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For those within the mainstream of the tradition, mathematics and logic are generally considered a priori disciplines. Statements such as "2 + 2 = 4", for example, are considered to be "a priori", because they are thought to come out of reflection alone.
The natural and social sciences are usually considered a posteriori disciplines. Statements like "The sky is usually mostly blue", for instance, might be considered "a posteriori" knowledge.
Philosophers have used the term in many different ways.
Aristotle used the term in a manner slightly different from that used by contemporary philosophers. When Aristotle wrote of "a priori" knowledge, he meant to say knowledge of the causes of things.The use of the term gained foothold through rationalist thinkers like René Descartes and Gottfried Leibniz, who argued that knowledge is gained through reason, not experience. Descartes considered the knowledge of the self, or cogito ergo sum, to be a priori, because he thought that one needn't refer to past experience to consider one's own existence.
Modern use of a priori began with Immanuel Kant who added the distinction between synthetic and analytic truths to the distinction between a priori and a posteriori knowledge.
He argues that propositions known a priori are necessarily true, while propositions known a posteriori are contingent, because a priori knowledge has always been true, according to Kant (e.g. two plus two equals four). A posteriori propositions will depend on external conditions, which may change in time, making the proposition false (e.g. Jean Chrétien is Canada's Prime Minister, which was once true but is now false).
Saul Kripke argues in Naming and Necessity , against Kant, that aprioricity is an epistemologicalEpistemology is the branch of philosophy that deals with the nature, origin and scope of knowledge. Definition of knowledge Justified true belief Plato's Theaetetus''. defined knowledge as justified true belief. One implication of this definition is that property, and should not be conflated with the separate, metaphysicalMetaphysics is a branch of philosophy, and related to the natural sciences, like physics, psychology and the biology of the brain; and also to mysticism, religion, and other spiritual subjects. It is notoriously difficult to define, but for purposes of br matter of necessityNecessity (as a term of jurisprudence) is a possible justification for breaking the law. Defendants who use this defense are arguing that they should not be held liable for a crime, since the actions taken were, for some reason or other, "necessary".. In support of this argument he offers several pleas to intuition: " Hesperus is PhosphorusPhosphorus is the chemical element in the periodic table that has the symbol P and atomic number 15. A multivalent, nonmetal of the nitrogen group, phosphorus is commonly found in inorganic phosphate rocks and in all living cells but is never naturally fo" (the evening star and morning star respectively, both (we now know) names for the planet VenusVenus is the second planet from the Sun, named after the Roman goddess Venus. It is a terrestrial planet, very similar in size and bulk composition to Earth; it is sometimes called Earth's "sister planet" as a result of this similarity. Although all plane) necessary if true (see rigid designation), but known a posteriori; while, on the other hand, (of the bar in Paris that formerly served as the standard for the meter), "That bar is one meter long" is contingent (we could have taken another length to define the meter, etc.) but known a priori. That is because one meter is defined as the length of that bar, so the bar must be one meter long - it is a tautology. Radical empiricists such as John Stuart Mill reject the notion of a priori truths entirely, claiming that all truths come out of experience, and so are a posteriori.Major contemporary philosophers of a priori thought include Alfred Ayer, Roderick Chisholm and W.V.O. Quine.
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