The progress of science from a computational point of view: the drive towards ever higher solvability
2019
scientific article
english
- effective solvability
- intuitive solvability
- decidability
- speedup
- second-order logic
- solvability
- oracle
- mathematical intuition
- progress of science
- algorithmic procedures
EN 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. A more detailed summary can be obtained through juxtaposing the textboxes labelled with letters A...F. Conclusion: in the progress of science an essential role is played by the feedback between intellectual intuitions (intuitive solvability) and algorithmic procedures(effective solvability).
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