Distinguish a priori from a posteriori knowledge and analytic from synthetic truths, and evaluate the rationalist and empiricist accounts of the sources of knowledge

What this dot point is asking

SEAB wants you to handle two key distinctions, a priori versus a posteriori and analytic versus synthetic, and to use them to evaluate the long debate between rationalism and empiricism about the sources of knowledge. The central live question is whether reason on its own can deliver substantive knowledge of the world, or whether all such knowledge ultimately traces back to experience. This is the rationalism strand that complements the perception strand.

The answer

A priori and a posteriori

A piece of knowledge is a priori if its justification does not depend on experience: you can see that it holds by thinking, as with "all triangles have three sides" or "7 plus 5 equals 12." It is a posteriori if its justification depends on experience, as with "Singapore is humid" or "this metal expands when heated." The distinction is about how a belief is justified, not about how a person first came across the idea.

Analytic and synthetic

A truth is analytic if it is true purely in virtue of the meanings of its terms, so that denying it is a kind of contradiction: "all bachelors are unmarried." It is synthetic if its truth depends partly on how the world is, so that the predicate adds something not contained in the subject: "the bachelor next door is tall." Analytic truths can seem uninformative because they only unpack concepts; synthetic truths tell us something new.

Rationalism

Rationalists, with Descartes as the leading figure, hold that reason is an independent source of substantive knowledge. By methodical doubt Descartes reaches one indubitable truth, that he thinks and therefore exists, grasped by reason alone. He treats clear and distinct ideas as a mark of truth and builds outward from them. Mathematics is the rationalist's showpiece: necessary, certain, and apparently known by proof rather than observation.

Empiricism

Empiricists, with Hume as the leading figure, hold that all the materials of knowledge come from experience. Hume divides all knowledge into relations of ideas (analytic, necessary, but empty of new factual content) and matters of fact (synthetic, but only ever known a posteriori). On this scheme there is no synthetic a priori knowledge: reason alone can secure only trivial truths or unpack what experience has supplied. This sets up Hume's problem of induction, where reason cannot justify inferences about unobserved matters of fact.

The battleground: synthetic a priori knowledge

The dispute crystallises around whether there is synthetic a priori knowledge, substantive yet known without experience. Mathematics is the test case. If "7 plus 5 equals 12" is both informative and knowable a priori, empiricism is in trouble. Empiricists reply that mathematics is analytic or a matter of convention and so not genuinely substantive. Kant argued famously that mathematics is synthetic a priori, made possible by the structure the mind imposes on experience. The reliability of supposed rational intuition is itself questionable, since beliefs once held to be a priori certain, such as the necessity of Euclidean geometry, were later revised in the light of physics.

Examples in context

Example 1. The cogito. Descartes notes that even a systematic deceiver could not make him wrong that he is thinking, since doubting is itself thinking. "I think, therefore I am" is meant to be known by reason alone, with certainty, and to serve as the foundation of rebuilt knowledge. It is the classic illustration of a priori knowledge claimed by rationalism, and a target for empiricists who ask what substantive conclusions can really be built on it.

Example 2. Geometry and physics. For centuries Euclidean geometry was treated as a body of synthetic a priori truths about physical space. The development of non-Euclidean geometries and their use in modern physics showed that the geometry of actual space is an empirical question. This case is used both ways: by empiricists to show supposed a priori certainties answer to experience, and by Kantians to refine what the a priori can claim.

Try this

Q1. Define a priori knowledge and analytic truth, and explain why they are different distinctions. [6 marks]

• Cue. A priori concerns justification without experience; analytic concerns truth by meaning. They differ because the key question is whether there is synthetic (not-by-meaning) yet a priori knowledge.

Q2. Explain Hume's division of knowledge into relations of ideas and matters of fact, and what follows for a priori knowledge. [8 marks]

• Cue. Relations of ideas are analytic, necessary but empty of new fact; matters of fact are synthetic but only known a posteriori. It follows there is no synthetic a priori knowledge, so reason alone yields only trivial truths.

Q3. Why is mathematics a problem case for empiricism? [6 marks]

• Cue. It looks both a priori (known by proof) and informative (substantive, widely applicable), so it seems synthetic a priori, which empiricism denies; empiricists reply it is analytic or conventional.