The distinction between relations of ideas and matters
of fact (Hume's fork) - the scope of each
1 CONTEXT & SIGNIFICANCE: Section IV. Hume outlines what he sees as the two ways in which our thoughts might constitute knowledge, either as Relations of Ideas or
Matters of Fact (distinction known as Hume's fork). All human knowledge falls into one category or another; no possibility of combination or a third category.
2 RELATIONS OF IDEAS: truths concerning ROA are
discoverable 'by mere operation of thought without
dependence on what is anywhere existent in the
universe". Intuitivley/demonstratively certain and
can't be doubted without self-contradiction.
Geometry/algebra/arithmetic; "that the square of the
hypotenuse is equal to the square of two sides"
"that five times three is equal to the half of thirty".
2.1 Known a priori, are analytic, and necessary.
3 MATTERS OF FACT: these claims to knowledge can only be
justified by appeal to the testimony of sense experience and
sentiments. Can be denied without self-contradiction; "the
contrary of every matter of fact is still possible, because it
can never imply a contradiction". "that the sun will not rise
to-morrow is no less an intelligible proposition, and implies
no more contradiction, that the affirmation, that it will rise."
3.1 Known a posteriori, are synthetic, and contingent.