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A sophisticated original introduction to the philosophy of mathematics from one of its leading contemporary scholarsMathematics is one of humanitys most successful yet puzzling endeavors It is a model of precision and objectivity but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers sets and functions How can these two aspects of mathematics be reconciled This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question the philosophy of mathematicsWritten by Øystein Linnebo one of the worlds leading scholars on the subject the book introduces all of the classical approaches to the field including logicism formalism intuitionism empiricism and structuralism It also contains accessible introductions to some more specialized issues such as mathematical intuition potential infinity the iterative conception of sets and the search for new mathematical axioms The groundbreaking work of German mathematician and philosopher Gottlob Frege one of the founders of analytic philosophy figures prominently throughout the book Other important thinkers whose work is introduced and discussed include Immanuel Kant John Stuart Mill David Hilbert Kurt Gödel W V Quine Paul Benacerraf and Hartry H FieldSophisticated but clear and approachable this is an essential introduction for all students and teachers of philosophy as well as mathematicians and others who want to understand the foundations of mathematics
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A sophisticated original introduction to the philosophy of mathematics from one of its leading contemporary scholarsMathematics is one of humanitys most successful yet puzzling endeavors It is a model of precision and objectivity but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers sets and functions How can these two aspects of mathematics be reconciled This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question the philosophy of mathematicsWritten by Øystein Linnebo one of the worlds leading scholars on the subject the book introduces all of the classical approaches to the field including logicism formalism intuitionism empiricism and structuralism It also contains accessible introductions to some more specialized issues such as mathematical intuition potential infinity the iterative conception of sets and the search for new mathematical axioms The groundbreaking work of German mathematician and philosopher Gottlob Frege one of the founders of analytic philosophy figures prominently throughout the book Other important thinkers whose work is introduced and discussed include Immanuel Kant John Stuart Mill David Hilbert Kurt Gödel W V Quine Paul Benacerraf and Hartry H FieldSophisticated but clear and approachable this is an essential introduction for all students and teachers of philosophy as well as mathematicians and others who want to understand the foundations of mathematics
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