A priori

From The Book of THoTH (Leaves of Wisdom)

For the concept in constructed language, see a priori (languages). For the data mining algorithm, see apriori algorithm.

A priori is a Latin phrase meaning "from the former" or less literally "before experience". In much of the modern Western tradition, the term a priori is considered to mean propositional knowledge that can be had without, or "prior to", experience. It is usually contrasted with a posteriori knowledge meaning "after experience", which requires experience (In law, the term ex post facto replaces a posteriori).

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.

Contents 1 Philosophical thought 2 Engineering 3 Statistics and Mathematical Modeling 4 See also

Philosophical thought

One of the fundamental questions in epistemology is whether there is any non-trivial a priori knowledge. Generally speaking rationalists believe that there is, while empiricists believe that all knowledge is ultimately derived from some kind of experience (usually external), or else is in some sense trivial.

The use of the term gained foothold through rationalist thinkers, such as 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.

John Locke, in believing that reflection is a part of experience, gave a platform by which the entire notion of the "a priori" might be abandoned.

David Hume considered all a priori knowledge to be a Relation of Ideas, mentioning it several times in his Enquiry Concerning Human Understanding.

Modern use of a priori began with Immanuel Kant who offered the distinction between synthetic and analytic truths to supplement 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, criticizing Kant in Naming and Necessity (1980), argues that aprioricity is an epistemological property, and should not be conflated with the separate, metaphysical matter of necessity. In support of this argument he offers several pleas to intuition. First he argues that an a posteriori truth can be known necessarily: for instance, that "Hesperus is Phosphorus". (Known as the "evening star" and the "morning star" respectively, we now know that both are names for the planet Venus). They are both necessarily the same (see rigid designation), but known a posteriori. Also, he argues, it is possible to have contingent a priori propositions. For example, in Paris there is a bar that formerly served as the standard for the metre. The accompanying proposition, "That bar is one metre long", is contingent since we could have taken another length to define the metre. However, it is known a priori, because one metre was defined as the length of that bar, so the bar must have been one metre long (at the time it served as the standard) - it is a tautology.

Bertrand Russell, in The Problems of Philosophy, considered a priori knowledge to be the relation between universals. "2 + 2 = 4," for example, is an a priori principle that shows the relationship between "2", "+", "=", and "4", all universals according to Russell.

Major contemporary philosophers of a priori thought include Alfred Ayer, Jean-Paul Sartre, Roderick Chisholm and W.V.O. Quine.

Engineering

Synthetic a priori knowledge is the main objective of the process of analogical modelling in systems engineering.

Statistics and Mathematical Modeling

In statistics, a priori knowledge refers to a knowledge of the actual population, rather than that estimated by observation. Suppose for example that we pick two red beads and three black beads from a bag; what is the probability that the next bead we pick out will be red? Without a priori knowledge, we can only estimate this from the statistics we have observed, so in this case we might estimate the probability of picking out a red bead as 0.4. But if we knew, a priori, that there were only two red beads in the bag, then we would know for certain that the probability of picking out another red bead was in fact zero. See also Bayes' theorem.

In mathematical modeling and data mining, we might try to spot classes and clusters of data. For example if a credit card company examines its data it could search for patterns representing fraudulent use; with a priori knowledge of which data represents fraud it can classify different behaviour into known categories of fraud and non-fraud, but without this knowledge, it can only identify different clusters or typical patterns of data.

Use of a priori knowledge is typical in supervised learning, whereas detecting clusters in data without a priori knowledge is an example of unsupervised learning.

See also

• Analogical models
• Analytic proposition
• List of Latin phrases
• Synthetic proposition