A priori is knowledge that is deduced from first principles. A posteriori is knowledge that results from experience or empirical evidence. Common areas of a priori knowledge include mathematics, logic and thought experiments. For example, you can know that if you add 5 apples and 4 apples you'll get 9 apples, even if you've never seen a physical apple. It is common for scientific theories to be developed and proven with a priori techniques. In many areas, such as physics, a priori proofs are important due to the difficulties and expenses of obtaining empirical evidence. It is common for a well accepted theory to be confirmed with empirical evidence decades or even centuries after being proven with mathematics or logic.
A Priori Definition
Knowledge or arguments based deductions from first principles.
A Posteriori Definition
Knowledge or arguments based on experience or empirical evidence.
A priori and a posteriori both originate from a 13 volume work of mathematics and geometry known as Euclid's Elements first published sometime around 300 BC. The Latin phase a priori can be translated "from what comes before" and a posteriori means "from what comes later."
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