- Category theory(as used in mathematical logic)
- A highly abstract branch of mathematics that studies how different mathematical structures relate to and transform into each other, rather than focusing on the structures themselves.
- Closed set(as used in logic and mathematics)
- In mathematics, a collection of items where any operation you perform on the items keeps you within that same collection—nothing escapes outside the boundaries.
- Proof-theoretic(as used in logic)
- Relating to how we prove statements are true using formal logical rules and methods, rather than thinking about what statements mean in the world.
- epistemology(Contrasted with purely descriptive scientific inquiry)
- A normative enterprise that tells us how we ought to reason from evidence and how we ought to justify our beliefs, as distinct from merely describing how we do reason or justify beliefs
- intuitionism(Mill's characterisation of a target he rejected; linked to conservative deference to inherited belief)
- The view that anything a person believes deeply enough must be true, such that conviction itself is taken as justification.
- law of excluded middle(Classical logic; shown to be incompatible with smooth infinitesimal analysis)
- The classical logical principle that for any proposition, either the proposition or its negation holds — applied here as: every real number is either equal to 0 or not equal to 0.
- paraconsistent logic(Used to challenge the modal inference from □¬p to ¬◇p in Fitch's knowability argument)
- A logical system in which contradictions do not entail arbitrary conclusions, and in which a necessarily false statement may be both false and true at some world — making it both necessarily false and possible