The progress of science from a computational point of view: the drive towards ever higher solvability

Abstract

This essay’s content is rendered by the titles of the successive sections. 1. Effective solvability versus intuitive solvability. — 2. Decidability, i.e. effective solvability, in predicate logic. The speedup phenomenon — 3. Contributions of the second-order logic to the problems of solvability — 4. The infinite progress of science in the light of Turing’s idea of the oracle. The term “oracle” is a technical counterpart of the notion of mathematical intuition.

Keywords

• effective solvability
• intuitive solvability
• decidability
• speedup
• second-order logic
• solvability
• oracle
• mathematical intuition
• progress of science
• algorithmic procedures