Indispensability, Causation and Explanation. Sorin Bangu. Basingstoke: Palgrave Macmillan, ISBN Hbk. Platonism and Anti-Platonism in Mathematics. Mark Balaguer - - Oxford University Press. Oystein Linnebo - - Dissertation, Harvard University. Platonism in the Philosophy of Mathematics. Zalta ed. Naturalized Platonism Versus Platonized Naturalism. Zalta - - Journal of Philosophy 92 10 The Nature of Mathematical Objects.
Mathematical Association of America. Mathematical Platonism. James Robert Brown - - Routledge. Against Maddian Naturalized Platonism. Mark Balaguer - - Philosophia Mathematica 2 2 Provability and Mathematical Truth. David Fair - - Synthese 61 3 - Problems with Profligate Platonism. Colin Cheyne - - Philosophia Mathematica 7 2 A Platonist Epistemology. Mark Balaguer - - Synthese 3 - Added to PP index Total views 1 1,, of 2,, Recent downloads 6 months 1 1,, of 2,, How can I increase my downloads?
Downloads Sorry, there are not enough data points to plot this chart. Sign in to use this feature. Applied ethics. History of Western Philosophy. Normative ethics. Philosophy of biology. Philosophy of language. Furthermore, they also point out another common supposition: that the conceptualizations we humans develop are consistent with Peano-like axioms.
Moreover, this evidence suggests that even highly educated adults routinely conceptualize the natural numbers in ways that are radically different from, or even at odds with, Peano-like characterizations. Among the positive claims they make is the one that the collection of counting numbers differs in important ways from the formal mathematical set of natural numbers. An important upshot of this analysis Francis is that natural number concepts may not arise naturally from our counting experience.
He first notes the existence of many reports about the role of beauty for finding truth in mathematics. For a long time, philosophical theorizing has dealt with the epistemic jus- tification of aesthetic factors. Yet, as Reber notes, empirical evidence, and a theory about the underlying mental mechanisms, are largely missing.
He discusses a particular theory, the processing fluency theory of aesthetic plea- sure, which claims that the ease with which information can be processed is the common mechanism underlying perceived beauty and judged truth. The chapter summarizes some of the existent philosophical discussion on this topic; after this, it introduces the assumptions of the processing flu- ency theory before reviewing the empirical evidence for this account.
Three major questions arise. Earlier analyses investigated the role of fluency in subjectively judged and objective truth, and they dealt with the evidence for the claim that familiarity with, and the coherence of, information results in fluency. These investigations also outlined the conditions under which fluency is epistemically justified—that is, related to actual truth.
Likewise, according to Reber, it seems plausible that the familiarity of mathematicians with their field, and the coherence of mathematical rules, results in fluency. Hence a positive relationship between beauty and truth is plausible. It fittingly closes the volume, as it deals with a key question for any naturalist-friendly philosophy—namely, how should we conceive of the very method of math- ematics if we take a naturalist stance?
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Sterpetti indicates the origin of the problem: mathematical knowledge has long been considered to be the very paradigm of certain knowledge, and, as he also points out, this is so because Taylor mathematics is taken to be based on the axiomatic method. A source of additional problems is that natural science is thoroughly mathematized and thus accounting for the role of science and its relation to mathematics are crucial tasks in outlining any version of the naturalist perspective.
Sterpetti examines, and expresses doubts about, the idea to naturalize the traditional view of mathematics by relying on evolutionism. One interesting upshot is that we must then conceive of mathematical knowledge as plausible knowledge. Reasoning: Studies of human inference and its founda- tions. Cambridge: Cambridge University Press. Baillargeon, R. Object permanence in five- month-old infants. Cognition, 20, — Baker,, G. Not- turno Ed. Leiden: Brill. Bangu, S.
