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1. Philosophy and model theory [2018]
 Button, Tim, author.
 First edition.  Oxford : Oxford University Press, 2018.
 Description
 Book — xvi, 517 pages : illustrations ; 24 cm
 Summary

 A: Reference and realism
 1: Logics and languages
 2: Permutations and referential indeterminacy
 3: Ramsey sentences and Newman's objection
 4: Compactness, infinitesimals, and the reals
 5: Sameness of structure and theory B: Categoricity
 6: Modelism and mathematical doxology
 7: Categoricity and the natural numbers
 8: Categoricity and the sets
 9: Transcendental arguments
 10: Internal categoricity and the natural numbers
 11: Internal categoricity and the sets
 12: Internal categoricity and truth
 13: Booleanvalued structures C: Indiscernibility and classification
 14: Types and Stone spaces
 15: Indiscernibility
 16: Quantifiers
 17: Classification and uncountable categoricity D: Historical appendix Wilfrid Hodges: A short history of model theory.
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(source: Nielsen Book Data) 9780198790402 20190204
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B791 .B95 2018  Unknown 
 Essays. Selections
 Holt, Jim, 1954 author.
 First edition.  New York : Farrar, Straus and Giroux, 2018.
 Description
 Book — xi, 368 pages ; 24 cm
 Summary

 Part I: The moving image of eternity. When Einstein walked with Gödel ; Time
 the grand illusion?
 Part II: Numbers in the brain, in platonic heaven, and in society. Numbers guy: the neuroscience of math ; The Riemann Zeta conjecture and the laughter of the primes ; Sir Francis Galton, the father of statistics...and eugenics
 Part III: Mathematics, pure and impure. A mathematical romance ; The avatars of higher mathematics ; Benoit Mandelbrot and the discovery of fractals
 Part IV: Higher dimensions, abstract maps. Geometrical creatures ; A comedy of colors
 Part V: Infinity, large and small. Infinite visions: Georg Cantor v. David Foster Wallace ; Worshipping infinity: why the Russians do and the French don't ; The dangerous idea of the infinitesimal
 Part VI: Heroism, tragedy, and the computer age. The Ada perplex: was Byron's daughter the first coder? ; Alan Turing in life, logic, and death ; Dr. Strangelove makes a thinking machine ; Smarter, happier, more productive
 Part VII: The cosmos reconsidered. The string theory wars: is beauty truth? ; Einstein, "Spooky action," and the reality of space ; How will the Universe end?
 Part VII: Quick studies: a selection of shorter essays. Little big man ; Doom soon ; Death: bad? ; The lookingglass war ; Astrology and the demarcation problem ; Gödel takes on the U.S. Constitution ; The law of least action ; Emmy Noether's beautiful theorem ; Is logic coercive? ; Newcomb's problem and the paradox of choice ; The right not to exist ; Can't anyone get Heisenberg right? ; Overconfidence and the Monty Hall problem ; The cruel law of eponymy ; The mind of a rock
 Part IX: God, sainthood, truth, and bullshit. Dawkins and the deity ; On moral sainthood ; Truth and reference: a philosophical feud ; Say anything.
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PS3608 .O4943595 A6 2018  Unknown 
 Silva, Jairo José da, author.
 Cham, Switzerland : Springer, [2017]
 Description
 Book — vii, 275 pages ; 25 cm.
 Summary

 1. The applicability of mathematics in science: a problem?.
 2. Form and Content. Mathematics as a formal science.
 3. Mathematical ontology: what does it mean to exist?.
 4. Mathematical structures: what are they and how do we know them?.
 5. Playing with structures: the applicability of mathematics.
 6. How to use mathematics to find out how the world is.
 7. Logical, epistemological, and philosophical conclusions.
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(source: Nielsen Book Data) 9783319630724 20171017
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4. Philosophy of mathematics [2017]
 Linnebo, Øystein, author.
 Princeton, New Jersey : Princeton University Press, [2017]
 Description
 Book — vi, 203 pages ; 23 cm.
 Summary

