Church's Thesis and Principles for Mechanisms

  title={Church's Thesis and Principles for Mechanisms},
  author={Robin O. Gandy},
  journal={Studies in logic and the foundations of mathematics},
  • R. Gandy
  • Published 1980
  • Philosophy
  • Studies in logic and the foundations of mathematics

The Broad Conception of Computation

A myth has arisen concerning Turing's article of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine; this supposed principle is sometimes incorrectly termed the Church-Turing thesis.

What is Church's Thesis? An Outline*

  • J. Doyle
  • Philosophy
    Minds and Machines
  • 2004
My suspicion is that physics is easily rich enough so that E2, the functions compatable in principle given Turing’s operations and equilibriating, include non-recursive functions.

The Church-Turing Thesis

The notion of an effective method is an informal one, and attempts to characterise effectiveness, such as the above, lack rigour, for the key requirement that the method demand no insight or

A Natural Axiomatization of Computability and Proof of Church's Thesis

It is shown that augmenting those postulates about algorithmic computation with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's Thesis, as Gödel and others suggested may be possible.

On mind & Turing’s machines

  • W. Sieg
  • Philosophy
    Natural Computing
  • 2006
G Gödel’s perspective on mechanical computability as articulated in his [193?], where he drew a dramatic conclusion from the undecidability of certain Diophantine propositions, namely, that mathematicians cannot be replaced by machines, is discussed.

K-graph machines : generalizing Turing's machines and arguments

K-graph machines are introduced and used to give a detailed mathematical explication of the first two aspects of Turing's considerations for general configurations, i.e. boundedness and locality conditions and mechanical operations, which provide a significant strengthening of Turing’s argument for his central thesis.

Turing’s Theory of Computation

This work discusses the historical and philosophical reasons that led to the widely accepted classic-computational interpretation of the Turing machine, and argues that this interpretation is wrong, because it treats the tape of a Turing machine as its internal memory, rather than as the external environment.

On Effective Procedures

This paper presents an alternative to Turing's analysis; it unifies, refines, and extends my earlier work on this topic, and has the advantage of applying to ordinary, everyday procedures such as recipes and methods, as well as the more refined procedures of mathematics and computer science.

Church Without Dogma: Axioms for Computability

An analysis of computability that leads to precise concepts, but dispenses with theses is presented, which leads to axioms for discrete dynamical systems (representing human and machine computations) and allows the reduction of models of theseAxioms to Turing machines.

A Natural Axiomatization of Church's Thesis

The Abstract State Machine Thesis asserts that every classical algorithm is behaviorally equivalent to an abstract state machine. This thesis has been shown to follow from three natural postulates



Finite combinatory processes—formulation

The present formulation should prove significant in the development of symbolic logic along the lines of Gödel's theorem on the incompleteness of symbolic logics and Church's results concerning

Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)

This work presents a mathematical definition of an analog generable function of a real variable in terms of a simultaneous set of nonlinear differential equations possessing a "domain of generation," which includes functions generated by existing general-purpose analog computers.

Subgroups of finitely presented groups

  • G. Higman
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1961
The main theorem of this paper states that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. It

On computable numbers, with an application to the Entscheidungsproblem

  • A. Turing
  • Computer Science
    Proc. London Math. Soc.
  • 1937
This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.

An algebraic characterization of groups with soluble word problem

The following theorem is the focal point of the present paper. It stipulates an algebraic condition equivalent, in any finitely generated group, to the solubility of the word problem. THEOREM I. A


Zusammenfassung P. Bernays hat darauf hingewiesen, dass man, um die Widerspruchs freiheit der klassischen Zahlentheorie zu beweisen, den Hilbertschen flniter Standpunkt dadurch erweitern muss,