This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result1 provides a restricted equivalence between the two: where the Bayesian model for MAXENT inference uses an “a priori“ probability that is uniform, and where all MAXENT constraints are limited to 0–1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result2 established a sensitivity of MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacian principle of Insufficient Reason also plague MAXENT theory. Result3 builds upon the findings of Friedman and Shimony (1971; 1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes's (1978) prescription for his (1963) Brandeis Dice problem. Lastly, Result4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events.

This paper contributes to the recently renewed debate over methodological individualism (MI) by carefully sorting out various individualist claims and by making use of recent work on reduction and explanation outside the social sciences. My major focus is on individualist claims about reduction and explanation. I argue that reductionist versions of MI fail for much the same reasons that mental predicates cannot be reduced to physical predicates and that attempts to establish reducibility by weakening the requirements for reduction also fail. I consider and reject a number of explanatory theses, among them the claims that any adequate theory must refer only to individuals and that individualist theory suffices to explain fully. The latter claim, I argue, is not entailed by the supervenience of social facts on individual facts. Lastly, I argue that there is one individualist restriction on explanation which is far more plausible and significant than one would initially suspect.

The paper deals with the semantics of mathematical notation. In arithmetic, for example, the syntactic shape of a formula represents a particular way of specifying, arriving at, or constructing an arithmetical object (that is, a number, a function, or a truth value). A general definition of this sense of “construction“ is proposed and compared with related notions, in particular with Frege's concept of “function” and Carnap's concept of “intensional isomorphism.“ It is argued that constructions constitute the proper subject matter of both logic and mathematics, and that a coherent semantic account of mathematical formulas cannot be given without assuming that they serve as names of constructions.

The psychofunctionalist claim that psychological terms can be defined through the use of an experimental theory has been criticized on the grounds that it is “chauvinistic“: that it denies mentality to any creature of which the selected theory is false. I analyze the “argument from science fiction” that is thought to establish this conclusion, and show that its plausibility rests on a scope ambiguity in formulations of functional definitions. One formulation is indeed chauvinistic, but an alternative rendering is not, and is perfectly consistent with ascribing mentality to creatures of which the selected psychological theory is false. This alternative interpretation of psychofunctionalism is set out in detail, defended from several objections, and finally tied to the semantics of ordinary language psychological terms.

One central debate in cognitive science is over imagery. Do images constitute, or constitute evidence for, a distinctive, depictive form of mental representation? The most sophisticated advocacy of this view has been developed by Kosslyn and his coworkers. This paper focuses on his position and argues (i) that though Kosslyn has not developed a satisfactory account of depiction, there is nothing in principle unintelligible about the idea of depictive neural representation, but (ii) Kosslyn's model of imagery rescues the intelligibility of pictorialism at the cost of its explanatory power.

In his new book What is a Law of Nature?, David Armstrong gives an account of functional laws on the basis of the theory, originally proposed independently by Armstrong himself, Dretske, and Tooley, and further developed in this work, which asserts that laws are relations of necessitation between properties. On the theory, properties and relations are universals, and so a law is a relation between universals and is itself a universal. There are two reasons why Armstrong's account of functional laws is worth discussing. First, any theory that purports to be about laws that are investigated by science–I assume that we are only interested in such theories–must cover functional laws and not merely be adequate for generalizations about ravens or grue. Second, Armstrong claims that the main rival to his theory, the regularity theory of laws, cannot give a satisfactory account of functional laws (p. 22 and p. 37, all references to What is a Law of Nature? unless otherwise stated). If this is true, and if Armstrong's theory can provide a satisfactory account of functional laws, then this may incline us towards his point of view.

The preface by Parsons begins: “This book contains the most substantial philosophical papers I wrote for publication up to 1977, with one new essay added. … The collection is unified by a common point of view underlying the essays and by certain problems that are approached from different angles in different essays. Most are directly concerned with the philosophy of mathematics, and even in those that are not … the connection between the issues discussed and mathematics is never far from the surface … in the Introduction I articulate some elements of my general point of view and point out some connections between the essays.“ The nine previously published papers are unrevised except in some cases for added postscripts and footnotes. Of the essays written for publication before 1977, essay 7, “Quine on the Philosophy of Mathematics,” has not been, in fact, previously published. The eleventh, “Sets and modality,“ is the new essay. A general point of view does indeed show itself in these essays, but it is rigorously subordinated to careful and balanced analyses of the problems discussed. That is why, without sharing all elements of the point of view, I have profited so much from these essays and, seeing them collected together, am so impressed by them.