- Lotze's theory (arithmetic propositions can be demonstrated without any recourse to intuition)
- Removing intuition from arithmetic requires replacing natural language with logic (Boole's program)
- Quantifiers and variables allow for "predicate calculus"
- Mathematics becomes a branch of Logic (Cantor's program)
- "Sense" (intension) vs "reference" (extension): "the star of the morning" and "the star of the evening" (same extension because they refer to the same thing, but different intensions)
- Propositions of Logic can only have one of two referents, true or false, but many senses
- Logic as an objective (not subjective) discipline
- Cardinal numbers constructed by a purely logical method (not relying on intuition: Kant was wrong)