An Enquiry Concerning Human Understanding

I.

20. All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, _Relations of Ideas_, and _Matters of Fact_. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. _That the square of the hypothenuse is equal to the square of the two sides_, is a proposition which expresses a relation between these figures. _That three times five is equal to the half of thirty_, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.