Virtually any appraisal of a person’s welfare, integrity, or moral status, as well as the moral and political theories built on such appraisals, will rely crucially on the presumption that her preferences and values are in some important sense her own. In particular, the nature and value of political freedom is intimately connected with the presupposition that actions one is left free to do flow from desires and values that are truly an expression of the ‘self-government’ of the agent. However, we all know that no person is self-made in the sense of being a fully formed and intact ‘will’ blossoming out of nowhere. Our values and preferences are explained by essential reference to a variety of influences that have come to bear on our development throughout our personal histories. What is needed, then, is to establish an account of self-determination or autonomy that would help determine just when and if the values and preferences we find ourselves with deserve the centrality that moral and political theories place on them.

This paper is about David Gauthier’s concept of constrained maximization. Attending to his most detailed and careful account, I try to say how constrained maximization works, and how it might be changed to work better. In section I, that detailed account is quoted along with amplifying passages. Difficulties of interpretation are explained in section II. An articulation, a spelling out, of Gauthier's account is offered in section III to deal with these difficulties. Next, in section IV, constrained maximization thus articulated is tested on several choice problems and shown to be seriously wanting. It appears that there are prisoners’ dilemmas in which constrained maximizers would not cooperate to mutual advantage, but would interact sub-optimally just as straight-maximizers would. ‘Coordination problems’ are described with which constrained maximizers might, especially if transparent to one another, not be able to cope–problems in which they might not be able to make up their minds to do anything at all. And I prove that there are prisoners’ dilemmas that, though possible for real agents and for straight maximizers, are not possible for constrained maximizers, so that agents’ internalising dispositions of constrained maximization could not be of help in connection with such possibly impending dilemmas. Taking constrained maximization as it stands, there are many problems for which it does not afford the ‘moral solutions’ with which Gauthier would have it replace Hobbesian political ones. After displaying these shortcomings of constrained maximization as presently designed, I sketch, in section V, possible revisions that would reduce them, stressing that these revisions would not be cost-free. Whether finishing the job of fixing up and making precise constrained maximization would be worth the considerable trouble it would involve lies beyond the issues taken up in this paper. So, of course, do substantive comparisons of constrained maximization, perfected and made precise, and straight maximization.

Philip Kitcher has proposed an account of mathematical truth which he hopes avoids platonistic commitment to abstract mathematical objects. His idea is that the truth-conditions of mathematical statements consist in certain general structural features of physical reality. He codifies these structural features by reference to various operations which are performable on objects: the world is structured in such a way that these operations are possible. Which operations are performable cannot be known a priori; rather, we hypothesize, conjecture, idealize, and eventually wind up with theories which are true of the world (taking into account our idealizations), just as we do in the sciences. Kitcher argues that mathematical and physical knowledge are continuous, in that they concern the same subject matter (the physical world) and are subject to the same epistemological and methodological constraints.