LEADER 02832nam 2200481 450 001 996418194603316 005 20210307160707.0 010 $a3-030-56700-1 024 7 $a10.1007/978-3-030-56700-2 035 $a(CKB)4100000011493495 035 $a(DE-He213)978-3-030-56700-2 035 $a(MiAaPQ)EBC6369425 035 $a(PPN)251095371 035 $a(EXLCZ)994100000011493495 100 $a20210307d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe essence of numbers /$fFre?de?ric Patras 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XI, 176 p. 1 illus.) 225 1 $aLecture notes in mathematics, History of mathematics subseries ;$vVolume 2278 311 $a3-030-56699-4 320 $aIncludes bibliographical references and index. 330 $aThis book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves. 410 0$aLecture notes in mathematics (Springer-Verlag).$pHistory of mathematics subseries ;$vVolume 2278. 606 $aNumber theory$xHistory 606 $aMathematics$xPhilosophy$xHistory 615 0$aNumber theory$xHistory. 615 0$aMathematics$xPhilosophy$xHistory. 676 $a512.7 700 $aPatras$b Fre?de?ric$0596450 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418194603316 996 $aPossibilité des nombres$91907567 997 $aUNISA