a priori and a posteriori
Yes, one more time.
The expressions “a priori” and “a posteriori” are Latin idioms. They are phrases. They 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]”. Without the "a", the expressions don't mean anything; "a priori" is not equivalent to "one priori."
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.”
Empiricism, in the broad sense, is the philosophical outlook that stresses the power of a posteriori reasoning — reasoning from observation or experience — to grasp substantial truths about the world. When a priori ideas conflict with the a posteriori, the a posteriori wins, according to empiricism. Empiricism is usually opposed to rationalism — the view that reason rather than sensation or observation is the source of knowledge.
Continental Rationalism was a movement in epistemology in the modern period of philosophy (when was that? See the Chronological List of Western Philosophers). The major figures of Continental Rationalism are Descartes, Spinoza, and Leibniz. All the Continental Rationalists are rationalists in the broad sense.
British Empiricism was a movement in epistemology in the modern period of philosophy. The major figures of British Empiricism are Locke, Berkeley, and Hume. The ancient Greek philosopher Aristotle is usually considered a forerunner of modern empiricism.
Empiricists tend to see modern science as the paradigm of knowledge. The empiricist approach is hands-on, down-to-earth. Empiricists urge us to trust our senses, observe the world carefully, perform experiments, and learn from experience. They urge us not to accept explanations that cannot be grounded in human experience. So, empiricists would say, we should be suspicious of explanations that make reference to non-observable entities such as gods. We do not explain lightning, for example, by saying "The Thunder God is angry"; instead we should take Ben Franklin's experimental approach.