The Passions and Volition; 6.

The Principle of Morals.
Hume's views respecting necessary truths, and more particularly concerning causation, have, more than any other part of his teaching, contributed to give him a prominent place in the history of philosophy.
"All the objects of human reason and inquiry 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 two 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 whatever is anywhere existent in the universe.