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Lectures on the philosophy of mathematics / [electronic resource]
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| 자료유형 | E-Book |
|---|---|
| 개인저자 | Hamkins, Joel David. |
| 단체저자명 | Recorded Books, Inc. |
| 서명/저자사항 | Lectures on the philosophy of mathematics /Joel David Hamkins.[electronic resource] |
| 발행사항 | [S.l.] : The MIT Press, 2021. |
| 형태사항 | 1 online resource |
| 소장본 주기 | Master record variable field(s) change: 050, 650 |
| ISBN | 9780262362658 0262362651 |
| 발행자번호 | EB00822532 |
| 내용주기 | Intro -- Title Page -- Copyright -- Dedication -- Table of Contents -- Preface -- About the Author -- 1. Numbers -- 1.1. Numbers versus numerals -- 1.2. Number systems -- Natural numbers -- Integers -- Rational numbers -- 1.3. Incommensurable numbers -- An alternative geometric argument -- 1.4. Platonism -- Plenitudinous platonism -- 1.5. Logicism -- Equinumerosity -- The Cantor-Hume principle -- The Julius Caesar problem -- Numbers as equinumerosity classes -- Neologicism -- 1.6. Interpreting arithmetic -- Numbers as equinumerosity classes -- Numbers as sets -- Numbers as primitives Numbers as morphisms -- Numbers as games -- Junk theorems -- Interpretation of theories -- 1.7. What numbers could not be -- The epistemological problem -- 1.8. Dedekind arithmetic -- Arithmetic categoricity -- 1.9. Mathematical induction -- Fundamental theorem of arithmetic -- Infinitude of primes -- 1.10. Structuralism -- Definability versus Leibnizian structure -- Role of identity in the formal language -- Isomorphism orbit -- Categoricity -- Structuralism in mathematical practice -- Eliminative structuralism -- Abstract structuralism -- 1.11. What is a real number? -- Dedekind cuts Theft and honest toil -- Cauchy real numbers -- Real numbers as geometric continuum -- Categoricity for the real numbers -- Categoricity for the real continuum -- 1.12. Transcendental numbers -- The transcendence game -- 1.13. Complex numbers -- Platonism for complex numbers -- Categoricity for the complex field -- A complex challenge for structuralism? -- Structure as reduct of rigid structure -- 1.14. Contemporary type theory -- 1.15. More numbers -- 1.16. What is a philosophy for? -- 1.17. Finally, what is a number? -- Questions for further thought -- Further reading -- Credits -- 2. Rigor 2.1. Continuity -- Informal account of continuity -- The definition of continuity -- The continuity game -- Estimation in analysis -- Limits -- 2.2. Instantaneous change -- Infinitesimals -- Modern definition of the derivative -- 2.3. An enlarged vocabulary of concepts -- 2.4. The least-upper-bound principle -- Consequences of completeness -- Continuous induction -- 2.5. Indispensability of mathematics -- Science without numbers -- Fictionalism -- The theory/metatheory distinction -- 2.6. Abstraction in the function concept -- The Devil's staircase -- Space-filling curves Conway base-13 function -- 2.7. Infinitesimals revisited -- Nonstandard analysis and the hyperreal numbers -- Calculus in nonstandard analysis -- Classical model-construction perspective -- Axiomatic approach -- "The" hyperreal numbers? -- Radical nonstandardness perspective -- Translating between nonstandard and classical perspectives -- Criticism of nonstandard analysis -- Questions for further thought -- Further reading -- Credits -- 3. Infinity -- 3.1. Hilbert's Grand Hotel -- Hilbert's bus -- Hilbert's train -- 3.2. Countable sets -- 3.3. Equinumerosity -- 3.4. Hilbert's half-marathon |
| 요약 | An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations. |
| 일반주제명 | Mathematics -- Philosophy. MATHEMATICS / History & Philosophy. Mathematics. |
| 언어 | 영어 |
| 기타형태 저록 | Print version:02625422349780262542234 |
| 대출바로가기 | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2483406 |
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| No. | 등록번호 | 청구기호 | 소장처 | 도서상태 | 반납예정일 | 예약 | 서비스 | 매체정보 |
|---|---|---|---|---|---|---|---|---|
| 1 | WE00020282 | 510.1 | 가야대학교/전자책서버(컴퓨터서버)/ | 대출가능 |
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