A Study Guide for Students in Bill Gay's Modern Philosophy Class on

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