Online research in philosophy

In World Without Design: The Ontological Consequences of Naturalism, I argued that there is an important sense in which naturalism’s current status as methodological orthodoxy is without rational foundation, and I argued that naturalists must give up two views that many of them are inclined to hold dear—realism about material objects and materialism. In a review recently published in Faith and Philosophy, Dale Jacquette alleges (among other things) that my arguments in World Without Design are directed mainly against strawmen and that I have neglected to discuss at least one formulation of naturalism that straightforwardly addresses my main objections. In this reply, I show that these and other objections raised by Jacquette are unsound and, in fact, rest on egregious misrepresentations of the book.

persuasive argument for the claim that we ought to evaluate mathematics from a mathematical point of view and reject extra-mathematical standards. Maddy considers the objection that her arguments leave it open for an ‘astrological naturalist’ to make an analogous claim: that we ought to reject extra-astrological standards in the evaluation of astrology. In this paper, I attempt to show that Maddy's response to this objection is insufficient, for it ultimately either (1) undermines mathematical naturalism itself, leaving us with only scientific naturalism, or (2) leaves open the possibility of other unpalatable naturalisms.

The instability inherent in the historical inventory of mathematical objects challenges philosophers. Naturalism suggests we can construct enduring answers to ontological questions through an investigation of the processes whereby mathematical objects come into existence. Patterns of historical development suggest that mathematical objects undergo an intelligible process of reification in tandem with notational innovation. Investigating changes in mathematical languages is a necessary first step towards a viable ontology. For this reason, scholars should not modernize historical texts without caution, as the use of anachronistic notation tends to impede, rather than enhance, our ability to recognize the emergent nature of mathematical objects.

While "moral naturalism" is sometimes used to refer to any approach to metaethics intended to cohere with naturalism in metaphysics more generally, the label is more usually reserved for naturalistic forms of moral realism according to which there are objective moral facts and properties and these moral facts and properties are natural facts and properties. Views of this kind appeal to many as combining the advantages of naturalism and realism but have seemed to many others to do inadequate justice to central dimensions of our practice with our moral concepts. This entry examines some of these concerns and some ways in which moral naturalists have responded to them. It also profiles central aspects of the more particular views of some leading contemporary advocates of moral naturalism.

In response to the charge that methodological naturalism in science logically requires the a priori adoption of a naturalistic metaphysics, I examine the question whether methodological naturalism entails philosophical (ontological or metaphysical) naturalism. I conclude that the relationship between methodological and philosophical naturalism, while not one of logical entailment, is the only reasonable metaphysical conclusion given (1) the demonstrated success of methodological naturalism, combined with (2) the massive amount of knowledge gained by it, (3) the lack of a method or epistemology for knowing the supernatural, and (4) the subsequent lack of evidence for the supernatural. The above factors together provide solid grounding for philosophical naturalism, while supernaturalism remains little more than a logical possibility.

Contemporary philosophy's three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion's share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section 6.

Philosophical naturalism, according to which philosophy is continuous with the natural sciences, has dominated the Western academy for well over a century, but Michael Rea claims that it is without rational foundation. Rea argues compellingly to the surprising conclusion that naturalists are committed to rejecting realism about material objects, materialism, and perhaps realism about other minds.

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.

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.

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.