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The neo-Fregean program in the philosophy of arithmetic

In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 87--112 (2006)

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  1. Philosophical method and Galileo's paradox of infinity.Matthew W. Parker - 2009 - In Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. World Scientific.
    We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet less (...)
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  • Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos.Melanie Frappier, Derek Brown & Robert DiSalle (eds.) - 2011 - Dordrecht and London: Springer.
    The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...)
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