HEADS UP! a priori and a posteriori
These expressions function as adjectives or adverbs: that is, they modify a noun (such as “knowledge,” “statement,” or “claim”), a verb (such as "know") or an adjective (such as “true” or “false”).
The “a” in these expressions is the Latin preposition meaning “from.” So “a priori” means “from before [observation]” and “a posteriori” means “from after [observation]”. The expressions “a priori” and “a posteriori” describe how we know the truth or falsity of a statement.
A statement is true or false a priori if no observation or experiment is required to determine if it is true or false. Examples of a priori statements are mathematical assertions, statements true or false by definition, and logical truths and falsehoods. We “just know” when some claims are a priori true or false. For example, we “just know” that the same statement cannot be both true and false in the same sense at the same time (a rule of logic called the law of non-contradiction).
A statement is true or false a posteriori if observation or experiment is required to determine if it is true or false; we don’t “just know” it. Examples of a posteriori statements are statements about the world, e.g., “Dogs are carnivores” or “Ottawa is the capitol of Canada.”
Rationalism, in the broad sense, is the philosophical outlook that stresses the power of a priori reasoning to grasp substantial truths about the world. It is usually opposed to empiricism -- the view that experience rather than reason is the source of knowledge.
The first rationalist in Western Philosophy was the ancient Greek philosopher Plato. Plato was monumentally important in the history of philosophy. Quiz 3 will focus entirely on Plato's philosophy.
Continental Rationalism is a movement in epistemology in the modern period of philosophy (when was that? See the Chronological List of Western Philosophers). So Plato was a rationalist, but not a "Continental Rationalist." The major figures of Continental Rationalism are Descartes (the focus of Quiz 4), Spinoza, and Leibniz. All the Continental Rationalists are rationalists in the broad sense; i.e., all share the basic rationalist viewpoint with Plato.
Rationalism in the philosophical sense is NOT the optimistic view of the power of scientific inquiry and education associated with 18th-century Enlightenment thinkers (such as Voltaire and Thomas Jefferson).
The word "rationalism" also sometimes connotes an anti-religious, anti-clerical outlook. The word is not used this way in philosophy; in fact, philosophical rationalists tend to be theists (the empiricists tend to atheism).
So rationalism in philosophy is not anti-religious and simply emphasizes the superiority of reason (ratio in Latin — hence the name rationalism) over experience in acquiring knowledge.
Rationalists tend to see mathematics as the paradigm of knowledge. Plato's philosophical views were heavily influenced by his study of geometry with the Pythagoreans. Descartes made numerous contributions to mathematics; he discovered analytic geometry and "Cartesian" coordinates are named after him. Spinoza worked daily with math in his profession as a lens grinder; and Leibniz is known world-wide as the discoverer of calculus (though Isaac Newton usually gets the credit in the English-speaking world).