Online research in philosophy

Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets.

, Philip Kitcher has argued that science ought to meet both the epistemic goals of significant truth and the nonepistemic goals of serving the interests of a democratic society. He opposes this science as servant model to both the theology of science as source of salvific truth and the theology of science as anti-Christ. In a recent critical comment, Paul A. Roth argues that Kitcher remains entangled in the theology of salvific truth, not realizing that its goal is either vacuous or unattainable. Instead of theologies, Roth proposes demythologization. In the end, science attains neither truth nor value, for these goals are incomprehensible and unattainable. Consequently, science’s goals are entirely pedestrian and without special interest. Adopting Kitcher’s own scientific naturalistic epistemology, the author argues for a naturalized theology of science, using a science as mediator model, in which both nature and scientist have a role in the acquisition of significant truth. Key Words: epistemic values • Kitcher • nonepistemic values • Roth • science and values • scientific realism • scientific truth.

Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the only available argument for it. I argue that this argument, the so-called Failure Argument, itself fails. My overall conclusion is that although there is no self-refutation argument against reinterpretation naturalism, there are as yet no good reasons to accept it. Naturalism in mathematics The consistency of mathematical naturalism The failure argument Objections to the failure argument Philosophy as the default.

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Philip Kitcher's account of scientific progress incorporates a conception of explanatory unification that invites the so-called 'obsessive unifier' worry, to wit, that in our drive to unify the phenomena we might impose artificial structure on the world and consequently produce an incorrect view of how things, in fact, are. I argue that Kitcher's attempt to address this worry is unsatisfactory because it relies on an ability to choose between rival patterns of explanation which itself rests on the relevant choice having already been made. I also suggest a way of answering the worry that Kitcher is not likely to endorse.

Kitcher urges us to think of mathematics as an idealized science of human operations, rather than a theory describing abstract mathematical objects. I argue that Kitcher's invocation of idealization cannot save mathematical truth and avoid platonism. Nevertheless, what is left of Kitcher's view is worth holding onto. I propose that Kitcher's account should be fictionalized, making use of Walton's and Currie's make-believe theory of fiction, and argue that the resulting ideal-agent fictionalism has advantages over mathematical-object fictionalism.

Mathematical explanation -- What is naturalism? -- Perception, practice, and ideal agents: Kitcher's naturalism -- Just metaphor?: Lakoff's language -- Seeing with the mind's eye: the Platonist alternative -- Semi-naturalists and reluctant realists -- A life of its own?: Maddy and mathematical autonomy.

Philip Kitcher's The Advancement of Science sets out, programmatically, a new naturalistic view of science as a process of building consensus practices. Detailed historical case studies--centrally, the Darwinian revolution--are intended to support this view. I argue that Kitcher's expositions in fact support a more conservative view, that I dub 'Legend Naturalism'. Using four historical examples which increasingly challenge Kitcher's discussions, I show that neither Legend Naturalism, nor the less conservative programmatic view, gives an adequate account of scientific progress. I argue for a naturalism that is more informed by psychology and a normative account that is both more social and less realist than the views articulated in The Advancement of Science.

Recent years have seen a number of naturalist accounts of mathematics. Philip Kitcher’s version is one of the most important and influential. This paper includes a critical exposition of Kitcher’s views and a discussion of several issues including: mathematical epistemology, practice, history, the nature of applied mathematics. It argues that naturalism is an inadequate account and compares it with mathematical Platonism, to the advantage of the latter.

Philip Kitcher has advanced an epistemology of science that purports to be naturalistic. For Kitcher, this entails that his epistemology of science must explain the correctness of belief-regulating norms while endorsing a realist notion of truth. This paper concerns whether or not Kitcher's epistemology of science is naturalistic on these terms. I find that it is not but that by supplementing the account we can secure its naturalistic standing.