000			06784cam a2200721Ii 4500
001			ocn929851435
003			OCoLC
005			20220908100100.0
006			m o d
007			cr cnu|||unuuu
008			151118s2015 nju ob 001 0 eng d
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020			_a9781400874002 _q(electronic bk.)
020			_a1400874009 _q(electronic bk.)
020			_z9780691167510
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029	1		_aDEBBG _bBV043892574
035			_a(OCoLC)929851435
037			_a22573/ctt1dr3ct0 _bJSTOR
037			_a9452411 _bIEEE
050		4	_aQA8.4
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082	0	4	_a510.1 _223
049			_aMAIN
100	1		_aFerreir�os Dom�inguez, Jos�e, _eauthor. _964619
245	1	0	_aMathematical knowledge and the interplay of practices / _cJos�e Ferreir�os.
264		1	_aPrinceton : _bPrinceton University Press, _c2015.
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
504			_aIncludes bibliographical references and index.
588	0		_aOnline resource; title from PDF title page (Ebsco, viewed on November 19, 2015).
505	0		_aCover -- Contents -- List of Illustrations -- Foreword -- 1 On Knowledge and Practices: A Manifesto -- 2 The Web of Practices -- 2.1. Historical Work on Practices -- 2.2. Philosophers Working on Practices -- 2.3. What Is Mathematical Practice, Then? -- 2.4. The Multiplicity of Practices -- 2.5. The Interplay of Practices and Its Basis -- 3 Agents and Frameworks -- 3.1. Frameworks and Related Matters -- 3.2. Interlude on Examplars -- 3.3. On Agents -- 3.4. Counting Practices and Cognitive Abilities -- 3.5. Further Remarks on Mathematics and Cognition -- 3.6. Agents and "Metamathematical" Views -- 3.7. On Systematic Links -- 4 Complementarity in Mathematics -- 4.1. Formula and Meaning -- 4.2. Formal Systems and Intended Models -- 4.3. Meaning in Mathematics: A Tentative Approach -- 4.4. The Case of Complex Numbers -- 5 Ancient Greek Mathematics: A Role for Diagrams -- 5.1. From the Technical to the Mathematical -- 5.2. The Elements: Getting Started -- 5.3. On the Euclidean Postulates: Ruling Diagrams (and Their Reading) -- 5.4. Diagram-Based Mathematics and Proofs -- 5.5. Agents, Idealization, and Abstractness -- 5.6. A Look at the Future-Our Past -- 6 Advanced Math: The Hypothetical Conception -- 6.1. The Hypothetical Conception: An Introduction -- 6.2. On Certainty and Objectivity -- 6.3. Elementary vs. Advanced: Geometry and the Continuum -- 6.4. Talking about Objects -- 6.5. Working with Hypotheses: AC and the Riemann Conjecture -- 7 Arithmetic Certainty -- 7.1. Basic Arithmetic -- 7.2. Counting Practices, Again -- 7.3. The Certainty of Basic Arithmetic -- 7.4. Further Clarifications -- 7.5. Model Theory of Arithmetic -- 7.6. Logical Issues: Classical or Intuitionistic Math? -- 8 Mathematics Developed: The Case of the Reals -- 8.1. Inventing the Reals -- 8.2. "Tenths" to the Infinite: Lambert and Newton -- 8.3. The Number Continuum.
505	8		_a8.4. The Reinvention of the Reals -- 8.5. Simple Infinity and Arbitrary Infinity -- 8.6. Developing Mathematics -- 8.7. Mathematical Hypotheses and Scientific Practices -- 9 Objectivity in Mathematical Knowledge -- 9.1. Objectivity and Mathematical Hypotheses: A Simple Case -- 9.2. Cantor's "Purely Arithmetical" Proofs -- 9.3. Objectivity and Hypotheses, II: The Case of p(N) -- 9.4. Arbitrary Sets and Choice -- 9.5. What about Cantor's Ordinal Numbers? -- 9.6. Objectivity and the Continuum Problem -- 10 The Problem of Conceptual Understanding -- 10.1. The Universe of Sets -- 10.2. A "Web-of-Practices" Look at the Cumulative Picture -- 10.3. Conceptual Understanding -- 10.4. Justifying Set Theory: Arguments Based on the Real-Number Continuum -- 10.5. By Way of Conclusion -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.
520	8		_aAnnotation _bThis book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, Jose Ferreiros uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results.Describing a historically oriented, agent-based philosophy of mathematics, Ferreiros shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreiros demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty.Offering a wealth of philosophical and historical insights, "Mathematical Knowledge and the Interplay of Practices" challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science."
590			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aMathematics _xPhilosophy. _921296
650		6	_aMath�ematiques _xPhilosophie. _964620
650		7	_aMATHEMATICS _xEssays. _2bisacsh _964120
650		7	_aMATHEMATICS _xPre-Calculus. _2bisacsh _964121
650		7	_aMATHEMATICS _xReference. _2bisacsh _964122
650		7	_aMATHEMATICS _xGeneral. _2bisacsh _94635
650		7	_aMathematics _xPhilosophy. _2fast _0(OCoLC)fst01012213 _921296
655		4	_aElectronic books. _93294
776	0	8	_iPrint version: _nDruck-Ausgabe _tFerreir�os, Jos�e. Mathematical Knowledge and the Interplay of Practices
856	4	0	_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452411
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938			_aEBSCOhost _bEBSC _n1063799
938			_aProQuest MyiLibrary Digital eBook Collection _bIDEB _ncis32858876
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