03296nam 22006255 450 991048456550332120200919232904.03-319-05816-910.1007/978-3-319-05816-0(CKB)3710000000119117(DE-He213)978-3-319-05816-0(SSID)ssj0001244598(PQKBManifestationID)11701003(PQKBTitleCode)TC0001244598(PQKBWorkID)11319295(PQKB)10208436(MiAaPQ)EBC6312708(MiAaPQ)EBC1731082(Au-PeEL)EBL1731082(CaPaEBR)ebr10969107(OCoLC)880689138(PPN)178779806(EXLCZ)99371000000011911720140512d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierA Mathematical Prelude to the Philosophy of Mathematics /by Stephen Pollard1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XI, 202 p.) Bibliographic Level Mode of Issuance: Monograph3-319-05815-0 Includes bibliographical references and index.Preface -- Chapter 1: Recursion, Induction -- Chapter 2: Peano Arithmetic, Incompleteness -- Chapter 3: Hereditarily Finite Lists -- Chapter 4: Zermelian Lists -- Chapter 5: The Hierarchy of Sets. Chapter 6: Frege Arithmetic -- Chapter 7: Intuitionist Logic -- Chapter 8. Solutions of Odd-Numbered Exercises -- Index.This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic, and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.Philosophy and scienceMathematical logicPhilosophy of Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/E34000Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Philosophy and science.Mathematical logic.Philosophy of Science.Mathematical Logic and Foundations.510.1Pollard Stephenauthttp://id.loc.gov/vocabulary/relators/aut1227486MiAaPQMiAaPQMiAaPQBOOK9910484565503321A Mathematical Prelude to the Philosophy of Mathematics2849984UNINA