„My sole purpose in this paper is to try and correct what I take to be a common misinterpretation of Hume’s opinions on mathematics. I shall not enquire whether he was right or wrong in holding these opinions. Nor shall I offer opinions of my own.“.

In Chapter 4 of his essay Utilitarianism , “Of what sort of Proof the Principle of Utility is susceptible,” J. S. Mill undertakes to prove , in some sense of that term, the principle of utility. It has very commonly been argued that in the course of this “proof” Mill commits two very obvious fallacies. The first is the naturalistic fallacy which he is held to commit when he argues that since “the only proof capable of being given that an (...) object is visible, is that people actually see it. The only proof that a sound is audible is that people hear it: and so of the other sources of our experience. In like manner … the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it.” 1 Here Mill appears to hold that “X is desirable ”—a value judgment—follows deductively from “People desire x”—a factual statement. And the second is the fallacy of composition which seems to be involved in Mill'zs argument that since “each person's happiness is a good to that person … the general happiness , therefore, a good to the aggregate of all persons.” 2. (shrink)

Historical materialism I take to be the view expressed in the well-known Preface to the Critique of Political Economy and exemplified in Capital and in many other writings by Marx and by Marxists. I shall begin with a few introductory remarks, next sketch in the theory, and finally contend that, despite real attractions, it too far limits the scope of legitimate historical enquiry to be ultimately acceptable.

There is probably no student of modern philosophy, and certainly no listener to the Third Programme, who has never received the warning that he must on no account deduce an “ought” from an “is.” This prohibition, it is claimed, is securely based in established and unchallengeable principles of logic. Professor Flew was speaking for many others when he said, in the course of a broadcast entitled “Problems of Perspectives”, “I think it is very important indeed to make as clear as (...) we can and to underline with all possible emphasis that this is a point of inexorable logic”. And Professor Popper, to take but one other example, has expressed himself no less trenchantly: “Perhaps the simplest and most important point about ethics is purely logical, I mean the impossibility to derive nontautological ethical rules—imperatives, principles of policy, aims or however we may describe them—from statements of fact”—a view that is fully endorsed by Mr. Hare in his Language of Morals. (shrink)