Received by the IRE, October 24, 1960. The author's work summarized here—which was done at the MIT Lincoln Laboratory, a center for research operated by MIT at Lexington, Mass., with the joint Support of the U. S. Army, Navy, and Air Force under Air Force Contract AF 19-5200; and at the Res. Lab. of Electronics, MIT, Cambridge, Mass., which is supported in part by the U. S. Army Signal Corps, the Air Force Office of Scientific Research, and the ONR—is based (...) on earlier work done by the author as a Junior Fellow of the Society of Fellows, Harvard University. (shrink)

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

Originally published in 1966. Professor Rescher's aim is to develop a "logic of commands" in exactly the same general way which standard logic has already developed a "logic of truth-functional statement compounds" or a "logic of quantifiers". The object is to present a tolerably accurate and precise account of the logically relevant facets of a command, to study the nature of "inference" in reasonings involving commands, and above all to establish a viable concept of validity in command inference, so that (...) the logical relationships among commands can be studied with something of the rigour to which one is accustomed in other branches of logic. (shrink)

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)

But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...

In his important monograph, Hypothetical Reasoning, Nicholas Rescher develops a modal theory in order to throw some light on the nature of hypothetical reasoning and on the so-called "problem of counterfactual conditionals." I should like both to expound the theory and consider its application.