Innate ideas versus sensory foundations
Rationalism, represented by Descartes, Spinoza, and Leibniz, holds that reason and innate ideas are the primary source of knowledge. Descartes argued that the mind contains certain ideas (God, infinity, the self) that cannot derive from experience alone; they must be innate. Rationalists valued mathematics and logic as exemplars of knowledge, treating sensory experience as unreliable and subject to illusion.
Empiricism, championed by Locke, Hume, and Berkeley, argued the opposite: the mind begins as a blank slate, and all knowledge derives from sensory experience. Locke distinguished simple sensations (received passively) from complex ideas (assembled by the mind from sensations). Empiricists emphasized observation, experimentation, and the limits of reason. For Hume, even causation is not a logical necessity but a habit of mind built from observed constant conjunction.
Mathematical necessity and the limits of experience
The debate hinges on explaining mathematical knowledge. Rationalists argued that mathematical truths are necessary and universal, properties that pure sensory experience cannot provide (no two physical triangles are truly identical). Empiricists countered that mathematical concepts are abstractions from experience, highly refined but experientially grounded.
Kant attempted synthesis, arguing that knowledge requires both sensory content and mental structures (categories like causation and time) that organize experience. This influenced modern philosophy toward recognizing both innate cognitive structure and environmental input. The debate, though reformulated in contemporary terms (nativism versus learning), continues: how much of knowledge reflects mind-independent reality versus minds' contribution to knowing.