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    1、P1: JZP0521837820agg.xml CY530B/Tieszen 0 521 83782 0 November 3, 2005 5:13Phenomenology, Logic, and the Philosophyof MathematicsThis book is a collection of fifteen essays that deal with issues at theintersection of phenomenology, logic, and the philosophy of mathe-matics. The first of the three pa

    2、rts, “Reason, Science, and Mathemat-ics,” contains a general essay on Husserls conception of science andlogic, an essay on mathematics and transcendental phenomenology,and an essay on phenomenology and modern pure geometry. Part IIis focused on Kurt Godels interest in phenomenology. It exploresGodel

    3、s ideas and also some work of Quine, Penelope Maddy, andRoger Penrose. Part III deals with elementary, constructive areas ofmathematics areas of mathematics that are closer to their originsin simple cognitive activities and in everyday experience. This part ofthe book contains essays on intuitionism

    4、, Hermann Weyl, the notionof constructive proof, Poincare, and Frege.Richard Tieszen is Professor of Philosophy at San Jose State Univer-sity.iP1: JZP0521837820agg.xml CY530B/Tieszen 0 521 83782 0 November 3, 2005 5:13To my parents,James D. and Beverly J. TieszeniiP1: JZP0521837820agg.xml CY530B/Tie

    5、szen 0 521 83782 0 November 3, 2005 5:13Phenomenology, Logic, and thePhilosophy of MathematicsRICHARD TIESZENSan Jose State UniversityiiiCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, So PauloCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU

    6、, UKFirst published in print formatISBN-13 978-0-521-83782-8ISBN-13 978-0-511-33557-0 Richard Tieszen 20052005Information on this title: www.cambridge.org/9780521837828This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, n

    7、o reproduction of any part may take place without the written permission of Cambridge University Press.ISBN-10 0-511-33557-1ISBN-10 0-521-83782-0Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this

    8、publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.Published in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orghardbackeBook (NetLibrary)eBook (NetLibrary)hardbackP1: JZP0521837820agg.xml CY530B/Ties

    9、zen 0 521 83782 0 November 3, 2005 5:13ContentsAcknowledgments page viiIntroduction: Themes and Issues 1part i. reason, science, and mathematics1 Science as a Triumph of the Human Spirit and Science inCrisis: Husserl and the Fortunes of Reason 212 Mathematics and Transcendental Phenomenology 463 Fre

    10、e Variation and the Intuition of Geometric Essences:Some Reflections on Phenomenology and ModernGeometry 69part ii. kurt godel, phenomenology, and thephilosophy of mathematics4 Kurt Godel and Phenomenology 935Godels Philosophical Remarks on Logic and Mathematics 1126Godels Path from the Incompletene

    11、ss Theorems (1931)to Phenomenology (1961) 1257Godel and the Intuition of Concepts 1498Godel and Quine on Meaning and Mathematics 1779 Maddy on Realism in Mathematics 20110 Penrose on Minds and Machines 215vP1: JZP0521837820agg.xml CY530B/Tieszen 0 521 83782 0 November 3, 2005 5:13vi Contentspart iii

    12、. constructivism, fulfillable intentions,and origins11 Intuitionism, Meaning Theory, and Cognition 22712 The Philosophical Background of Weyls MathematicalConstructivism 24813 Proofs and Fulfillable Mathematical Intentions 27614 Logicism, Impredicativity, Formalism: Some Remarks onPoincare and Husse

    13、rl 29415 The Philosophy of Arithmetic: Frege and Husserl 314Bibliography 337Index 349P1: JZP0521837820agg.xml CY530B/Tieszen 0 521 83782 0 November 3, 2005 5:13AcknowledgmentsThe essays collected here were written over a period of fifteen years. Inpreparing them for publication in this volume I have

    14、 modified them in afew places, mostly for clarity and for continuity with other chapters in thecollection. I have also cut some material from a few of the essays. Someoverlap or repetition remains here and there, but the trade-off is that suchoverlapping allows the essays to be read independently of

    15、 one another.In any case, I think that a little repetition is not onerous. It may even behelpful to some readers. The Bibliography has been standardized, and inthe case of Husserls work in particular I have provided references to theoriginal publications, the relevant Husserliana editions, and the E

    16、nglishtranslations. Since Husserls works are usually composed in short sectionsI have adopted the convention in the essays of referring to quotationsfrom Husserls works by providing the title of the work and the sectionnumber. This method puts the reader in touch with the relevant texts butallows fo

    17、r choice in consulting the different editions and languages. Inthe case of Godels writings I have followed the citation style used in KurtGodel: Collected Works. The Bibliography for the present volume includesvery few works that were not cited in the original essays. I have included afew new refere

