A Priori and A Posteriori — The Fundamental Epistemological Distinction

Few distinctions have shaped the history of philosophy as profoundly as that between what we can know independently of experience and what we can know only through it. The distinction between a priori and a posteriori spans centuries of epistemological debate — from medieval logicians to Leibniz, from Hume to Kant, from nineteenth-century empiricist critiques to the upheavals of contemporary analytic philosophy. To understand it is to understand the very problem of knowledge.

This article traces the complete trajectory of this distinction: its terminological origins in medieval scholasticism, the classic formulations of Leibniz and Hume, Kant’s Copernican revolution and his synthetic a priori judgments, the empiricist objections of Mill and Quine, and the surprising dissociation between apriority and necessity proposed by Kripke.

1. Medieval origins of the terms

1.1 From Aristotelian demonstration to scholastic terminology

The terms a priori and a posteriori do not appear in Aristotle, but they derive from his logic. In the Posterior Analytics, Aristotle distinguishes two types of demonstration: one that proceeds from causes to effects (demonstration propter quid — “on account of the reason why”) and one that proceeds from effects to causes (demonstration quia — “of the fact”).

Medieval scholastics — notably Albert the Great and Thomas Aquinas — translated this distinction into the Latin terms we have inherited. A priori meant literally “from what is prior” — that is, from what is ontologically first: causes, principles, essences. A posteriori meant “from what is posterior” — from observed effects. Thus, in its original medieval formulation, a priori and a posteriori were terms of the order of being (ontology), not of the order of knowing (epistemology).

1.2 The transition to the epistemological sense

The transition from the ontological to the epistemological sense occurred gradually during the sixteenth and seventeenth centuries. Philosophers such as Gassendi and Leibniz began to use a priori to designate knowledge that is independent of sense experience — truths that reason can reach on its own — and a posteriori for knowledge that depends on sensory data. This reinterpretation reflected the new intellectual landscape of modernity, in which the central question was no longer the structure of being but the foundations and limits of human knowledge.

2. Leibniz: truths of reason and truths of fact

2.1 The two classes of truth

Gottfried Wilhelm Leibniz (1646–1716) offered one of the sharpest formulations of the distinction, although he did not systematically employ the terms a priori and a posteriori in the later Kantian sense. In the Monadology (1714, §§33–35), Leibniz distinguishes:

• Truths of reason (vérités de raison): necessary, and their opposite is impossible. Grounded in the principle of contradiction — denying them entails a logical contradiction. Examples: mathematical truths (“2 + 3 = 5”), definitions, logical tautologies.
• Truths of fact (vérités de fait): contingent, and their opposite is possible. Grounded in the principle of sufficient reason — they have a reason for being as they are and not otherwise, but could, without contradiction, have been different. Examples: “it is raining now,” “Caesar crossed the Rubicon.”

2.2 The strong rationalist thesis

For Leibniz, truths of reason are knowable a priori through pure conceptual analysis — one needs only decompose the subject to find the predicate contained within it. Truths of fact, by contrast, require recourse to experience. Yet Leibniz introduced an audacious thesis: for an infinite intellect (God), even truths of fact would ultimately be analytic — the predicate would be contained in the complete concept of the subject. In the New Essays on Human Understanding (composed 1703–1704, published posthumously in 1765), Leibniz argued against Locke that innate ideas exist, albeit in a latent state, like veins in marble that predispose the statue — an unequivocal defense of a priori knowledge.

3. Hume: relations of ideas and matters of fact

3.1 Hume’s Fork

David Hume (1711–1776), in the Enquiry Concerning Human Understanding (1748, section IV), formulated what has become known as Hume’s Fork: every legitimate object of human understanding belongs to one of two classes, and only one:

• Relations of ideas: propositions discoverable by the pure operation of thought, without recourse to experience. They are necessary — denying them entails a contradiction. They include the sciences of geometry, algebra, and arithmetic. Example: “The square of the hypotenuse is equal to the sum of the squares of the other two sides.”
• Matters of fact: propositions that depend on experience for their knowledge. They are contingent — the contrary is always conceivable without contradiction. Example: “The sun will rise tomorrow” — however probable, the opposite is not logically impossible.

