Hume's Distinction between Relations of Ideas and Matters of Fact

Relations of Ideas                                         Matters of Fact
Prob. of Relation of Ideas = 1 or 0

(1 = necessary; 0 = impossible)

Prob. of Matter of Fact = > 0 & < 1

(> 0 and < 1 = possible)

certain: determinate truth-value

tautology or contradiction

probable: indeterminate truth-value


formal (relational):

empty (not about the world)

material (empirical):

content (about the world)

analytic: a priori

no observation needed

synthetic: a posteriori

observation needed

independent of experience:

not determined by sense data

dependent on experience:

determined by sense data


arbitrary convention


given nature

predicate (conclusion) contained in subject (premises) predicate (conclusion) outside of subject (premises)
validity and deduction:

contrary never possible

invalidity and induction:

contrary always possible