Since my discussion of an experimental arrangement of the sciences for certain practical objectives, some comment has appeared which makes it necessary to re-emphasize certain points by a further example. There seems to be something like a desire to paralyze the hand that makes arrangements for fear that undue profound metaphysical significance may be seen in a “mere” arrangement. It is the perennial fear of the a priori, the fear of a principle being invoked because of its “self-evidence”, and then turning traitor on the actual evidence. I invoke no such principle either overtly or covertly.

Philip Kitcher and Wesley C. Salmon have edited an important anthology of new papers on scientific explanation, a central problem—possibly the central problem—in the theory of science (Kitcher and Salmon 1989). Their collection begins with a comprehensive essay by Salmon that attempts to trace the development of work on this issue from Hempel and Oppenheim (1948) to the present. The University of Minnesota Press has published this article as a separate volume (Salmon 1990), which it is promoting as “a definitive introduction” to this area of inquiry. Apart from its preface and indices, the Salmon volume is identical with the original essay.

The aim of Stich's book is to further the controversial thesis that the conceptual framework of ‘folk’ psychology will have no significant role to play in a mature cognitive science. Skepticism about the scientific relevance of folk psychology has been voiced by others (behaviorists and nonbehaviorists alike); but Stich's critique is both novel and more fully developed than earlier ones. The charge is not–-or not simply–-that ‘folk theory’ is a “degenerating paradigm“ (Churchlands), or that, in general, the constructs of folk theory fail to refer altogether (Rorty; Dennett). Stich's thesis is subtler, and rests on the claim that the individuation of folk-psychological states is irremediably vague and context-and-observer relative in a way that makes a folk-psychological taxonomy ill-suited to the requirements of scientific explanation and systematization. Stich, of course, does not reject mentalism as such, as did the behaviorists: he merely rejects the assumption–-often tacitly accepted by cognitive scientists and by their philosophical interpreters–-that the mental states posited by a mature cognitive science will essentially correspond to the intentional, propositional attitude states of folk psychology. Thus, for Stich, there is no reason to suppose that cognitive science will turn out to be a sophisticated extension of folk psychology. The “Panglossian prospect” (p. 5) of a conceptual reunification of the scientific image of mind with the ‘manifest’ image under the banner of cognitivism is just what this book calls into question.

Although accounts of evolutionary altruism which leave the question of whether altruism can evolve in nature open to empirical confirmation/refutation have been worked out for special (two-trait) cases, no real effort has been made to work out such accounts for general (N-trait) cases. It is tempting to take this lack of attention as evidence for an inextricably conventional element, which precludes such accounts from being of practical scientific value. I argue that such accounts do generalize in a natural way. As is often the case in science, generalizing theoretically simplified notions is not straightforward because of issues hidden in the special case. These issues do not, however, turn out to be essentially conventional.

When I undertook to write an article for mathematical laymen on the mathematical infinite. I did not realize the depths of my own layness, I do now. Having refreshed my memory of the classics of infinity by re-reading among other things the famous papers of Cantor and Zermelo, and having struggled like a boa constrictor to swallow the latest papal bull on the human significance of the infinite, I am completely reduced to what Professor E. W. Hobson aptly and somewhat indignantly calls Mathematical Nihilism.

1. Confirmation Theory One, which we shall construct, when applied to the Raven Hypothesis yields the following results:

1. (1.1) Any black raven confirms the Raven Hypothesis.

2. (1.2) Any black non-raven confirms the Raven Hypothesis.

3. (2) Any non-black raven disconfirms the Raven Hypothesis.

4. (3) Any non-black non-raven is neutral to the Raven Hypothesis.

Theory One consists of two parts: (A) six basic concepts from confirmation theory proper, and (B) the underlying logic.

Objective chance, or the “big bad bug” of David Lewis's account of Humean Supervenience forces, as is well known, is a modification of the Principal Principle. Here, I argue that standard assumptions regarding conditional probabilities entail several puzzling consequences for Lewis's New Principle, namely, an apparent requirement to account for the chance of a theory of chance. These problems, I argue, cannot be adequately answered within the received framework, and so I suggest that an interpretation of conditional probabilities in terms of Alan Hájek's recent work might go some distance toward their resolution.

The charge that the limit-frequency theory of probability is inconsistent due to incompatibility between the required features of randomness and limit convergence is inapplicable when probability sequences are taken to be empirically (i.e., extensionally) generated, as they must be on a strictly empirical conception of probability.

All past attempts to meet this charge by formulating constructive definitions of randomness that would still allow for a demonstrable limit-convergence have, in their exclusive concern with logically (i.e., intensionally) prescribed sequences, left the logic of extensional classes essentially untouched. In the light of a strict differentiation between intensional and extensional classes a generalized approach is possible under which several closely connected senses of randomness, i.e., the formal, material, restricted and unrestricted senses may be easily distinguished and related to the notion of relevance.

It may seem trivial to state that one of the major trends in biological investigation consists in an attempt to explain the structural and functional aspects of living matter in chemical terms, in an effort to obtain insight into the equivalent of macroscopic phenomena on the molecular level. I am sure you are aware of, and this meeting of the Association has brought ample additional evidence, in how many fields this tendency has become apparent. It can be recognized in genetics with the molecular analysis of chromosomes and the enzymatic or metabolic interpretation of hereditary properties like the eyecolor of Drosophila. In a purely morphological branch like histology we do not ask merely for a differentiation of stained cell structure but we ask for the nature of the staining reaction; in nerve physiology we try to interpret conduction as alterations of protein lipoid layers; or in pathology where the age old syndrome of inflammation is explored with biochemical methods. I should mention molecular models of membranes and cell surfaces, the molecular interpretation of secretion and of the macroscopic phenomena of metabolism. Yet insofar as this yield of data could be designated as a trend, it would rather seem to be the natural outcome to be expected from the application of the analytic method of science. In one instance, however, this approach has been carried farther than in all the other fields, and it would seem to be worthwhile to pause for one moment to ask whether this case is important merely because of its technical implications or whether it is meaningful in a wider sense.

Present-day logic regards definitions as syntactical devices of abbreviation. This view, summed up in the terse adage: “To define is to eliminate,” obscures the vital part played by definitions in deductive sciences. Abstract calculi, to become noetic tools, must be interpreted; so the richer the interpretation, the more efficient the tool. But most calculi are based on a restricted number of primitives; they thus embrace, at the outset, a restricted number of concepts and can be appraised through and only through the definitions they eventually yield. In a word, the richness of a calculus lies in its defining virtualities. The whole of PRINCIPIA MATHEMATICA would be a futile game of chess, did it not embody all our mathematical concepts; none of these being assumed as primitive, PRINCIPIA MATHEMATICA owes its momentous significance to its definitions and to its definitions only.

A gas relaxing into equilibrium is often taken to be a process in which a system moves from an “improbable” to a “probable” state. Given that the thermodynamic entropy increases during such a process, it is natural to conjecture that the thermodynamic entropy is a measure of the probability of a macrostate. For nonideal classical gases, however, I claim that there is no clear sense in which the thermodynamic entropy of a macrostate measures its probability. We must therefore reject the idea that (in classical mechanics) thermodynamic entropy and probability are connected in a deep and general way.