A. Of abstract ideas & their relations (certain) -- a.k.a. mathematical evidence
- intuitive evidence (i.e., the self-evidence of first principles)
- evidence of strict demonstration (from first principles)
B. Of things really existing
- from our own experience (certain): (1a) external and internal sense; (1b) memory; (1c) legitimate causal inference.
- from our own experience (probable): (2a) based on uniformity, i.e., inference from facts experienced to unexperienced facts of the same kind; (2b) based on analogy, i.e., inference from facts experienced to unexperienced facts of a similar kind.
- from the experience of others -- evidence of testimony.
Beattie then goes on to defend each of these from what he sees (with some justification) as Hume's skepticism about them.