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- Penelope Maddy (2007). Second Philosophy: A Naturalistic Method. Oxford University Press.Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy". Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second Philosopher". mhis Second Philosopher begins from perceptual common sense experimentation, theory formation and testing, working all the while to asses, correct and improve her methods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations. Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practice Second Philosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized.
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In World Without Design, Michael Rea says that naturalists are disposed to take the methods of science, and those methods alone, as basic sources of evidence. Supernaturalists, he says, share with naturalists the disposition to trust the methods of science in the basic way---that is, in the absence of any epistemic reason to do so. But unlike naturalists, supernaturalists are also disposed to take religious experience as a basic source of evidence. I raise a number of objections to these characterizations of naturalism and supernaturalism. First, they mistakenly presuppose both that the methods of science are all methods of inquiry and that the demarcation problem can be solved. Also, if they are correct, then both naturalism and supernaturalism are committed to an undesirable form of scientism. Finally, they overlook both the fact that most of the methods of science are not basic sources of evidence and the fact that the methods of science include the method of searching only for natural causes of natural phenomena. I close by proposing an alternative characterization of naturalism.
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The goal of this paper is to sketch a distinctive version of naturalism in the philosophy of science, both by tracing historical antecedents and by addressing contemporary objections.
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Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.
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.
and impressive applicability of mathematics in the natural sciences. Quineans hold that mathematics is confirmed by these applications, that only that part of mathematics with application is justified. Defenders of pure mathematics naturally disagree, finding justification for unapplied mathematics in various places, perhaps in some largely unspecified aesthetic virtues or in some philosophy of mathematics. My ultimate goal in this paper is to illuminate, from a naturalistic point of view, the significance of the application of mathematics in the natural sciences for the..
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Naturalism in philosophy is sometimes thought to imply both scientific realism and a brand of mathematical realism that has methodological consequences for the practice of mathematics. I suggest that naturalism does not yield such a brand of mathematical realism, that naturalism views ontology as irrelevant to mathematical methodology, and that approaching methodological questions from this naturalistic perspective illuminates issues and considerations previously overshadowed by (irrelevant) ontological concerns.
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.
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