Introduction: Science as approximation to truth



These essays were written over a fifteen-year period. During that time my views underwent a number of changes, especially on the philosophy of mathematics and on the interpretation of quantum mechanics. Nevertheless they have, I believe, a certain unity.

The major themes running through these essays, as I look at them today, are the following: (1) Realism, not just with respect to material objects, but also with respect to such ‘universals’ as physical magnitudes and fields, and with respect to mathematical necessity and mathematical possibility (or equivalently with respect to mathematical objects); (2) the rejection of the idea that any truth is absolutely a priori; (3) the complementary rejection of the idea that ‘factual’ statements are all and at all times ‘empirical’, i.e. subject to experimental or observational test; (4) the idea that mathematics is not an a priori science, and an attempt to spell out what its empirical and quasi-empirical aspects really are, historically and methodologically.




These papers are all written from what is called a realist perspective. The statements of science are in my view either true or false (although it is often the case that we don’t know which) and their truth or falsity does not consist in their being highly derived ways of describing reg­ularities in human experience. Reality is not a part of the human mind; rather the human mind is a part and a small part at that of reality. But no paper in this collection is entirely devoted to the topic of realism, for my interest in the last fifteen years has not been in beating my breast about the correctness of realism, but has rather been in dealing with specific questions in the philosophy of science from a specific realist point of view. (However, the reprinting of these volumes has given me the opportunity to include my essay on ‘Philosophy of logic’ which does discuss the case for realism.)

To prevent misunderstandings, let me say that by realism I do not mean materialism. Part of the burden of these essays is that a consistent realist has to be realistic not only about the existence of material objects in the customary sense, but also has to be realistic about the objectivity of mathematical necessity and mathematical possibility (or equivalently about the existence of mathematical objects) and about entities which are neither material objects nor mathematical objects in particular, fields and physical magnitudes. The importance of this latter kind of realism is discussed in the paper ‘On properties’ and also plays a key role in ‘An examination of Grùnbaum’s philosophy of geometry’. Grùnbaum, at the time I criticized him, maintained that the fundamental field in modern cosmology the gravitational field or metric field was simply a way of articulating relations between solid bodies; my rejection of this contention is an example of the kind of realism just alluded to.




Since the philosophy of science is, after all, not all of philosophy, it may be well to say a word or two about wider issues. It will be obvious that I take science seriously and that I regard science as an important part of man’s knowledge of reality; but there is a tradition with which I would not wish to be identified, which would say that scientific knowledge is all of man’s knowledge. I do not believe that ethical statements are expressions of scientific knowledge; but neither do I agree they are not knowledge at all. The idea that the concepts of truth, falsity, explanation, and even understanding are all concepts which belong exclusively to science seems to me to be a perversion. That Adolf Hitler was a monster seems to me to be a true statement (and even a ‘description’ in any ordinary sense of ‘description’), but the term ‘monster’ is neither reducible to nor eliminable in favour of ‘scientific’ vocabulary. (This is not something discussed in the present volume. It is a subject on which I hope to write in the future.)

If the importance of science does not lie in its constituting the whole of human knowledge, even less does it lie, in my view, in its technological applications. Science at the best is a way of coming to know, and hopefully a way of acquiring some reverence for, the wonders of nature. The philosophical study of science, at the best, has always been a way of coming to understand both some of the nature and some of the limitations of human reason. These seem to me to be sufficient grounds for taking science and philosophy of science seriously; they do not justify science worship.