A priori and a posteriori

Lore & Background

The terms a priori and a posteriori are Latin for 'from what comes before' and 'from what comes after,' respectively. They emerged from medieval logical and philosophical contexts, not from Euclid's Elements, despite common misconceptions. An early philosophical use of a notion of a priori knowledge is Plato's theory of recollection, related in the dialogue Meno, according to which something like a priori knowledge is inherent in the human mind. Scholastics like Thomas Aquinas and Duns Scotus used the terms in logical and metaphysical arguments, and later the early modern Thomistic philosopher John Sergeant differentiated them by the direction of inference regarding proper causes and effects: to demonstrate something a priori is to demonstrate proper effects from proper efficient causes, and a posteriori to demonstrate proper efficient causes from proper effects.

Reader's Guide

The a priori–a posteriori distinction is foundational in epistemology, marking the boundary between knowledge that can be gained through reason alone and knowledge that requires sensory experience. Fields such as mathematics and formal logic are predominantly a priori, while most sciences involve a posteriori justification. The distinction became prominent with Immanuel Kant's Critique of Pure Reason, where it was discussed in relation to the analytic–synthetic distinction. Later philosophers, including the logical positivists, sought to explain a priori knowledge through analyticity, arguing that all a priori knowledge is analytic and thus requires no special faculty of intuition. However, Willard Van Orman Quine criticized the analytic–synthetic distinction as illegitimate. Saul Kripke further separated aprioricity from necessity and analyticity, arguing for necessary a posteriori truths, such as 'water is H2O.' The relationship between aprioricity, analyticity, and necessity remains debated: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.

Did You Know?

• The terms a priori and a posteriori were used by medieval scholastics like Thomas Aquinas and Duns Scotus, not first by Albert of Saxony.
• Immanuel Kant's Critique of Pure Reason made the epistemological distinction prominent.
• The proposition 'Either it is sunny or it is not sunny in London today' can be known a priori.
• Saul Kripke argued for necessary a posteriori truths, such as 'water is H2O.'

The Fundamental Divide: Reason Versus Experience

In epistemology, the a priori–a posteriori distinction carves all knowledge, justification, and argument into two broad categories based on a single question: does the proposition depend on outside sensory experience? A statement is known a priori when it can be grasped through reason alone, requiring no empirical input beyond what is needed to comprehend its terms. A statement is known a posteriori when its truth or justification rests on evidence gathered from the world. The contrast becomes vivid in concrete examples. Whether it is sunny in London today is something one can only confirm by looking outside or checking a forecast, making it a posteriori. Yet the disjunctive claim that either it is sunny or it is not sunny in London today holds regardless of any weather report, and is therefore a priori. Similarly, the logical observation that reigning at least four days entails reigning more than three days is accessible to pure reason, while the historical fact that George V's reign spanned 1910 to 1936 demands empirical verification. Mathematics and formal logic tend to operate in the a priori domain, whereas most scientific disciplines rely predominantly on a posteriori justification.

From Medieval Logic to Kant's Revolution

The Latin phrases a priori ('from the earlier') and a posteriori ('from the later') did not begin life as epistemological labels. Their first recorded appearance in philosophical writing belongs to the 14th-century logician Albert of Saxony, who employed them to classify two directions of argumentation: reasoning from causes to effects (a priori) versus reasoning from effects back to causes (a posteriori). It was not until Immanuel Kant's Critique of Pure Reason that the distinction was elevated into a central epistemological framework, and Kant also explored how it interlocks with the analytic–synthetic divide. The terms have since migrated beyond philosophy into linguistics and language construction, where they indicate whether a language's vocabulary is derived from preexisting source languages or built independently. This cross-disciplinary reach underscores how foundational the underlying question is: does the knowledge in question depend on what came before it in experience, or does it stand on its own logical ground? The shift from Albert's argumentative taxonomy to Kant's theory of mind marks one of the most consequential reorientations in the history of ideas, transforming a technical label for inference direction into a lens through which all human knowledge can be interrogated.

The Analytic Explanation and Quine's Blow

In the wake of Kant, many philosophers felt uncomfortable with his appeal to what Paul Boghossian calls a 'special faculty of intuition' that has never been satisfactorily described. The logical positivists of the early twentieth century proposed an elegant alternative: the analytic explanation of the a priori. Under this theory, all a priori knowledge reduces to analytic knowledge—propositions true purely by virtue of their meanings, independently of any facts about the world. A posteriori propositions, by contrast, require both meaning and empirical facts for their truth. This move was celebrated because it supposedly dissolved the dubious metaphysical faculty of pure reason into the more tractable linguistic notion of analyticity. Yet Willard Van Orman Quine delivered a devastating counterattack. He argued that no clear boundary between analytic and synthetic statements has ever actually been drawn, and that the very existence of such a distinction is, in his words, an 'unempirical dogma of empiricists, a metaphysical article of faith.' Although the full soundness of Quine's challenge remains debated, its impact was enormous: it effectively shattered the project of grounding a priori knowledge in analyticity and forced philosophers to seek new foundations.

Kripke, Necessity, and the Great Separation

For much of the twentieth century, following Kant, philosophers treated aprioricity, analyticity, and necessity as virtually synonymous. Jerry Fodor observed that positivism simply assumed a priori truths must be necessary truths—statements whose negation is self-contradictory and which hold in every possible world, like the claim that all bachelors are unmarried. Jason Baehr offered a supporting intuition: sense experience can inform us only about the actual world, so it cannot tell us what must or must not be the case. This tight triad seemed airtight. Then Saul Kripke, in 1972, dismantled it. He presented compelling arguments for the existence of necessary a posteriori truths—propositions that are true in every possible world yet can only be known through empirical investigation. His famous example is the identity of water with H2O: if true, this statement is necessarily true because water and H2O are the same thing, yet discovering that identity required scientific investigation rather than pure reasoning. Kripke's intervention forced a clearer separation among aprioricity, analyticity, and necessity, permanently reshaping how philosophers map the landscape of knowledge.

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