3.2 Skeptical consequences

The destructive force of Hume’s distinction lies in its consequence: all factual knowledge ultimately rests on the relation of cause and effect, and this relation is not a relation of ideas — it cannot be discovered a priori. Causation, according to Hume, is merely a habit of the mind in the face of constantly observed conjunctions. Past experience does not logically guarantee future experience (the problem of induction).

If this is so, the pretensions of rationalist metaphysics — which aspired to know a priori the existence of God, the nature of the soul, and the ultimate structure of reality — are left without foundation. This was the challenge Kant would confront.

4. Kant: the Copernican revolution and synthetic a priori judgments

4.1 Awakening from dogmatic slumber

Immanuel Kant (1724–1804) acknowledged that it was Hume who “awakened him from his dogmatic slumber.” The Critique of Pure Reason (1781; 2nd ed. 1787) was born as an attempt to answer the question: is synthetic a priori knowledge possible? If the answer is negative, science (mathematics, physics) loses its foundation of necessity and universality. If positive, one must show how and within what limits.

4.2 Two crossed distinctions

Kant systematized the issue by crossing two independent distinctions:

The decisive cell is that of synthetic a priori judgments: judgments that extend our knowledge (they are synthetic — the predicate adds something new to the subject) and are simultaneously universal and necessary (they are a priori — they do not depend on any particular experience). Kant argued that propositions such as “every change has a cause” and “the straight line is the shortest distance between two points” belong to this class.

4.3 The Copernican revolution

Kant’s solution involves a radical reversal: just as Copernicus explained celestial motions by supposing that the observer moves (rather than just the heavenly bodies), Kant proposed that the objects of experience conform to the a priori conditions of the knowing subject — not the reverse. The mind does not passively adapt to objects; rather, the objects of experience are structured according to the forms the mind imposes.

4.4 Pure forms of sensibility: space and time

In the Transcendental Aesthetic, Kant demonstrates that space and time are not properties of things in themselves but pure a priori forms of sensibility — conditions under which any object can be given to intuition. Space is the form of outer sense; time, the form of inner sense (and, indirectly, of all experience). Geometry is possible as a synthetic a priori science because it refers to the a priori structure of space; arithmetic, because it is grounded in temporal succession.

4.5 Categories of the understanding

In the Transcendental Analytic, Kant identifies twelve categories — pure concepts of the understanding, derived from the logical forms of judgment. The categories (substance, causality, unity, plurality, necessity, etc.) are a priori rules that the understanding applies to the material of sensory intuition in order to constitute objective experience. Without categories, sensory data would be “blind”; without intuition, concepts would be “empty.”

The decisive point: the categories have legitimate use only when applied to phenomena — objects as they appear in experience, conditioned by space, time, and categories. When reason attempts to exceed experience and apply the categories to things in themselves (Ding an sich), it falls into illusions and antinomies — as Kant shows in the Transcendental Dialectic.

4.6 The Kantian synthesis

Kant’s position overcomes both dogmatic rationalism (which claimed to know a priori the nature of reality in itself) and skeptical empiricism (which denied any necessary knowledge about the world). Science is possible because the subject furnishes the universal forms of experience; but speculative metaphysics is impossible because those forms are valid only within the domain of experience, never for what lies beyond it.

5. Empiricist critiques: Mill and Quine

5.1 John Stuart Mill: arithmetic as empirical generalization

John Stuart Mill (1806–1873), in A System of Logic (1843), frontally rejected the existence of a priori knowledge. For Mill, even the truths of arithmetic and geometry are empirical generalizations — they derive from experience and are, in principle, subject to revision. “2 + 3 = 5” is not a necessary truth of reason but a summary of countless experiences of grouping objects. If we lived in a universe where grouping two objects with three somehow resulted in four, we would learn a different arithmetic.

The classic objection to Mill — formulated by Frege in the Foundations of Arithmetic (1884) — is that confusing the psychological origin of our beliefs (how we learn arithmetic) with their logical justification constitutes the fallacy of psychologism. The truth of “2 + 3 = 5” does not depend on counting physical objects.

5.2 Quine: “Two Dogmas of Empiricism”

W. V. O. Quine (1908–2000), in his celebrated article “Two Dogmas of Empiricism” (1951), attacked two pillars of the tradition: the distinction between analytic and synthetic and reductionism (the idea that each meaningful statement can be translated into terms of immediate experience).

