Abstract
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
Highlights
The title question of the article is a reference to the title of Mark Burgin’s article The Rise and Fall of Church-Turing Thesis, in which the author questions the value of Church’s thesis for computer science at the present stage of its development.2 As we know, almost eighty years after the formulation of CT, its logical value has not been resolved, which
If we consider an algorithm to be the basic tool of computing, CT severely limits the framework of what a computer scientist (IT specialist) can get, especially in terms of practical use
The task of this work is to defend the unique role of CT for computer science in the context of the whole class of proposed models of calculations having the feature of hypercomputability
Summary
The title question of the article is a reference to the title of Mark Burgin’s article The Rise and Fall of Church-Turing Thesis, in which the author questions the value of Church’s thesis for computer science at the present (and future) stage of its development. As we know, almost eighty years after the formulation of CT, its logical value has not been resolved, which. The central concepts for the whole computer science are algorithmic thinking, information representation and computer programs These authors provide a nice metaphor of this view saying that programmers are to a large extent playwrights and puppet actors (Murawski (2014), p. Summarizing these different descriptions of computer science, it can be seen that there is no general consensus on the scientific character of this discipline (in the sense of natural or formal science), most authors share this view; secondly, there are usually two parallel components – theory and engineering; thirdly, there is often an empirical element; and fourthly, the basic concepts are algorithms (procedures), programs and machines (computers) that process information (which involves the concept of structured data). The first component – theoretical – deals with algorithms and programs in abstracto, i.e. construction of programs and examination of their general properties, while the second component deals with implementations of a specific computation on appropriately constructed machines (computers). CT in this context could be seen as a kind of a link (or a bridge) between these two components
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