    18、nces where there has been some clear line of developmentof an argument or point in the essays.Chapter 1 was written for the volume Continental Philosophy of Science,edited by Gary Gutting (Oxford: Blackwell, 2004). It appears here withthe permission of Blackwell Publishing.Chapter 2 originally appea

    19、red under the title “Mathematics” in TheCambridge Companion to Husserls,B.Smith and D. Smith (eds.) (Cambridge:viiP1: JZP0521837820agg.xml CY530B/Tieszen 0 521 83782 0 November 3, 2005 5:13viii AcknowledgmentsCambridge University Press, 1995), pp. 438462. It is reprinted herewith the permission of C

    20、ambridge University Press.Chapter 3, “Free Variation and the Intuition of Geometric Essences:Some Reflections on Phenomenology and Modern Geometry,” willappear in Philosophy and Phenomenological Research.Itisreprinted herewith the permission of the editors.Chapter 4 appeared as “Kurt Godel and Pheno

    21、menology,” Philosophy ofScience 59, 2 (1992), pp. 176194. It is reprinted here with the permissionof the Philosophy of Science Association.Chapter 5 was originally published as “Godels Philosophical Remarkson Logic and Mathematics: Critical Notice of Kurt Godel: Collected Works,Vols. I, II, III,” Mi

    22、nd 107 (1998), pp. 219232. It is reprinted by permissionof Oxford University Press.Chapter 6 appeared as “Godels Path from the IncompletenessTheorems (1931)toPhenomenology (1961),” Bulletin of Symbolic Logic4, 2 (1998), pp. 181203, C copyright 1998 Association for SymbolicLogic. It is reprinted here

    23、 with permission of the Association for SymbolicLogic.Chapter 7 appeared as “Godel and the Intuition of Concepts,” Synthese133, 3 (2002), pp. 363391, C copyright 2002 Kluwer Academic Publish-ers. It appears here with kind permission of Kluwer Academic Publishers.Chapter 8 appeared as “Godel and Quin

    24、e on Meaning and Mathe-matics,” in Between Logic and Intuition: Essays in Honor of Charles Parsons,R. Tieszen and G. Sher (eds.) (Cambridge University Press, 2000),pp. 232254. It is reprinted with the permission of Cambridge UniversityPress.Chapter 9 was originally published as “Review of Mathematic

    25、al Realism,by Penelope Maddy,” Philosophia Mathematica 3, 2 (1994), pp. 6981. It isreprinted here with the permission of the editor, Robert S. D. Thomas.Chapter 10 was originally published as “Review of Shadows of the Mind: ASearch for the Missing Science of Consciousness,byRoger Penrose,” Philosoph

    26、iaMathematica 4, 3 (1996), pp. 281290. It appears here with the permissionof the editor, Robert S. D. Thomas.Chapter 11 appeared as “Intuitionism, Meaning Theory and Cogni-tion,” History and Philosophy of Logic 21, 3 (2001), pp. 179194. It is reprint-ed here with the permission of Taylor Robert Trag

    27、esser at Barnard; and J. N. Mohanty and Izchak Miller at theGraduate Faculty of the New School for Social Research. Soon after Iarrived at Columbia, Charles Parsons gave a seminar on Husserls LogicalInvestigations. This allowed me to deepen the study of Husserls works thatI had already begun at the

    28、New School and in college. At the New School,J. N. Mohanty gave a year-long seminar on Husserls logical works. It wasthis kind of in-depth seminar that made the Graduate Faculty unique.As an undergraduate I benefited from studies of phenomenology withRobert Welsh Jordan and of modal logic and other

    29、systems of logic withFred Johnson. It was during my time at Columbia that I met and beganthe first of many discussions with Hao Wang about Godels philosophicalviews. Wang was one of the people I knew who most encouraged think-ing about mathematics from a phenomenological standpoint. I also metDagfin

    30、n Fllesdal while I was a graduate student, and although he wasP1: JZP0521837820agg.xml CY530B/Tieszen 0 521 83782 0 November 3, 2005 5:13x Acknowledgmentsnever formally my teacher I have been discussing Husserls work withhim since that time. Several other people were especially helpful and en-courag

    31、ing early on: Michael Resnik, Gian-Carlo Rota, Bill Tait, and BillMcKenna come to mind. I am indebted to Mike Resnik in particular.As I began to focus even more on constructive mathematics I benefitedfrom discussions with Dirk van Dalen, Per Martin-Lof, Anne Troelstra,Dag Prawitz, and Goran Sundholm

    32、. Van Dalen has been especially help-ful. After I arrived in California I began to attend many of the logicevents at Stanford. These were often organized by Sol Feferman, and Ihave profited from many exchanges with him over the years.In addition to all of those mentioned, I would like to thank manyo