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Iyyun: The Jerusalem Philosophical Quarterly, 61, — Later Wittgenstein on the logicist definition of number. Costreie Ed. Western Ontario Series in Philosophy of Science. Dordrecht: Springer. Benacerraf, P. Mathematical truth. Journal of Philosophy, 70, — Brown, J. Platonism, naturalism and mathematical knowledge. Abing- don, UK: Routledge. Truth, thought, reason: Essays on Frege. Oxford: Oxford Univer- sity Press.
Butterworth, B. The mathematical brain. London: Macmillan. Mathematical cognition Vol. Hove, UK: Psychology Press. Campbell, J. Handbook of mathematical cognition. Cappelletti, M. The cognitive basis of mathematical knowl- edge. Leng, A. Potter Eds.
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Cam- bridge: Cambridge University Press. Carey, S. The origin of concepts. New York: Oxford University Press. Carruthers, P. The innate mind. Oxford: Oxford University Press. Cohen, J. Frege and psychologism. Philosophical Papers, 27 1 , 45— Cohen Kadosh, R. Oxford handbook of mathematical cogni- tion. Conant, J. The search for logically alien thought: Descartes, Kant, Frege, ractatus. Philosophical Topics and the Tractatus. T , 20 1 , — Taylor Cowie, F. Nativism reconsidered reconsidered.. New York: Oxford Uni- versity Press. De Cruz, H.
An extended mind perspective on natural number representa- tion. Philosophical Psychology, 21 4 , — Dehaene, S. The number sense: How the mind creates mathematics 2nd ed. Dutilh Novaes, C. Formal languages in logic: A philosophical and cognitive analysis. Mathematical reasoning and external symbolic systems. Feldman, R. Naturalized epistemology. Zalta Ed.
Giaquinto, M. Francis Mind and Language, 7 4 , — Concepts and Calculations. Cipolotti Eds. Knowing numbers. Journal of Philosophy, 98 1 , 5— Goldman, A. A causal theory of knowing. Journal of Philosophy, 64, — Epistemology and cognition. Liaisons: Philosophy meets the cognitive and social sciences. Cambridge: MIT Press. Knowledge in a social world. Oxford: Clarendon Press. Philosophy and Phe- nomenological Research, 71 2 , — Haack, S. Evidence and inquiry: Towards reconstruction in epistemology.
Oxford: Blackwell. Harman, G. Change in view: Principles of Reasoning. Jenkins, C. Grounding concepts: An empirical basis for arithmetical knowledge. How we reason. Johnson-Laird, P. Hillsdale: Lawrence Erlbaum Associates, Inc. Kim, J. The role of perception in a priori knowledge: Some remarks. Philo- sophical Studies, 40, — Kitcher, P. Philosophical Review, 86, — The nature of mathematical knowledge.
Kornblith, H. Introduction: What is naturalistic epistemology? Korn- blith Ed.
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Naturalistic epistemology and its critics. Philosophical Topics, 23 1 , — Knowledge and its place in nature. Kusch, M. Psychologism: A case study in the sociology of philosophical knowledge. Abingdon, UK: Routledge. Lakoff, G. Where mathematics comes from: How the embod- ied mind brings mathematics into being. New York: Basic Books. Taylor Longo, G. Mathematical intuition and the cognitive roots of mathematical concepts. Horsten and I. Maddy,, P.
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Perception and mathematical intuition. Philosophical Review, 89 2 , — Maddy, P. Realism in mathematics. Second philosophy: A naturalistic method. The logical must. Wittgenstein on logic. McCulloch, W. What is a number that a man may know it, and a man, that he may know a number? Pantsar, M. An empirically feasible approach to the epistemology of arith- metic. Synthese, 17 , — Francis Pantsar,, M. Bootstrapping of the natural number concept: Regu- larity,, progression and beat induction. Papineau, D. Platonism, metaphor, and mathematics. Dia- logue, 43 1 , 47— Paseau, A.
Naturalism in mathematics and the authority of philosophy. Brit- ish Journal for the Philosophy of Science, 56, — Piaget, J. New York: W. Quine, W. Epistemology naturalized. In Ontological relativity and other essays pp. New York: Columbia Press.