What Is A Priori Knowledge?

What Is A Priori Knowledge?

A priori knowledge is knowledge that is independent of experience. The Latin phrase a priori means "from what comes before" — in this case, before experience. A person who knows that 7 + 5 = 12 does not need to count seven objects, add five more, and count the total. They can see that it is true by understanding the concepts involved. This is a priori knowledge: justified by reason alone, without relying on observation, experimentation, or sensory evidence.

The distinction between a priori and a posteriori knowledge is one of the most important in epistemology. It separates claims that can be known just by thinking about them from claims that require empirical investigation. "All bachelors are unmarried" can be known a priori — once you understand the concepts, you see the truth. "There are bachelors in Berlin" requires experience — you need to check. The first is a matter of meaning; the second is a matter of fact.

This distinction raises deep questions. What exactly does "independent of experience" mean? After all, you need experience to learn the concepts of mathematics and logic — you had to learn what "7" and "5" and "12" mean. But the justification of the claim "7 + 5 = 12" does not depend on any particular experience of counting. Once the concepts are in place, the truth is accessible to reason. This is what philosophers mean by a priori: not that experience plays no role in acquiring the concepts, but that the justification of the belief does not depend on further experience.

Historical Background

The distinction between knowledge by reason and knowledge by experience goes back to the ancient Greeks. Plato held that the highest knowledge — knowledge of the Forms — was accessible through reason alone, not through the senses. The senses give us information about the changing world of appearances, but genuine knowledge concerns eternal, unchanging realities that can be grasped only intellectually.

In the early modern period, this distinction became the dividing line between two major philosophical movements. Rationalists like Descartes, Spinoza, and Leibniz held that reason is the primary source of knowledge and that significant truths about the world can be discovered a priori. Descartes argued that the existence of God, the nature of the mind, and fundamental principles of physics could be established by reason alone. Leibniz held that all truths are either truths of reason (a priori) or truths of fact (a posteriori), and that truths of reason are necessary while truths of fact are contingent.

Empiricists like Locke, Berkeley, and Hume took the opposite view. Locke argued that the mind is a blank slate at birth and that all ideas come from experience. Hume drew a sharper distinction: all objects of human reason are either "relations of ideas" (knowable a priori, like mathematics and logic) or "matters of fact" (knowable only a posteriori, through observation). Hume's fork, as this came to be called, restricted a priori knowledge to analytic truths — truths that are true by definition and carry no substantive information about the world.

Kant's Synthesis

Immanuel Kant transformed the debate in the Critique of Pure Reason (1781). Kant agreed with the empiricists that all knowledge begins with experience, but he denied that all knowledge arises from experience. He argued that the mind contributes structure to experience — categories like causality, substance, and unity — that makes experience possible. These structures are known a priori because they are conditions of any experience at all, not generalizations from experience.

Kant introduced two distinctions that reshaped epistemology. The first is the a priori / a posteriori distinction (source of justification). The second is the analytic / synthetic distinction (nature of the truth). Analytic truths are true by definition: the predicate is contained in the subject. "All bachelors are unmarried" is analytic because the concept of being unmarried is contained in the concept of bachelor. Synthetic truths add something: the predicate is not contained in the subject. "This bachelor is tall" is synthetic because tallness is not part of the concept of bachelor.

Kant's crucial innovation was the category of the synthetic a priori: truths that are substantive (not true merely by definition) but knowable by reason alone. Kant held that mathematical truths like "7 + 5 = 12" are synthetic a priori — the concept of 12 is not contained in the concepts of 7, 5, and addition, but we can know the truth a priori by constructing it in intuition. He also held that certain fundamental principles, like "every event has a cause," are synthetic a priori — they are conditions of possible experience, not generalizations from it.

Key Thinkers

Descartes and the Rationalist Tradition

Descartes exemplified the rationalist confidence in a priori reason. In the Meditations, he sought to establish knowledge through pure reasoning, without relying on the potentially deceptive senses. His method of doubt was designed to find beliefs that are immune to empirical challenge — beliefs known a priori. The cogito ("I think, therefore I am") is a paradigm of a priori reasoning: its truth is established by reflection, not by observation.

Descartes went further, arguing that even knowledge of the physical world could be established a priori, through the clear and distinct ideas implanted by a non-deceiving God. This ambitious rationalism was challenged by later thinkers, but it set the standard for what a priori knowledge might accomplish.

Hume and the Empiricist Challenge

Hume was the most rigorous empiricist critic of a priori knowledge. His "Hume's fork" divided all objects of reason into relations of ideas (analytic, a priori, necessary) and matters of fact (synthetic, a posteriori, contingent). On Hume's view, there is no synthetic a priori knowledge. If a truth is substantive — if it tells us something about the world — it can only be known through experience. If it is knowable a priori, it is merely analytic — a matter of definition, carrying no real information.

This was a devastating challenge to the rationalist program. It meant that reason alone could tell us about the meanings of concepts but not about the nature of reality. Causal connections, the existence of an external world, the nature of the self — all of these, on Hume's view, are matters of fact that cannot be established a priori.

