and what is prior and better known to man. I mean that objects nearer to sense are prior and better known to man; objects without qualification prior and better known are those further from sense. (Aristotle, An. Post. I/2).

The first recorded occurrence of the phrases appears in the writings of the 14th century German philosopher Albert of Saxony (ca. 1316 – 1390), who differentiated between demonstratio a priori (the proof from what is before, i.e. from the cause), and demonstratio a posteriori (the proof from what is after, i.e. from the effect). For Albert, the proof of an a priori argument is established from cause to effect, while the proof of an a posteriori argument is established from effect to cause. The terms denote formal logic in that they refer to rational processes.

By the 18th century, a priori came to refer to propositions and objects which possess universal and necessary validity, and are completely independent of sense experience.  A posteriori referred to propositions and objects whose truth must be gleaned from observable fact and sense experience, or “contingent truth.” Thus, the distinction between a priori and a posteriori came to be a distinction between what is derived from experience and what is not.
The classic distinction was set forth by Immanuel Kant in his Critique of Pure Reason and relates explicitly to the distinctions between a priori/a posteriori that exist today:
This, then, is a question which at least calls for closer examination, and does not allow of any off-hand answer: whether there is any knowledge that is thus independent of experience and even of all impressions of the senses. Such knowledge is entitled a priori, and distinguished from the empirical, which has its sources a posteriori, that is, in experience. (Kant, Critique of Pure Reason, 42-43)
However, Kant’s thesis introduces still another problem. As he defined it, the a priori is supposed to be that which can be known independently of any experience. In other words, it is possible to know something independently of experience. But, for whom is it possible? A better option is to refocus Kant’s definition away from a priori statements to the knower. Does the knower know something a priori or at least believe it to be true based on a priori evidence? (Kripke 1980)Experience is arguably not the source of numerous mental states; they are innate. The concern should be with the justification of beliefs, not with their empirical sources. (Devitt)
Kant's ambition was to move beyond the traditional dichotomy between rationalism and empiricism. Rationalists insisted that the meticulous use of reason (a priori) leads to incontrovertible truth even if serious questions about its practical content remain. Empiricists, on the other hand, argued that all knowledge must be firmly grounded in sense experience (a posteriori); practical content is safe, but certainty remains elusive.
Kant reasoned that both approaches were philosophically impoverished, since both were founded on the same mistaken assumption. For Kant, the crucial epistemological question is not how humanity can bring itself to understand fundamental convictions about the natural world, but how the natural world comes to be understood by humanity. Instead of attempting, through either reason or experience, to make concepts match the nature of objects, Kant held that the structure of the concepts must shape the experience of objects.
Current scholarly opinion concerning the two terms remains at odds. Proponents of the a priori regularly assert that rejecting it is analogous to rejecting philosophy as a respectable intellectual discipline. Opponents respond that no intellectually respectable theory of knowledge can accommodate the a priori. To a large extent, how one views the a priori determines one’s answers to other pressing philosophical questions. It would not be incorrect to conclude that the most fundamental division in contemporary philosophy is between those who accept and those who reject the existence of a priori knowledge. Kant’s legacy plays a leading role in the ongoing debate.
Ben Craver