Advanced · a field of logic
Non-Classical Logics
Intuitionistic, many-valued, relevant, and fuzzy logics: systems that revise or reject the classical laws, each for a reason.
- The problem
- Must every proposition be simply true or false, and must we always accept the law of excluded middle?
- The turning point
- Intuitionism rejects excluded middle: a disjunction is asserted only when one side can be constructively proved.
- An open question
- Is there one “true” logic, or are classical and non-classical systems simply tools for different purposes?
The Canon
- On the Foundations of Mathematics 1907
- Constructivism in Mathematics
To study it
- An Introduction to Non-Classical Logic
- An Introduction to Substructural Logics
- Many-Valued Logic