Quine and the Dissolution of the Distinction

W. V. O. Quine delivered the most influential twentieth-century challenge to the a priori in "Two Dogmas of Empiricism" (1951). Quine argued that the analytic-synthetic distinction — the very distinction that separates a priori truths (analytic) from empirical truths (synthetic) — is not well-founded. There is no sharp line between truths that are true by definition and truths that are true by fact. All beliefs, including logical and mathematical ones, are part of a "web of belief" that faces experience as a whole.

On Quine's view, even the truths of logic and mathematics are revisable in principle, though they sit near the center of the web and are highly resistant to revision. We would revise a belief in elementary arithmetic only under extreme pressure — but we would revise it if doing so produced a simpler, more adequate overall system. This holism undermined the idea that any knowledge is genuinely independent of experience.

Quine's challenge did not end the debate. Many philosophers have defended the analytic-synthetic distinction against Quine's arguments, and the existence of a priori knowledge remains contested. But Quine shifted the burden of proof: those who believe in a priori knowledge must explain what makes it special, given that all beliefs seem to be part of a single interconnected system.

The Scope of A Priori Knowledge

If a priori knowledge exists, what does it cover?

Mathematics is the paradigm case. The truths of arithmetic, geometry, and algebra seem to be knowable by reason alone. A person who understands the concepts can see that the interior angles of a triangle sum to 180 degrees (in Euclidean geometry) without measuring every triangle. Mathematical knowledge is the strongest candidate for a priori status.

Logic is another standard case. The law of non-contradiction (nothing can be both true and false at the same time), the law of identity (everything is identical to itself), and the rules of valid inference all seem to be knowable a priori. Their truth does not depend on any observation of the world.

Conceptual truths — truths that hold in virtue of the meanings of the concepts involved — are also cited as a priori. "All squares have four sides," "nothing is simultaneously red and green all over," and "if A is taller than B and B is taller than C, then A is taller than C" are all knowable by understanding the concepts, without empirical investigation.

The controversial question is whether there is any synthetic a priori knowledge — substantive truths about the world that can be known by reason alone. Kant thought there was. Most empiricists think there is not. Contemporary philosophy remains divided.

Contemporary Relevance

The a priori / a posteriori distinction matters for several contemporary debates.

In the philosophy of mathematics, the question is whether mathematical truths are discovered by reason (a priori) or are empirical generalizations (a posteriori). Most philosophers treat mathematics as a priori, but the nature of this a priori status — whether it is about abstract objects, formal systems, or something else — remains contested.

In the philosophy of science, the distinction is relevant to the status of scientific laws. Are laws of nature empirical generalizations (a posteriori) or necessary truths knowable a priori? Most philosophers treat them as empirical, but some have argued that certain fundamental principles have a quasi-a priori status.

In ethics, the question is whether moral truths can be known a priori. Intuitionists like W. D. Ross held that basic moral principles are self-evident — knowable by reflection alone. This view has been revived in recent decades by philosophers who argue that moral knowledge is analogous to mathematical knowledge.

The rise of cognitive science has added a new dimension. Studies of infant cognition suggest that humans may have innate numerical and spatial concepts that structure experience from the start. This empirical finding about the mind's structure is different from the philosophical claim of a priori knowledge, but it raises the question of whether the distinction between a priori and a posteriori is as clean as philosophers have assumed.

How to Apply This

1. Distinguish definitional truths from factual truths. When you encounter a claim, ask: is this true by definition (all bachelors are unmarried) or by fact (there are bachelors in Berlin)? The first is a priori; the second requires investigation.

2. Recognize the role of conceptual analysis. Much philosophical and legal reasoning involves clarifying concepts — determining what "justice," "personhood," or "consent" means. This is a priori work: establishing what follows from the meanings of terms.

3. Be cautious about claiming a priori knowledge of the world. The rationalist tradition's most ambitious claims — that the nature of reality can be known by reason alone — have not fared well. Empirical investigation remains essential for substantive knowledge of the world.

4. Understand Quine's challenge. Even your most fundamental beliefs — in logic, in mathematics — are part of a web. They are highly resistant to revision, but they are not absolutely immune. This is a reason for humility, even about your most certain convictions.

5. Use a priori reasoning to clarify, not to substitute for experience. A priori reasoning is powerful for analyzing concepts, identifying implications, and checking for consistency. But it cannot tell you what the world is like — that requires looking.

Sources

1. Internet Encyclopedia of Philosophy, "A Priori and A Posteriori." Overview of the distinction and its history.
2. Stanford Encyclopedia of Philosophy, "Kant." Context for the synthetic a priori and the categories.
3. Stanford Encyclopedia of Philosophy, "Rationalism vs. Empiricism." Context for the historical debate about the sources of knowledge.
4. Stanford Encyclopedia of Philosophy, "Quine." Context for the challenge to the analytic-synthetic distinction.

Related Topics

• What is knowledge? — the broader framework in which a priori knowledge is situated.
• What is a posteriori knowledge? — the complement of a priori knowledge.
• What is belief? — the mental state that a priori reasoning produces.
• Exploring epistemology — the broader field of which the a priori / a posteriori distinction is a part.