 Acknowledgments vii Introduction
 1
 1 Mathematics as a Philosophical Challenge
 4
 2 Frege's Logicism
 21
 3 Formalism and Deductivism
 38
 4 Hilbert's Program
 56
 5 Intuitionism
 73
 6 Empiricism about Mathematics
 88
 7 Nominalism
 101
 8 Mathematical Intuition
 116
 9 Abstraction Reconsidered
 126
 10 The Iterative Conception of Sets
 139
 11 Structuralism
 154
 12 The Quest for New Axioms
 170 Concluding Remarks
 183 Bibliography
 189 Index 199.
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(source: Nielsen Book Data) 9780691161402 20171227
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 Delo akademika Nikolai͡a Nikolaevicha Luzina. English.
 Providence, Rhode Island : American Mathematical Society, [2016]
 Description
 Book — xxxi, 375 pages, 8 unnumbered pages of plates : illustrations ; 26 cm.
 Summary

 * Introduction* The case of academician Luzin in the collective memory of the scientific community* Minutes of the meetings of the USSR Academy of Sciences Commission in the case of academician Luzin* Minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin:
 7 July Minutes of the meeting of the USSR Academy of Sciences Commission on the matter of academician Luzin*9 July Minutes of the meeting of the USSR Academy of Sciences Commission on the matter of academician Luzin*11 July Minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin*13 July Minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin*15 July Commentaries on the minutes of the meetings of the USSR Academy of Sciences Commission in the case of academician Luzin* Commentaries on the minutes of the meetings of the USSR Academy of Sciences Commission in the case of academician Luzin Commentary on the minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin*7 July
 1936 Commentary on the minutes of the USSR Academy of Sciences Commission in the matter of academician Luzin*9 July
 1936 Commentary on the minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin*11 July
 1936 Commentary on the minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin*13 July
 1936 Commentary on the minutes of the meeting of the USSR Academy of Sciences Commission in the matter of academician Luzin*15 July
 1936 Literature Appendices* Appendices introduction* A pleasant disillusionment* Reply to academician N. Luzin* Enemies wearing a Soviet mask* Letter from L. Z. Mekhlis, editor of $\textit{Pravda}$, to the Central Committee,
 3 July 1936* Resolution concerning the articles "Response to academician Luzin" and "Enemies wearing a Soviet mask" in $\textit{Pravda}$* Draft of the proposal of the special session of the Presidium of the USSR Academy of Sciences,
 4 July 1936* Letter from P. L. Kapitsa to Molotov,
 6 July 1936* Excerpt from the minutes of the Presidum meeting of
 7 July 1936* Letters from V. I. Vernadski iand N. V. Nasonov to the Academy of Sciences Division of Mathematical and Natural Sciences and to academicians A. E. Fersman and N. P. Gorbunov in support of academician Luzin* Letter from academician N. N. Luzin to the Central Committee of the Communist Party
 7 July 1936* Traditions of servility* Resolution of the General Assembly of Scientists of the Department of Mechanics and Mathematics and Institute of Mathematics, Mechanics, and Astronomy at Moscow University* Letter from Luzin to an undetermined addressee,
 11 July 1936* Enemies wearing a Soviet mask* The Leningrad scholars respond* Letter from L. Z. Mekhlis, Editor of Pravda, to Stalin and Molotov,
 14 July 1936* The enemy exposed Luzin's statement to the Presidium of the Academy of Sciences,
 14 July 1936* Academician Gubkin on socalled academician Luzin* The Belarus scholars on the exposed enemy Luzin* The scholarly community condemns enemies wearing a Soviet mask* Note accompanying the draft of the findings of the Presidium of the USSR Academy of Sciences regarding academician N. N. Luzin,
 25 July 1936* Conclusion of the Commission On academician N. N. Luzin* Findings of the Presidium of the USSR Academy of Sciences,
 5 August 1936* To rid academia of Luzinism* Glossary of Soviet terms and people* Subject index* Name index.
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(source: Nielsen Book Data) 9781470426088 20160711
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Q127 .S65 D4513 2016  Unknown 
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Q127 .S65 D4513 2016  Unknown 
6. Rigor and structure [2015]
 Burgess, John P., 1948
 1st ed.  Oxford, UK : Oxford University Press, 2015.
 Description
 Book — vii, 215 p. ; 23 cm
 Summary

 Preface
 Acknowledgments
 1. Rigor and Rigorization
 2. Rigor and Foundations
 3. Structure and Structuralism
 4. Structure and Foundations
 Bibliography.
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(source: Nielsen Book Data) 9780198722229 20160618
Philosophy Library (Tanner), Science Library (Li and Ma)
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QA8.4 .B855 2015  Unknown 
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QA8.4 .B855 2015  Unknown 
 Hacking, Ian.
 New York : Cambridge University Press, 2014.
 Description
 Book — xv, 290 pages ; 23 cm
 Summary

