Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own…
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how basic arithmetic principles can be derived from logical…
A sequence of numbers where each element is chosen without any predetermined rule or algorithm. It's a concept central to…
A formal system is a set of symbols and rules for manipulating them, used to derive statements or theorems in…
Finitary arithmetic is a mathematical approach that emphasizes constructive methods, avoiding infinite concepts. It focuses on operations and proofs that…
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…
Combinatorialism posits that any arbitrary collection of elements forms a valid mathematical structure, regardless of its definability. This philosophical stance…
Frege's Basic Law V aimed to ground arithmetic in logic. It states that the extension of a concept is defined…