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A priori knowledge is justified independently of sensory experience — mathematics and logic provide the canonical examples, since we can establish that 2+2=4 or that all bachelors are unmarried through reasoning alone. A posteriori (empirical) knowledge depends essentially on sensory experience for its justification. Kant famously complicated this picture by arguing that some a priori knowledge is synthetic (genuinely informative about the world, not merely definitional), generating the puzzle of how pure reason can extend our knowledge beyond conceptual truths.
Contrast clear cases: 'All triangles have three sides' (a priori) vs. 'Water boils at 100°C at sea level' (a posteriori). Then examine boundary cases — mathematical knowledge, knowledge of modal truths, moral knowledge — to see where intuitions about priority become contested.
One of epistemology's most useful distinctions cuts across every field of knowledge: some things we can figure out by thinking alone, and other things we can only know by going out and looking. This is the a priori / a posteriori distinction. "A priori" (Latin: "from the earlier") means knowable before or independently of experience; "a posteriori" (Latin: "from the later") means knowable only through experience. The distinction is about justification — what entitles us to believe something — not about how we first encountered the claim.
The clearest cases are easy. "All triangles have three sides" is a priori: you can verify it by analyzing what a triangle is, without measuring any physical object. "The boiling point of water is 100°C at sea level" is a posteriori: you must run an experiment (or trust someone who did). Mathematics and logic supply the canonical body of a priori knowledge; natural science supplies the canonical body of a posteriori knowledge. Most philosophical work involves the boundary cases — moral claims, modal claims about what is possible or necessary, introspective reports — where it is genuinely contested which side applies.
Kant added a second dimension to this picture by crossing the a priori/a posteriori distinction with the analytic/synthetic distinction. An analytic statement is one where the predicate is already contained in the subject ("All bachelors are unmarried"). A synthetic statement genuinely extends our knowledge ("The cat is on the mat"). Before Kant, the dominant assumption was that all a priori knowledge was analytic — all you could know without experience was what was already packed into your concepts. Kant challenged this by arguing for synthetic a priori knowledge: claims that are both genuinely informative and knowable through pure reason. His examples included arithmetic, geometry, and fundamental causal principles. This claim is still debated today.
A third important wrinkle comes from Saul Kripke's 20th-century work, which showed that the a priori/a posteriori distinction is logically independent from the necessary/contingent distinction (about whether a truth could have been otherwise). We might assume: necessary truths are a priori, contingent truths are a posteriori. Kripke dismantled this assumption. "Water is H₂O" is a necessary truth — in any possible world, water just is H₂O — but we could only discover this empirically, through chemistry. So it is necessary a posteriori. Conversely, "the meter is the length of this particular rod in Paris" was once contingently true but was stipulated to be true by definition — making it contingent a priori in some sense. These cases reveal that what's necessary about a thing and how we come to know it are different questions.
For epistemology, the a priori/a posteriori distinction matters because it shapes debates about the limits of reason. Empiricists (Hume, Locke, the Logical Positivists) tend to restrict a priori knowledge to analytic truths — definitional or logical — and insist that anything substantive about the world requires experience. Rationalists (Descartes, Leibniz, Kant) argue that reason can reach further. Knowing which side of the line a given claim falls on is often itself the philosophical question under investigation.
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