Social Constructivism as a Philosophy of MathematicsProposing social constructivism as a novel philosophy of mathematics, this book is inspired by current work in sociology of knowledge and social studies of science. It extends the ideas of social constructivism to the philosophy of mathematics, developing a whole set of new notions. The outcome is a powerful critique of traditional absolutist conceptions of mathematics, as well as of the field of philosophy of mathematics itself. Proposed are a reconceptualization of the philosophy of mathematics and a new set of adequacy criteria. The book offers novel analyses of the important but under-recognized contributions of Wittgenstein and Lakatos to the philosophy of mathematics. Building on their ideas, it develops a theory of mathematical knowledge and its relation to the social context. It offers an original theory of mathematical knowledge based on the concept of conversation, and develops the rhetoric of mathematics to account for proof in mathematics. Another novel feature is the account of the social construction of subjective knowledge, which relates the learning of mathematics to philosophy of mathematics via the development of the individual mathematician. It concludes by considering the values of mathematics and its social responsibility. |
Contents
A Critique of Absolutism in the Philosophy of Mathematics | 1 |
Reconceptualizing the Philosophy of Mathematics | 39 |
Wittgensteins Philosophy of Mathematics | 64 |
Lakatoss Philosophy of Mathematics | 97 |
The Social Construction of Objective Knowledge | 131 |
Conversation and Rhetoric | 162 |
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Common terms and phrases
absolute absolutist accepted argues assumptions axioms basis central concepts concerns conjecture construction conversation criteria criticism cultural dialectical dialogue discourse ematics epistemological existence explicit fallibilism fallibilist formal Foundations of Mathematics Frege genesis GLMD Harré Hegel heuristic history of mathematics human individual informal mathematical intuition intuitionism intuitionists justification Kitcher Lakatos Lakatos's LMD Lakatos's philosophy language games linguistic logic of mathematical London mathematical community mathematical discovery mathematical knowl mathematical knowledge mathematical objects mathematical practice mathematical proof mathematical theories mathematical truth mathematicians Mathematics Education matics meaning methods nature of mathematics notion objective knowledge objects of mathematics persons philosophy of mathe philosophy of mathematics philosophy of science Platonism Popper position problems propositional knowledge propositions refutation rejection rhetoric role rules school mathematics scientific semiotic shared signifiers social constructivism social constructivist social context structure tacit knowledge theorems tion traditional transformations University Press values Vygotsky warranting Wittgenstein 1978 Wittgenstein's philosophy