Before an aggregation of persons can be said to constitute a community there must exist a sharing of a body of norms or values, or asystem of beliefs or morals. In sociology this conception frequentlyappears in the term “consensus,” and in political science a similar conception goes by the phrase “social contract.” The two conceptions are not identical and an important point of difference will be touched on later, but according to this position knowledge of and adherence to the fundamental rules is necessary to group unity or cohesion.

If a rational argument is to be advanced for the existence of God, it must be some form of the cosmological, depending on the concept of causation, or the ontological, an elaboration of the concept of being. The metaphysical fertility of the axiological approach to theism consists in its reformulation of the ontological argument—viz., that the nature of existent reality itself is indicative of supra natural being.

The history of Western Thought since the seventeenth Century leaves little doubt as to the practical validity of the method of natural investigation discovered by Galileo, interpreted by Descartes, and variously generalized by Newton and Einstein. The repercussions of its success on every level of human activity, religious, political, commercial, and educational (to mention only the more obvious ones) have awakened the most diverse ánd even contradictory speculations as to the nature of this science and the objectives of the scientist. Often enough one gets the impression that these speculations are founded on an arbitrary and unjustifiable conception of the nature of modern science; a conception formulated in terms of what one thinks or wishes to think science is from its effects upon the extra-scientific domain (which, in this context, includes philosophy) rather than in terms of a patient and critical penetration of its intrinsic structure.

In a short article, published in an earlier volume of Philosophy1 under the title “Philosophy and Mathematics,” I tried to explain the current conception of pure mathematics as the study of abstract structure by construction and elaboration of appropriate axiomatic formalisms. In the present paper I propose to consider certain philosophical problems, of interest to philosophers and mathematicians alike, which have their origin in the relation between such formalisms and any applications to experience that they may possess. Consideration of problems of this kind is no new undertaking, and in Reichenbach's Wahrscheinlichkeitslehre, for instance, a considerable amount of space is devoted to the Anwendungsproblem or problem of application of the formal calculus under consideration. Most such discussions, however, are at bottom an appendage to an account of the formalism itself, and the author's interest is primarily mathematical. The result is that the philosophical issues involved are not given due weight; and it is these philosophical issues that I wish to discuss in the present paper.

Mr. A. M. Turing was quoted in The Times about a year ago as saying it would be interesting to discover the degree of intellectual activity of which a machine was capable and to what extent it could think for itself. He has now pressed this suggestion further and given the results of his researches in an article called “Computing Machines and Intelligence,” together with a brief account of a “child-machine” which he has attempted to educate (Mind, October 1950). I intend to discuss this article in some detail and examine his claim that “machines can think.”

In the series Collezione di Filosofia published by Taylor of Turin since 1947, some of the most significant works on Italian existentialism have appeared. The series was inaugurated by two books by the writer of this article: Introduzione all esistenzialismo, second edition, 1947 (the first edition having been published at Milan in 1942); and Filosofia religione scienza, 1947. These were followed by Pietro Chiodi, L'esistenzialismo di Heidegger, 1947; Armando Vedaldi, Essere gli altri, 1948; Uberto Scarpelli, Esistenzialismo e marxismo, 1949; Enzo Paci, II nulla e il problema dell'uomo, 1950; Luigi Pareyson, Esistenza e persona, 1950; and Armando Vedaldi, Struttura della proprietà, 1951.

Please note that the publishers of Radhakrishnan: Comparative Studies in Philosophy, by various authors, reviewed by Meyrick H. Carré in the January 1952 issue of Philosophy, on page 90, are George Allen and Unwin Ltd.