Some recent and historical writers in the philosophy of science have concerned themselves with a certain problem which seems to occupy, at least in the minds of those who have written about it, a position of peculiar importance. Whether the problem is really as significant as its authors maintain need not be decided here; certainly many writers in this area have either neglected it or made only vague allusions to it. It can best be described as the problem of the development of science, and it is usually solved in terms of a certain theory that science passes in its growth, either naturally or under the control of conscious logical techniques, through various “stages” or “phases.” For some strange reason these levels are usually exactly three in number. One would like to believe that this number is not a magic one, but empirically demanded by the actual way in which the sciences develop. But the fact that the descriptions of these stages in the writings of the various authors appear to agree only in their triplicity, and not in content, would incline one to believe otherwise. There is, in fact, the slight suspicion that the number three has been preferred to the number two simply because a triad may be ordered in a way in which a couple may not, and to the number four or any larger number merely because of the preference for simplicity over complexity.

1. Introduction. It is generally admitted that a large part of man's knowledge is based on inductive arguments. Hence any philosophical theory concerning the nature of inductive arguments constitutes an epistemological theory. Any such philosophical theory of induction must, if it is to be satisfactory, take adequate account of Hume's criticism of inductive arguments. One way of treating his criticism is to say that the validity of inductive arguments is in an important sense relative to some broad factual assumptions about the general nature of the universe and that these general factual assumptions are presupposed in a certain way by the users of inductive arguments (8, 10). Let us call any theory of this general type a postulate theory of induction.

The term “value” has a wide range of current usage in philospohy and the sciences. Descriptively, a man's “values” may refer to all his attitudes for-or-against anything. His values include his perferences and avoidances, his desire-objects and aversion-objects, his pleasure and pain tendencies, his goals, ideals, interests and disinterests, what he takes to be right and wrong, good and evil, beautiful and ugly, useful and useless, his approvals and disapprovals, his criteria of taste and standards of judgment, and so forth.

1. Introduction. Nowadays metaphysics is so far out of fashion, with scientists at any rate, that a few words of justification may be required for putting it in relation with science, as in this paper.

Metaphysics is nothing occult, nor is it necessarily dogmatic or allied to theology. Strictly, it is a science itself, the science of being. But since a large section of being—even the whole of it, according to some metaphysics—consists of phenomena, and since the ostensible business of natural science is with phenomena, a distinction has to be made. The use of ‘metaphysics’ in this paper is restricted to the non-phenomenal mode of being. More explicitly, it is restricted to formal and general things, such as category, class, variable, relation, order. General words, which I take to be all the words except certain proper names, are, accordingly, metaphysical signs; and the metaphysical matrix is by no means limited to science but extends to all discourse in which there are general terms.

During my recent work on machine translation (3), I have come across many problems of a linguistic nature that should be of general methodological interest. Some of these problems have never been treated extensively before. Others that have been discussed previously appear now in a different and rather interesting light.