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Confirming mathematical theories: An ontologically agnostic stance

Anthony Peressini

Synthese 118 (2):257-277 (1999)

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Mathematical Practice and Naturalist Epistemology: Structures with Potential for Interaction.Bart Van Kerkhove & Bendegem - 2005 - Philosophia Scientiae 9 (2):61-78.details In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and epistemology. Download Export citation Bookmark
Mathematical naturalism: Origins, guises, and prospects. [REVIEW]Bart Van Kerkhove - 2006 - Foundations of Science 11 (1-2):5-39.details During the first half of the twentieth century, mainstream answers to the foundational crisis, mainly triggered by Russell and Gödel, remained largely perfectibilist in nature. Along with a general naturalist wave in the philosophy of science, during the second half of that century, this idealist picture was finally challenged and traded in for more realist ones. Next to the necessary preliminaries, the present paper proposes a structured view of various philosophical accounts of mathematics indebted to this general idea, laying the (...) Download Export citation Bookmark 4 citations
Proof, Reliability, and Mathematical Knowledge.Anthony Peressini - 2003 - Theoria 69 (3):211-232.details With respect to the confirmation of mathematical propositions, proof possesses an epistemological authority unmatched by other means of confirmation. This paper is an investigation into why this is the case. I make use of an analysis drawn from an early reliability perspective on knowledge to help make sense of mathematical proofs singular epistemological status. Download Export citation Bookmark 3 citations
Confirmational holism and its mathematical (w)holes.Anthony Peressini - 2008 - Studies in History and Philosophy of Science Part A 39 (1):102-111.details I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science. Download Export citation Bookmark 3 citations
Mathematical Naturalism: Origins, Guises, and Prospects.Bart Kerkhove - 2006 - Foundations of Science 11 (1):5-39.details During the first half of the twentieth century, mainstream answers to the foundational crisis, mainly triggered by Russell and Gödel, remained largely perfectibilist in nature. Along with a general naturalist wave in the philosophy of science, during the second half of that century, this idealist picture was finally challenged and traded in for more realist ones. Next to the necessary preliminaries, the present paper proposes a structured view of various philosophical accounts of mathematics indebted to this general idea, laying the (...) Download Export citation Bookmark

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