Against the analytic/synthetic distinction. Quine argued that there is no clear, non-circular criterion for separating analytic statements (true “by virtue of meaning”) from synthetic ones. The notion of “cognitive synonymy” — which would underpin analyticity — cannot be defined without appealing to equally problematic concepts (such as “necessity” or “definition”). The distinction, according to Quine, is a “dogma” of empiricist philosophy that does not withstand scrutiny.

Epistemological holism. In its place, Quine proposed a holistic conception: our knowledge forms a web or field of force that meets experience only at its edges. When recalcitrant experience conflicts with the system, any statement — from logic to physics — can in principle be revised to restore coherence. No statements are absolutely immune to revision; therefore, there is no principled distinction between a priori and a posteriori.

Quine’s article sent shockwaves through analytic philosophy. If he is correct, the entire Kantian architecture — with its sharp separation of analytic and synthetic judgments, of a priori and a posteriori — loses its foundation.

6. Kripke: the contingent a priori and the necessary a posteriori

6.1 Dissociating apriority, necessity, and analyticity

Saul Kripke (1940–2022), in Naming and Necessity (1972/1980), produced one of the most revolutionary contributions of twentieth-century philosophy by showing that three notions traditionally treated as equivalent — apriority, necessity, and analyticity — are in fact distinct concepts that can come apart:

• A priori / a posteriori: an epistemological distinction — it concerns how we know (independently of experience or through it).
• Necessary / contingent: a metaphysical distinction — it concerns how things are (could not have been otherwise or could have).
• Analytic / synthetic: a semantic distinction — it concerns the relation between subject and predicate in a statement.

6.2 The necessary a posteriori

Kripke argued that there are truths that are necessary (could not have been otherwise in any possible world) and yet knowable only a posteriori (through empirical investigation):

• “Water is H₂O.” If water is in fact H₂O, then it is H₂O in all possible worlds — it is a necessary truth. But we discovered this empirically, through chemical investigation, not through pure reflection.
• “Hesperus is Phosphorus.” The morning star and the evening star are the same celestial body (Venus). This is necessary (they are identical in all possible worlds) but was discovered by astronomical observation.

6.3 The contingent a priori

Conversely, Kripke suggested that there are truths knowable a priori that are nonetheless contingent (could have been otherwise):

• Consider the proposition: “The standard metre bar in Paris is one metre long.” Whoever fixed the reference of the term “metre” by means of the platinum-iridium bar at Sèvres could know a priori that the bar is one metre long — it is true by stipulation. However, the bar could have had a different length (if heated, for instance); hence, the proposition is contingent.

6.4 Philosophical consequences

Kripke’s dissociation demolished the traditional equation: a priori = necessary = analytic. It showed that epistemology (how we know) and metaphysics (how things are) are independent dimensions. This paved the way for a renewed metaphysical essentialism — the idea that things have essential properties (such as the chemical composition of water) that are necessary but not discoverable by conceptual analysis.

7. The contemporary landscape

The a priori / a posteriori distinction remains at the center of philosophical debate. After Kripke, several positions coexist:

• Moderate rationalism: philosophers such as Laurence BonJour defend the existence of genuine a priori knowledge (rational intuition), irreducible to experience.
• Naturalized empiricism: heirs of Quine (such as Philip Kitcher) maintain that all knowledge is ultimately empirical and revisable.
• Deflationary apriorism: Timothy Williamson and others argue that the a priori / a posteriori distinction is less sharp than traditionally supposed — most cognitive processes blend experiential and non-experiential elements.
• Renewed Kantian apriorism: philosophers such as Robert Hanna seek to reconstruct the Kantian notion of synthetic a priori judgments in light of contemporary philosophy.

What none of these positions disputes is the importance of the question: is there anything we can know about the world without experience teaching us? The answer to this question defines the horizon and limits of all philosophical and scientific inquiry.

Conclusion

From Aristotle to the medievals, from Leibniz to Hume, from Kant to Quine and Kripke, the distinction between a priori and a posteriori runs through the history of philosophy as a connecting thread linking logic, metaphysics, epistemology, and philosophy of language. Kant made the question the central axis of modern philosophy; Quine attempted to dissolve it; Kripke showed that the pieces of the puzzle can recombine in unexpected ways. The distinction may have changed its shape — but the question it poses remains, perhaps, the most fundamental in philosophy: what can we know, and how do we know it?

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