I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

The description of data and computer programs with the use of numbers is epistemologically valuable, because it allows to identify the limits of different types of computations. This applies in particular to discrete computations, which can be described by means of computable numbers in the Turing sense. The mathematical fact that there are real numbers of a different type, i.e. uncomputable numbers, determines the minimal limitations of digital techniques; on the other hand, however, it points to the possibility of the (...) theoretical development and physical implementation of computationally stronger techniques, such as analogue-continuous computation. The analyses presented in this article lead to the conclusion that physical implementations of unconventional computations require the occurrence of actually infinite quantities in nature. Although some arguments of theoretical physics support the physical existence of such quantities, they are not definitive. (shrink)

Two different types of analog computations are discussed in the paper: 1) analog-continuous computations (performed physically upon continuous signals), 2) analog-analogical computations (performed naturally by means of so called natural analogons of mathematical operations). They are analyzed with regard to such questions like: a) are continuous computations physically implementable? b) what is the actual computational power of different analog techniques? c) can natural (empirical) computations be such reliable as digital? d) is it possible to develop universal analog computers (assuming that (...) they should be functionally similar to universal Turing machine)? Presented analyses are rather methodological than formal. (shrink)

A true Turing machine requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime, but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar to our world. But curiously enough-and this is (...) the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation, a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...) our world. But curiously enough-and this is the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation (e.g. intuitive, finitely programmed, limited in computational capability), a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

This article presents the evolution of philosophical and methodological considerations concerning empiricism in computer/computing science. In this study, we trace the most important current events in the history of reflection on computing. The forerunners of Artificial Intelligence H.A. Simon and A. Newell in their paper Computer Science As Empirical Inquiry started these considerations. Later the concept of empirical computer science was developed by S.S. Shapiro, P. Wegner, A.H. Eden and P.J. Denning. They showed various empirical aspects of computing. This led (...) to a view of the science of computing - the science of general scope. Some interesting contemporary ways towards a generalized perspective on computations were also shown. (shrink)