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Russell’s method of analysis and the axioms of mathematics

In Sandra Lapointe Christopher Pincock (ed.), Innovations in the History of Analytical Philosophy. London: Palgrave-Macmillan. pp. 105-126 (2017)

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  1. Reichenbach, Russell and scientific realism.Christopher Pincock - 2021 - Synthese 199 (3-4):8485-8506.
    This paper considers how to best relate the competing accounts of scientific knowledge that Russell and Reichenbach proposed in the 1930s and 1940s. At the heart of their disagreements are two different accounts of how to best combine a theory of knowledge with scientific realism. Reichenbach argued that a broadly empiricist epistemology should be based on decisions. These decisions or “posits” informed Reichenbach’s defense of induction and a corresponding conception of what knowledge required. Russell maintained that a scientific realist must (...)
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  • Case for the Irreducibility of Geometry to Algebra†.Victor Pambuccian & Celia Schacht - 2022 - Philosophia Mathematica 30 (1):1-31.
    This paper provides a definitive answer, based on considerations derived from first-order logic, to the question regarding the status of elementary geometry, whether elementary geometry can be reduced to algebra. The answer we arrive at is negative, and is based on a series of structural questions that can be asked only inside the geometric formal theory, as well as the consideration of reverse geometry, which is the art of finding minimal axiom systems strong enough to prove certain geometrical theorems, given (...)
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