A Priori versus A Posteriori
a posteriori = inductive reasoning
Term used to describe knowledge that comes from experience. Literally, the Latin term maens "from behindhand". The experience comes first and the knowledge afterwards.
a priori = deductive reasoning
Knowledge which, it is argued, can be acquired through pure reason alone - independently and, perhaps, before experience. Literally it means "from beforehand".
A Priori and A Posteriori are two contrasting methods of reasoning.
By an a priori argument was originally meant one from law or cause to effect; by a posteriori, one from effect to cause. Kant introduced a new distinction.
Reasoning on the fundamental laws of the mind, he asserts that there are certain 'transcendental ideas' (called by him categories), which exist independently of experience, and arguments from these are a priori Such ideas are those of space, time, reality, and negation, which, he says, we do not derive from experience, but through the application of which we acquire experience. In morality also he declares that the ideas implied in the words good and bad are innate and imperative in every mind, independently of actual observation.
A posteriori arguments, on the other hand, are deduced from experience founded on observation. That school of philosophy which sets the highest value on the Kantian a priori reasoning is called intuition-alist or transcendental; those most directly opposed to it are called empiricists. In current usage, the term a priori refers to whatever seems not to derive from experience, such as formal argument, necessary propositions, or concepts.