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001469583 020__ $$a9783031273049$$q(electronic bk.)
001469583 020__ $$a3031273044$$q(electronic bk.)
001469583 020__ $$z9783031273032
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001469583 0247_ $$a10.1007/978-3-031-27304-9$$2doi
001469583 035__ $$aSP(OCoLC)1382320348
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001469583 08204 $$a510.1$$223/eng/20230613
001469583 1001_ $$aFelgner, Ulrich,$$eauthor.
001469583 24010 $$aPhilosophie der Mathematik in der Antike und in der Neuzeit.$$lEnglish
001469583 24510 $$aPhilosophy of mathematics in antiquity and in modern times /$$cUlrich Felgner.
001469583 264_1 $$aCham :$$bBirkhäuser,$$c[2023]
001469583 264_4 $$c©2023
001469583 300__ $$a1 online resource (xi, 317 pages) :$$billustrations.
001469583 336__ $$atext$$btxt$$2rdacontent
001469583 337__ $$acomputer$$bc$$2rdamedia
001469583 338__ $$aonline resource$$bcr$$2rdacarrier
001469583 4901_ $$aScience networks historical studies ;$$vvolume 62
001469583 504__ $$aIncludes bibliographical references and indexes.
001469583 5050_ $$aThe concept of mathematics -- Plato's philosophy of mathematics -- The Aristotelian conception of mathematics -- The axiomatic method of Euclid -- Finitism in Greek mathematics -- The paradoxes of Zeno -- On certainty in mathematics -- The Cartesian nativism, the Prometheus myth, Augustinian illuminism, and Cartesian rationalism -- John Locke's thoughts on mathematics -- Rationalism -- Empiricism in mathematics -- Immanuel Kant's conception of mathematics -- Psychologism in mathematics -- Logicism -- The concept of "set" -- Contemporary Platonism -- The problem of non-constructive proofs of existence -- The formal and the contentual position -- Dedekind and the emergence of structuralism -- Hilbert's critical philosophy -- Epilogue -- Index of names -- Index of subjects -- Index of abbreviations.
001469583 506__ $$aAccess limited to authorized users.
001469583 520__ $$aPhilosophy of Mathematics is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time. The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.
001469583 546__ $$aTranslated from the German.
001469583 588__ $$aDescription based on print version record.
001469583 650_0 $$aMathematics$$xPhilosophy$$xHistory.
001469583 650_0 $$aMathematics$$xHistory.
001469583 655_7 $$aHistory.$$2fast$$0(OCoLC)fst01411628
001469583 655_0 $$aElectronic books.
001469583 77608 $$iPrint version:$$aFelgner, Ulrich.$$tPhilosophy of mathematics in antiquity and in modern times.$$dCham : Springer, 2023$$z9783031273032$$w(OCoLC)1371862896
001469583 830_0 $$aScience networks historical studies ;$$vv. 62.
001469583 852__ $$bebk
001469583 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-27304-9$$zOnline Access$$91397441.1
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