The question was simple, the answer was not: where does knowledge come from? Descartes's 1641 Meditations argued that the senses can deceive and that real knowledge must be derived from innate rational principles — intuitively clear truths like 'I think, therefore I am'. Spinoza's 1677 Ethics turned this into an axiomatic system; Leibniz kept the notion of 'innate ideas' and, through his 'pre-established harmony', treated the mind as a self-contained logical domain. This line is known as rationalism: the model of certain knowledge is mathematics, and reason can discover reality without recourse to experiment.

In Britain a different line developed. John Locke's 1689 Essay Concerning Human Understanding described the mind at birth as 'tabula rasa' — a blank slate: all ideas come ultimately from sensation and reflection, there is no innate content. George Berkeley pushed the line to 'to be is to be perceived'. David Hume, in the 1739 Treatise of Human Nature and the 1748 Enquiry, took empiricism to its sceptical limit: causation is only the mind's habitual expectation of conjoined events, induction has no rational ground, the 'self' is a bundle of perceptions rather than a stable substance. These conclusions collided head-on with the rationalists' central claims.

Immanuel Kant's 1781 Critique of Pure Reason reframed the debate. He said Hume had awoken him from his 'dogmatic slumber', but Hume's scepticism could not explain why mathematics and Newtonian physics worked. Kant's solution was a distinction: all knowledge begins with experience (so far empiricism is right), but experience is organised by the mind's own a priori forms — space, time, the category of causation (so far rationalism is right). Science advances by also investigating the mental structures that make experience possible.

The debate is not just an academic episode. Locke's empiricism carried the idea of 'no authority by birth' into politics and, through the 1689 Two Treatises of Government, prepared the language of the American Declaration of Independence. Hume's scepticism about causation begins a line in the philosophy of science — Popper, Quine, Kuhn — that runs into the 20th century. The rationalist, mathematics-first approach survives in the inner intuitions of modern theoretical physics (Einstein, quantum mechanics). Today's competing answers to 'how do we know reality' — lab experiment, mathematical proof, modelling, big data — are still argued within the tension of these two poles. The split itself is somewhat schematic in modern reading: historians remind us that Descartes also trusted observation and Locke also reasoned by inference; but as schools, the distinction remains the map of modern epistemology.