... intuition. In other words, the axioms are logically true statements (or theorems of logic), and their negations are self-contradictions. In this case, infallibility of the axioms is given on the same basis as the validity of deduction (i.e. the power of logic), and since logic has some intimate rela ...

# Imre Lakatos

Imre Lakatos (Hungarian: Lakatos Imre [ˈlɒkɒtoʃ ˈimrɛ]; November 9, 1922 – February 2, 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes.