Where two objects are contrary, the one
destroys the other; that is, the cause of its annihilation, and the
idea of the annihilation of an object, implies the idea of its
former existence.
Sect. IV. Sceptical Doubts concerning the
Operations of the Understanding
PART 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.
21. Matters of fact, which are the second objects of human reason,
are not ascertained in the same manner; nor is our evidence of their
truth, however great, of a like nature with the foregoing.
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