 Foreword
 1. A Cartesian introduction
 2. What makes mathematics mathematics?
 3. Why is there philosophy of mathematics?
 4. Proofs
 5. Applications
 6. In Plato's name
 7. CounterPlatonisms Disclosures.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9781107658158 20160612
Philosophy Library (Tanner), Science Library (Li and Ma)
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QA8.4 .H33 2014  Unknown 
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QA8.4 .H33 2014  Unknown 
8. Free will and modern science [2011]
 Oxford ; New York : Published for the British Academy by Oxford University Press, 2011.
 Description
 Book — xviii, 206 p. : ill. ; 24 cm.
 Summary

 Foreword
 Introduction
 1. Does Brain Science Change our View of Free Will?
 2. Free Will and the Sciences of Human Agency
 3. Physicalism and the Determination of Action
 4. Dualism and the Determination of Action
 5. Determinacy or its Absence in the Brain
 6. Godel's incompleteness theorems, free will, and mathematical thought
 7. Response to Feferman
 8. The Impossibility of Ultimate Moral Responsibility?
 9. Moral Responsibility and the Concept of Agency
 10. Substance Dualism and its Rationale
 11. What Kind of Responsibility must Criminal Law Presuppose?
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(source: Nielsen Book Data) 9780197264898 20160607
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 Graham, Loren R.
 Cambridge, Mass. : Belknap Press of Harvard University Press, 2009.
 Description
 Book — x, 239 p. : ill., ports. ; 22 cm.
 Summary

 Storming a monastery
 A crisis in mathematics
 The French trio : Borel, Lebesgue, Baire
 The Russian trio : Egorov, Luzin, Florensky
 Russian mathematics and mysticism
 The legendary Lusitania
 Fates of the Russian trio
 Lusitania and after
 The human in mathematics, then and now.
(source: Nielsen Book Data) 9780674032934 20160528
 Berlin ; New York : Walter De Gruyter, c2008.
 Description
 Book — vi, 327 p. : ill. ; 24 cm.
 Summary

The development of the calculus during the 17th century was successful in mathematical practice, but raised questions about the nature of infinitesimals: were they real or rather fictitious? This collection of essays, by scholars from Canada, the US, Germany, Japan and Switzerland, gives a comprehensive study of the controversies over the nature and status of the infinitesimal.Aside from Leibniz, the scholars considered are Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. The collection also contains newly discovered marginalia of Leibniz to the writings of Hobbes.
(source: Nielsen Book Data) 9783110202168 20160528
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B2598 .I54 2008  Unknown 
11. Mathematical thought and its objects [2008]
 Parsons, Charles, 1933
 Cambridge ; New York : Cambridge University Press, 2008.
 Description
 Book — xx, 378 p. ; 24 cm.
 Summary

 Preface
 1. Objects and logic
 2. Structuralism and nominalism
 3. Modality and structuralism
 4. A problem about sets
 5. Intuition
 6. Numbers as objects
 7. Intuitive arithmetic and its limits
 8. Mathematical induction
 9. Reason.
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(source: Nielsen Book Data) 9780521452793 20160528
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QA8.4 .P366 2008  Unknown 
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QA8.4 .P366 2008  Available 
 Burgess, John P., 1948
 Cambridge ; New York : Cambridge University Press, 2008.
 Description
 Book — xiii, 301 p. : ill. ; 24 cm.
 Summary

 Introduction Part I. Mathematics:
 1. Numbers and ideas
 2. Why I am not a nominalist
 3. Mathematics and Bleak House
 4. Quine, analyticity, and philosophy of mathematics
 5. Being explained away
 6. E pluribus unum
 7. Logicism: a new look Part II. Models, Modality, and More:
 8. Tarski's tort
 9. Which modal logic is the right one?
 10. Can truth out?
 11. Quinus ab omni noevo vindicatus
 12. Translating names
 13. Relevance: a fallacy?
 14. Dummett's case for intuitionism.
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(source: Nielsen Book Data) 9780521880343 20160528
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QA8.6 .B87 2008  Unknown 
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13. Philosophy of mathematics : a contemporary introduction to the world of proofs and pictures [2008]
 Brown, James Robert.
 2nd ed.  New York : Routledge, 2008.
 Description
 Book — xiv, 245 p. : ill. ; 24 cm.
 Summary