    33、ther people with whom I have discussed my work: Mark van Atten,Michael Friedman, David Smith, Barry Smith, Ed Zalta, John Corcoran,Albert Visser, Karl Schuhmann, Robin Rollinger, Paolo Mancosu, ThomasRyckman, Karl Ameriks, Guglielmo Tamburrini, Ernan McMullin, GaryGutting, Charles Chihara, Jerrold K

    34、atz, Paul Cortois, Grisha Mints, DieterLohmar, Claire Hill, Jairo da Silva, Peter Hadreas, and Kai Hauser. (It ispossible that as I write this I have not remembered everyone who deservesto be mentioned.)Finally, I thank my wife, Nancy, for her patience and her meditativeways. Nam MoADiDaPha.t.Idedic

    35、ate this book to my parents, James D.and Beverly J. Tieszen.P1: IWV052183782int.xml CY530B/Tieszen 0 521 83782 0 March 11, 2005 14:12IntroductionThemes and IssuesThis volume is a collection of fifteen of my thematically related paperson phenomenology, logic, and the philosophy of mathematics. All of

    36、 theessays are concerned with the interpretation, analysis, and developmentof ideas in Husserlian phenomenology in connection with recent andhistorical issues in the philosophy of mathematics and philosophy of logic.Many of the interesting questions about phenomenology and the ex-act sciences that e

    37、ngaged such thinkers as Frege, Carnap, Schlick, andWeyl with the early phenomenologists have unfortunately been neglectedin more recent times. One could speculate on why this has happened.On the one hand, it no doubt resulted from the development of certaintrends in what has since been called analyt

    38、ic philosophy. On the otherhand, it resulted from the particular trajectory of Continental philosophyafter Husserl. Husserls emphasis on science and the analysis of essencegave way almost immediately on the Continent to various philosophiesof human existence under the influence of Husserls student H

    39、eidegger.In addition, there were long delays in the English translation of manyof Husserls writings, and to complicate matters further, philosophy cur-ricula at many universities came to be organized around the divisionbetween analytic and Continental philosophy.In my view, this general division bet

    40、ween the analytic and Continentaltraditions has not always been good for philosophy. Least of all shouldit be maintained in the case of philosophers such as Brentano, Husserl,and some others in the early phases of the phenomenological movement,for here there is still direct engagement with major fig

    41、ures in Anglo-American philosophy. Many of the essays in this book are concerned withissues and ideas that are common to both the Continental and the analytic1P1: IWV052183782int.xml CY530B/Tieszen 0 521 83782 0 March 11, 2005 14:122 Introductiontraditions of philosophical thinking about logic and m

    42、athematics. I hopethe book can be seen as adding to the growing literature that encouragescommunication between the traditions and puts some of these artificialdivisions behind us.1The methods and ideas of analytic and Continentalphilosophy, where they are in fact different, can inform and enrich ea

    43、chother in many ways. There are of course significant disagreements onsome of the issues, but I expect that by examining them we will onlyreach a deeper understanding.1In order to appreciate the approach I take to phenomenology in thisbook it is necessary to realize that Husserls own thinking about

    44、logic andmathematics went through several transformations. It will be useful tosituate my work in a general way with respect to three main stages thatcan be discerned in Husserls writings on these subjects. Roughly speak-ing, there is the early work of the Philosophy of Arithmetic (PA) and relatedwr

    45、itings (18911900), the middle period of the Logical Investigations (LI)(19001907), and the later period starting with the Ideas Pertaining to aPure Phenomenology and to a Phenomenological Philosophy (Ideas I) (19071938). (For much more detail see Tieszen 2004.) Some of the centralchanges that divide

    46、 these periods from one another and that are relevantto my work in this volume are as follows: the Philosophy of Arithmetic con-sists of descriptive psychological and logical investigations of arithmetic.Husserls ontology at this point includes physical entities and processesand mental entities and

    47、processes. The ideal or abstract objects that areclearly part of Husserls ontology from 1900 onward are not to be found(in any obvious way) in PA. Husserl analyzed the origins of the naturalnumber concept in PA by focusing on mental processes of abstraction,collection, and so on. As a result, some o

    48、f the critics of the book, mostnotably Frege, thought they detected a form of psychologism in PA. Psy-chologism is the view that mathematics and logic are concerned withmental entities and processes, and that these sciences are in some sensebranches of empirical psychology. Psychologism was a popula

    49、r form ofnaturalism about logic and mathematics in the late nineteenth century.1See, for example, Michael Dummetts Origins of Analytic Philosophy, Michael Friedmans AParting of the Ways: Carnap, Cassirer, and Heidegger and Reconsidering Logical Positivism, andmany of the writings of Dagfinn Fllesdal and J. N. Mohanty.P1: IWV052183782int.xml CY530B/Tieszen 0 521 83782 0 March 11, 2005 14:12Introduction 3Another important point about PA is that the view of intuitive orauthentic knowledge in arithmetic in the boo

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