<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p><p>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).</p></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.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).

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

Foundations of Computing and Decision Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

This essay’s content is rendered by the titles of the successive sections. 1. Effective solvability versus intuitive solvability. — 2. Decidability, i.e....

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

Publié en ligne: 28 mars 2019

Pages: 11 - 26

Reçu: 13 août 2018

Accepté: 25 févr. 2019

DOI: https://doi.org/10.2478/fcds-2019-0002

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

© 2019 Witold Marciszewski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Publié en ligne: 28 mars 2019

Pages: 11 - 26

Reçu: 13 août 2018

Accepté: 25 févr. 2019

DOI: https://doi.org/10.2478/fcds-2019-0002

Mots cléseffective solvability, intuitive solvability, decidability, speedup, second-order logic, solvability, oracle, mathematical intuition, progress of science, algorithmic procedures

© 2019 Witold Marciszewski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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