 Contents Preface and Acknowledgements
 Chapter 1: Introduction: The Mathematical Image
 Chapter 2: Platonism
 Chapter 3: Pictureproofs and Platonism
 Chapter 4: What is Applied Mathematics?
 Chapter 5: Hilbert and Godel
 Chapter 6: Knots and Notation
 Chapter 7: What is a Definition?
 Chapter 8: Constructive Approaches
 Chapter 9: Proofs, Pictures and Procedures in Wittgenstein
 Chapter 10: Computation, Proof and Conjecture
 Chapter 11: How to Refute the Continuum Hypothesis
 Chapter 12: Calling the Bluff Notes Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780415960472 20160527
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QA8.4 .B76 2008  Unknown 
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QA8.4 .B76 2008  Unknown 
 New York ; Oxford : Oxford University Press, 2007.
 Description
 Book — xv, 833 p. ; 25 cm.
 Summary

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially selfcontained, serve both to introduce the reader to the subject and to engage in it at its frontiers.Certain major positions are represented by two chaptersone supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a groundbreaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
(source: Nielsen Book Data) 9780195325928 20160528
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QA8.4 .O94 2007  Unknown 
 New York : Springer, c2006.
 Description
 Book — xxi, 326 p. : ill. ; 24 cm.
 Summary

 Introduction by Reuben Hersh. A. Renyi: Socratic Dialogue. C. Celluci: Filosofia e Matematica, introduction. W. Thurston: On Proof and Progress in Mathematics. A. Aberdein: The Informal Logic of Mathematical Proof. Y. Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology. B. Rotman: Towards a Semiotics of Mathematics. D. Mackenzie: Computers and the Sociology of Mathematical Proof. T. Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management. R. Nunez: Do Numbers Really Move? T. Gowers: Does Mathematics Need a Philosophy? J. Azzouni: How and Why Mathematics is a Social Practice. G.C. Rota: The Pernicious Influence of Mathematics Upon Philosophy. J. Schwartz: The Pernicious Influence of Mathematics on Science. Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For?. A. Pickering: Concepts and the Mangle of Practice: Constructing Quaternions. E. Glas: Mathematics as Objective Knowledge and as Human Practice. L. White: The Locus of Mathematical Reality: An Anthropological Footnote. R. Hersh: Inner Vision, Outer Truth.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9780387257174 20160528
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QA8.6 .A13 2006  Unknown 
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QA8.6 .A13 2006  Unknown 
 Aczel, Amir D.
 New York : Broadway Books, c2005.
 Description
 Book — xiv, 273 p. : ill. ; 25 cm.
 Online
 Oxford ; New York : Oxford University Press, 2005.
 Description
 Book — xv, 833 p. ; 26 cm.
 Summary

 Philosophy of mathematics and its logic : introduction / Stewart Shapiro
 Apriority and application : philosophy of mathematics in the modern period / Lisa Shabel
 Later empiricism and logical positivism / John Skorupski
 Wittgenstein on philosophy of logic and mathematics / Juliet Floyd
 The logicism of Frege, Dedekind, and Russell / William Demopoulos, Peter Clark
 Logicism in the twentyfirst century / Bob Hale, Crispin Wright
 Logicism reconsidered / Agustín Rayo
 Formalism / Michael Detlefsen
 Intuitionism and philosophy / Carl Posy
 Intuitionism in mathematics / C.C. McCarty
 Intuitionism reconsidered / Roy Cook
 Quine and the web of belief / Michael D. Resnik
 Three forms of naturalism / Penelope Maddy
 Naturalism reconsidered / Alan Weir
 Nominalism / Charles Chihara
 Nominalism reconsidered / Gideon Rosen, John P. Burgess
 Structuralism / Geoffrey Hellman
 Structuralism reconsidered / Fraser MacBride
 Predicativity / Solomon Feferman
 Mathematics  application and applicability / Mark Steiner
 Logical consequence, proof theory, and model theory / Stewart Shapiro
 Logical consequence from a constructivist point of view / Dag Prawitz
 Relevance in reasoning / Neil Tennant
 No requirement of relevance / John P. Burgess
 Higherorder logic / Stewart Shapiro
 Higherorder logic reconsidered / Ignacio Jané.
(source: Nielsen Book Data) 9780195148770 20160528
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QA8.4 .O94 2005  Unknown 
 Franzén, Torkel.
 Urbana, Ill. : Association for Symbolic Logic ; Wellesley, Mass. : A K Peters, c2004.
 Description
 Book — xi, 251 p. ; 23 cm.
 Summary

Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results necessary to understand the arguments are introduced as needed, making the presentation selfcontained and thorough.
(source: Nielsen Book Data) 9781568811758 20160528
Godels Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results necessary to understand the arguments are introduced as needed, making the presentation selfcontained and thorough.
(source: Nielsen Book Data) 9781568811741 20160528
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QA9.56 .F73 2004  Unknown 
 Philosophie der Arithmetik. English
 Husserl, Edmund, 18591938.
 Dordrecht ; Boston : Kluwer Academic Publishers, c2003.
 Description
 Book — lxiv, 513 p. ; 25 cm.
 Summary

 Foreword. First Part: The Authentic Concepts of Multiplicity, Unity and Whole Number. Introduction. I: The Origination of the Concept of Multiplicity through that of the Collective Combination. The Analysis of the Concept of the Whole Number Presupposes that of the Concept of Multiplicity. The Concrete Bases of the Abstraction Involved. Independence of the Abstraction from the Nature of the Contents Colligated. The Origination of the Concept of the Multiplicity through Reflexion on the Collective Mode of Combination. II: Critical Developments. The Collective Unification and the Unification of Partial Phenomena in the Total Field of Consciousness at a Given Moment. The Collective "Together" and the Temporal "Simultaneously". Collection and Temporal Succession. The Collective Synthesis and the Spatial Synthesis. A: F.A. Lange's Theory. B: Baumann's Theory. Colligating, Enumerating and Distinguishing. Critical Supplement. III: The Psychological Nature of the Collective Combination. Review. The Collection as a Special Type of Combination. On the Theory of Relations. Psychological Characterization of the Collective Combination. IV: Analysis of the Concept of Number in Terms of its Origin and Content. Completion of the Analysis of the Concept of Multiplicity. The Concept 'Something'. The Cardinal Numbers and the Generic Concept of Number. Relationship between the Concepts 'Cardinal Number' and 'Multiplicity'. One and Something. Critical Supplement. V: The Relations "More" and "Less". The Psychological Origin of these Relations. Comparison of Arbitrary Multiplicities, as well as of Numbers, in Terms of More and Less. The Segregation of the Number Species Conditioned upon the Knowledge of More and Less. VI: The Definition of NumberEquality through the Concept of Reciprocal OnetoOne Correlation. Leibniz's Definition of the General Concept of Equality. The Definition of NumberEquality. Concerning Definitions of Equality for Special Cases. Application to the Equality of Arbitrary Multiplicities. Comparison of Multiplicities of One Genus. Comparison of Multiplicities with Respect to their Number. The True Sense of the Equality Definition under Discussion. Reciprocal Correlation and Collective Combination. The Independence of NumberEquality from the Type of Linkage. VII: Definitions of Number in Terms of Equivalence. Structure of the Equivalence Theory. Illustrations. Critique. Frege's Attempt. Kerry's Attempt. Concluding Remark. VIII: Discussions Concerning Unity and Multiplicity. The Definition of Number as a Multiplicity of Units. One as an Abstract, Positive Partial Content. One as Mere Sign. One and Zero as Numbers. The Concept of the Unit and the Concept of the Number One. Further Distinctions Concerning One and Unit. Sameness and Distinctness of the Units. Further Misunderstandings. Equivocations of the Name "Unit". The Arbitrary Character of the Distinction between Unit and Multiplicity. The Multiplicity Regarded as One Multiplicity, as One Enumerated Unit, as One Whole. Herbartian Arguments. IX: The Sense of the Statement of Number. Contradictory Views. Refutation, and the Position Taken. Appendix to the First Part: The Nominalist Attempts of Helmholtz and Kronecker. Second Part: The Symbolic Number Concepts and the Logical Sources of Cardinal Arithmetic. X: Operations on Numbers and the Authentic Number Concepts. The Numbers in Arithmetic are Not Abstracta. The Fundamental Activities on Numbers. Addition. Partition. Arithmetic Does Not Operate with "Authentic" Number Concepts. XI: Symbolic Representations of Multiplicities. Authentic and Symbolic Representations. Sense Perceptible Groups. Attempts at an Explanation of How We Grasp Groups in an Instant. Symbolizations Mediated by the Full Process of Apprehending the Individual