<abstract xmlns="http://www.w3.org/1999/xhtml">The article analyses the role of Church’s Thesis (hereinafter CT) in the context of the development of hypercomputation research. The text begins by presenting various views on the essence of computer science and the limitations of its methods. Then CT and its importance in determining the limits of methods used by computer science is presented. Basing on the above explanations, the work goes on to characterize various proposals of hypercomputation showing their relative power in relation to the arithmetic hierarchy.The general theme of the article is the analysis of mutual relations between the content of CT and the theories of hypercomputation. In the main part of the paper the arguments for abolition of CT caused by the introduction of hypercomputable methods in computer science are presented and critique of these views is presented. The role of the efficiency condition contained in the formulation of CT is stressed. The discussion ends with a summary defending the current status of Church’s thesis within the framework of philosophy and computer science as an important point of reference for determining what the notion of effective calculability really is. The considerations included in this article seem to be quite up-to-date relative to the current state of affairs in computer science.1</abstract>

The article analyses the role of Church’s Thesis (hereinafter CT) in the context of the development of hypercomputation research. The text begins by presenting various views on the essence of computer science and the limitations of its methods. Then CT and its importance in determining the limits of methods used by computer science is presented. Basing on the above explanations, the work goes on to characterize various proposals of hypercomputation showing their relative power in relation to the arithmetic hierarchy.The general theme of the article is the analysis of mutual relations between the content of CT and the theories of hypercomputation. In the main part of the paper the arguments for abolition of CT caused by the introduction of hypercomputable methods in computer science are presented and critique of these views is presented. The role of the efficiency condition contained in the formulation of CT is stressed. The discussion ends with a summary defending the current status of Church’s thesis within the framework of philosophy and computer science as an important point of reference for determining what the notion of effective calculability really is. The considerations included in this article seem to be quite up-to-date relative to the current state of affairs in computer science.1

Is Church’s Thesis Still Relevant?

The Pontifical University of John Paul II in Cracow

Philosophy Department, & Copernicus Center for Interdisciplinary Studies

Studies in Logic, Grammar and Rhetoric

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Is Church\u2019s Thesis Still Relevant?"}

The article analyses the role of Church’s Thesis (hereinafter CT) in the context of the development of hypercomputation research. The text begins by presenting...

Is Church’s Thesis Still Relevant?

Published Online: Nov 04, 2020

Page range: 31 - 51

DOI: https://doi.org/10.2478/slgr-2020-0026

Keywords
hypercomputation, Church’s thesis, effective computations, computer science & philosophy

© 2020 Jerzy Mycka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Is Church’s Thesis Still Relevant?

Published Online: Nov 04, 2020

Page range: 31 - 51

DOI: https://doi.org/10.2478/slgr-2020-0026

Keywordshypercomputation, Church’s thesis, effective computations, computer science & philosophy

© 2020 Jerzy Mycka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
hypercomputation, Church’s thesis, effective computations, computer science & philosophy