A metatheorem is a theorem that describes properties of a formal system, such as consistency or completeness. It operates on…
Metamathematics examines mathematical systems and theories from an elevated viewpoint, employing principles of mathematical logic. It explores the foundations and…
Logicism is the philosophical view that mathematics is a branch of logic. Proponents believe all mathematical truths can be derived…
Löb's theorem in mathematical logic states that if a system can prove that a statement implies its own provability, then…
A logic designed for higher-order quantification and modalities. It emerged from discussions on the foundations of mathematics by Kreisel and…
Mathematics built on intuitionistic logic, prioritizing constructive proofs and avoiding non-constructive axioms like the law of excluded middle. It emphasizes…
Intuitionistic logic, a constructive approach to reasoning, diverges from classical logic by rejecting the law of excluded middle. It demands…
Intuitionism is a philosophy of mathematics that questions the existence of the mathematical infinite and the completeness of mathematical truth.…
Hume's principle states that two collections have the same number of objects if and only if a one-to-one correspondence can…
An ambitious project by David Hilbert to formalize all mathematics and prove its consistency using finitary methods. It aimed to…