Elements. New Attempts at an Explanation of Instantaneous Apprehensions of Groups. Hypotheses. The Figural Moments. The Position Taken. The Psychological Function of the Focus upon Individual Members of the Group. What is it that Guarantees the Completeness of the Traversive Apprehension of the Individuals in a Group? Apprehension of Authentically Representable Groups through Figural Moments. The Elemental Operations on and Relations between Multiplicities Extended to Symbolically Represented Multiplicities. Infinite Groups. XII: The Symbolic Representations of Numbers. The Symbolic Number Concepts and their Infinite Multiplicity. The NonSystematic Symbolizations of Numbers. The Sequence of Natural Numbers. The System of Numbers. Relationship of the Number System to the Sequence of Natural Numbers. The Choice of the "Base Number" for the System. The Systematic of the Number Concepts and the Systematic of the Number Signs. The Process of Enumeration via Sense Perceptible Symbols. Expansion of the Domain of Symbolic Numbers through Sense Perceptible Symbolization. Differences between Sense Perceptible Means of Designation. The Natural Origination of the Number System. Appraisal of Number through Figural Moments. XIII: The Logical Sources of Arithmetic. Calculation, Calculational Technique and Arithmetic. The Calculational Methods of Arithmetic and the Number Concepts. The Systematic Numbers as Surrogates for the Numbers in Themselves. The Symbolic Number Formations that Fall Outside the System, Viewed as Arithmetical Problems. The First Basic Task of Arithmetic. The Elemental Arithmetical Operations. Addition. Multiplication. Subtraction and Division. Methods of Calculation with the Abacus and in Columns. The Natural Origination of the Indic Numeral Calculation. Influence of the Means of Designation upon the Formation of the Methods of Calculation. The Higher Operations. Mixing of Operations. The Indirect Characterization of Numbers by Means of Equations. Result: The Logical Sources of General Arithmetic. Selbstanzeige  Philosophie Der Arithmetik. Supplementary Texts (1887  1901). A: Original Version of the Text through
 Chapter IV: On the Concept of Number: Psychological Analyses. Introduction. Chapter One. The Analysis of the Concept of Number as to its Origin and Content.
 1. The Formation of the Concept of Multiplicity [Vielheit] Out of that of the Collective Combination.
 2. Critical Exposition of Certain Theories.
 3. Establishment of the "Psychological". Nature of the Collective Combination.
 4. The Analysis of the Concept of Number as to its Origin and Content. Appendix To "On the Concept of Number: Psychological Analyses"  Theses. B: Essays. Essay I: (On the Theory of the Totality). I. The Definition of the Totality. II. Comparison of Numbers. III. Addenda.
 1. Addendum to p.
 367: Identity and Equality.
 2. On the Definition of Number. IV. The Classification of the Cardinal Numbers. V. Remark. VI. Corrections. VII. Addenda.
 1. Addendum to p.
 369.
 2. Addendum to p.
 377. Essay II: On the Concept of the Operation. I. Arithmetical Determinations of Number. II. Combinations (or Operations).
 1. Division.
 2. On the Concept of Combination. III. Addendum. On the Concept of Basic Operation. Essay III: Double Lecture: On the Transition through the Impossible ("Imaginary") and the Completeness of an Axiom System. I. For a Lecture before the Mathematical Society of Gottingen
 1901.
 1. Introduction.
 2. Theories Concerning the Imaginary.
 3. The Transition through the Imaginary.
 Appendix I:
 Appendix II:
 Appendix III: Notes on a Lecture by Hilbert. Husserl's Excerpts from an Exchange of Letters between Hilbert and Frege. Essay IV: (The Domain of an Axiom System /Axiom System  Operation System. System of Numbers. Arithmetizability of a Manifold. On the Concept of an Operation System. Essay V: The Question about the Clarification of the Concept of the "Natural" Numbers as "Given, " as "Individually Determinant". Essay VI: On the Formal Determination of Manifold. Index.
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(source: Nielsen Book Data) 9781402015465 20160528
20. The limits of abstraction [2002]
 Fine, Kit.
 Oxford ; New York : Clarendon Press : Oxford, 2002.
 Description
 Book — x, 203 p. ; 23 cm.
 Summary

 1. PHILOSOPHICAL INTRODUCTION THE CONTEXT PRINCIPLE THE ANALYSIS OF ACCEPTABILITY THE GENERAL THEORY OF ABSTRACTION.
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(source: Nielsen Book Data) 9780199533633 20190206