Among current views in the philosophy of mathematics and its foundations, structuralism has one of the leading roles. The origins of its core idea — that, roughly, mathematics is the study of structures and the relations holding among its places or the objects occupying those places, rather than the study of such objects themselves — can be traced back, like that of rival views such as logicism, to the developments in mathematics, geometry, and philosophy which took place around the middle of the nineteenth century. Analogously to the logicist tradition inaugurated by the works of Frege, structuralism too finds its inspiring hero in another German mathematician, Richard Dedekind, and a discussion of some of its founding insights and basic thoughts can be retrieved by looking at mathematicians and philosophers of mathematics working in those years and in subsequent decades. After criticism by Russell, the view had a rebirth in the second half of the past century thanks to a famous argument due to Paul Benacerraf [1965], and has since being explored in details and developed in various varieties. This book surveys and critically discusses several varieties of mathematical structuralism and their current relevance.
CRITICAL STUDIES/BOOK REVIEWS of Geoffrey Hellman and Stewart Shapiro. Mathematical Structuralism. Cambridge Elements in the Philosophy of Mathematics, Pene- lope Rush and Stewart Shapiro, eds. Cambridge University Press, 2019.
Andrea Sereni
2020-01-01
Abstract
Among current views in the philosophy of mathematics and its foundations, structuralism has one of the leading roles. The origins of its core idea — that, roughly, mathematics is the study of structures and the relations holding among its places or the objects occupying those places, rather than the study of such objects themselves — can be traced back, like that of rival views such as logicism, to the developments in mathematics, geometry, and philosophy which took place around the middle of the nineteenth century. Analogously to the logicist tradition inaugurated by the works of Frege, structuralism too finds its inspiring hero in another German mathematician, Richard Dedekind, and a discussion of some of its founding insights and basic thoughts can be retrieved by looking at mathematicians and philosophers of mathematics working in those years and in subsequent decades. After criticism by Russell, the view had a rebirth in the second half of the past century thanks to a famous argument due to Paul Benacerraf [1965], and has since being explored in details and developed in various varieties. This book surveys and critically discusses several varieties of mathematical structuralism and their current relevance.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
