In this paper an attempt is made to provide an analysis of the meaning of the term function and related terms as they are used by R. K. Merton in the first chapter of his book Social Theory and Social Structure. Several problems are suggested which must be solved if statements about functions are to be considered scientifically adequate. Secondly the term functionalism is defined and several of Merton's functionalist explanations of social phenomena are stated and criticized.

In a recent paper, the mathematician Harold Edwards claimed that Euler’s alleged proof, that Fermat’s last theorem is true for the case n = 3, is flawed. Fermat’s last theorem is the conjecture that there are no positive integers x, y, z, or n, such that n is greater than two and such that xn + yn = zn. In this paper we shall first briefly explain the specific flaw to which Edwards called attention. After that we briefly explain the (...) nature of mathematical proofs and with reference to such proofs explain the nature of gaps in proofs. Then we critically discuss an alternative view concerning the nature of proofs in mathematics and discuss the alternative view critically. Specifically we argue that advocates of this alternative view, which we call mathematical postulationism, have not provided a satisfactory account of the nature of gaps in proofs. The unsatisfactoriness of postulationist accounts of gaps in proofs is revealed through reflection concerning appropriate repairs to proofs with gaps. (shrink)

If the principle of equal pay for work of equal value is valid, then the practice of paying workers in third-world countries at a lower rate than workers doing the same jobs in industrialized nations is unjust. Recently Henry Shue argued that the principle is not valid. In this paper I criticize Shue's arguments and offer additional arguments in support of his conclusion.

Mathematical objects, according to intuitionists, exist only in the mind of the mathematician. Such objects are, in reality, structures which are created by the mathematician. Creation of such structures is limited by the capability of the mind to generate sequences of objects. Knowledge of mathematical objects or structures is possible through the mind’s capability to survey or inspect the structures that it has created. The platonist, contrary to the intuitionist, maintains that mathematical objects have an existence which is not causally (...) dependent on the mind of the mathematician. Such objects, he believes, are not created through the mind’s activity. Both platonists and intuitionists agree that there are mathematical objects; they disagree with respect to the causal origin of such objects. (shrink)

I have been told that for some twenty minutes after reading this paper Kripke believed I had shown that proper names could be non-rigid designators. (Then, apparently, he found a crucial error in the set-up.) I take great pride in this (alleged) fact.

Nussbaum seems to have had a spell during which she made villains heroes (and sometimes visa versa). Thus she has argued, in effect, that Steerforth is the hero of David Copperfield, and Heathcliff the most admirable character in Wuthering Heights. Here I discuss her more or less explicit claim that Alcibiades is the hero, (and Socrates the villain) in Plato’s Symposium. -/- .

I would like to get this published somewhere; but who would publish it?

In Analysis, Vol. 45, June 1984, George Rea published a paper attacking my claim that there could be ‘indeterminate minds'. This paper is a reply to his attack. I claim, again, that such ‘minds’ are possible – entities such that it is indeterminate whether or not these entities are people with minds. -/- .

In 1974 Putnam was a ‘realist’ in regard to the physical world. By 1981 he had become a 'non-realist' in this regard. (I don’t know where he stands today.) In this paper I argue that his realism was more plausible than his non-realism. The physical world is what it is independently of any rational being’s interpretation of it.

Parfit’s well known book, Reasons and Persons, argues, among other things, that ‘what matters’ in regard to ‘survival’ is not personal identity but something he calls ‘relation R.’ On this basis, plus other considerations, he rejects the ‘Self-interest’ theory as to what should be our aim in life. Here I show, or try to show, that his over-all argument is seriously defective. In particular, he fails to prove that personal identity is not what matters for survival.

It seems clear that second order fuzziness (indeterminacy) is possible. There can be borderline cases of borderline cases. But how about third order cases? Is there no end of degrees of borderlinehood? I offer a somewhat strange little 'language game' that seems to suggest that the ascension ends with second order cases. (The 'game' is intended to be somewhat like a simplified version of color perception.).

Descartes thought he could suppose he was the victim of massive deception in regard to the external world. In fact he undertakes the supposing of it.I will … suppose that … a certain evil spirit, not less clever and deceitful than powerful, has bent all his efforts to deceiving me. I will think that the sky, the air, the earth, colors, shapes, sounds, and all other external things are nothing but illusions and dreams that he has used to trick my (...) credulity. I will regard myself as having no hands, no eyes, no flesh, no blood, nor any senses, but believing falsely that I have all these things.Seated comfortably by his fire, Descartes imagines a remote possibility. Perhaps he is just a mind in the clutches of a deceiving demon. If Descartes is this man lounging here in his dressing gown, he is not vastly deceived; but if he is that mind, he is deceived indeed. The two possibilities are taken to be experientially indiscernible; and Descartes is assuming that the contents of his beliefs and the senses of his claims remain the same in either case. Thus, for example, whether he is this man or that mind, he believes he has two hands. But, and this is crucial, his belief is false if he is that mind, and true if he is this man. We begin to see what is required of cartesian semantics, and cartesian theories of the content of belief. (shrink)

This is a boiled down version of my doctoral dissertation. Ryle wouldn’t publish it, claiming that it is like ‘a well sharpened pencil that no one will ever use.’ I guess he turned out to be right. Nevertheless I think it was, and is, a good paper.