DOCSLIB.ORG

Volume 4, Number 9 September 2010

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Volume 4, Number 9 September 2010 Volume 4, Number 9 September 2010 www.thereasoner.org ISSN 1757-0522 decided to ask Professor Ilkka Niiniluoto for an inter- Contents view. During the last forty years, Niiniluoto has pub- lished an impressive number of papers on virtually all x1 Editorial 133 fields of contemporary philosophy of science, focussing particularly on probability and inductive logic, truth and x2 Features 134 verisimilitude (also known as truthlikeness or truth ap- proximation), realism and scientific progress, and the x3 News 137 evaluation of theories within natural and social sciences. Let me briefly survey his main contributions, which ex- x4 What’s Hot in . 143 plain why he is the right person to answer my questions. Niiniluoto is presently Chancellor of the Univer- x5 Events 144 sity of Helsinki, where he teaches Theoretical Phi- x6 Courses and Programmes 147 losophy, and Chairman of the Philosophical Society of Finland. He is one of the most x7 Jobs and Studentships 148 prominent figures of the philosoph- ical school going back to Eino Kaila, Georg H. von Wright, and Jaakko Hintikka. The development x1 of this tradition has been recently analyzed in a volume, Analytic Editorial Philosophy in Finland (Rodopi, 2003), edited by Niiniluoto himself I am delighted to return as guest editor of The Rea- (together with Leila Haaparanta), soner. Exactly one year ago, I opened the September is- for which Niiniluoto wrote also the sue with an interview with Theo Kuipers from the Uni- introductory, historical chapter. Within this tradition, versity of Groningen. In our conversation, we touched the Finnish School of inductive logic takes the lion’s upon a number of topics, in particular scientific real- share. Niiniluoto’s first important contribution to the ism, progress, truth, verisimilitude, and the method of School’s research programme is Theoretical Concepts philosophy of science. Nearly the same topics are the and Hypothetico-Inductive Inference (Reidel, 1973), central ones of this month’s interview. This is due not written together with Raimo Tuomela, in which the au- only to my lack of imagination, but also to the fact that, thors use Hintikka’s inductive logic in order to defend in my view, these are some of the most important prob- critical scientific realism. A few years later, Niiniluoto lems in the philosophy of science. For this reason, I and Tuomela also edited The Logic and Epistemology 133 of Scientific Change (Acta Philosophica Fennica, 30, and Roberto Festa and Luca Tambolo for many conver- 1979), a collection of papers devoted to four very recent sations on the topics of the interview, which inspired (at that time) methodological research programmes: most of the questions below. structuralism, cognitive decision theory, verisimilitude, and the logical theory of belief change. Gustavo Cevolani Sometimes, errors do trigger progress in the history Philosophy, Bologna of ideas. It is well-known that Popper’s attempt (in Con- jectures and Refutations, 1963) to explicate the notion of verisimilitude (construed as similarity or closeness to the comprehensive truth about a target domain) was x2 technically flawed, as Pavel Tichy´ and David Miller in- Features dependently proved in 1974. This failure opened the way to the post-Popperian theories of verisimilitude, Interview with Ilkka Niiniluoto which constitute a lively research programme in formal philosophy of science. The most developed and well- Gustavo Cevolani: First of all, thank you for agreeing known theory of verisimilitude is the so-called “simi- to be this month’s interviewee. As usual, let me start larity approach”, proposed since 1974 by Pavel Tichy´ by asking you about your intellectual history. How did and Risto Hilpinen, and subsequently developed by Ni- you first get into research in logic and philosophy of iniluoto, Tuomela and Graham Oddie. About a decade science? Who had the greatest influence on your philo- later, Niiniluoto published two books: Is Science Pro- sophical career? gressive? (Reidel, 1984), a collection of essays devoted Ilkka Niiniluoto: I did my Master’s degree in math- to explicating scientific progress in terms of increasing ematics in 1968, specializing in probability theory and verisimilitude, and Truthlikeness (Reidel, 1987), a pre- Bayesian statistics with Professor sentation of his own theory of verisimilitude, as well as Gustav Elfving. At the same time, a detailed discussion of the history, importance, and ap- I had started to study philosophy plicability of this notion, and a defence against its crit- and mathematical logic with Pro- ics. Truthlikeness is often referred to as “the Bible of fessor Oiva Ketonen. The philo- verisimilitude”, since it contains virtually all you need sophical devotion and personal in- to know for seriously studying the subject (in this case, tegrity of Academician Georg Hen- you will also find useful Niiniluoto’s survey article on rik von Wright made a strong im- “Verisimilitude: The third period” in the British Journal pression on me. I had already de- for Philosophy of Science, 49, 1998). cided to move from mathematics to In his most recent book on these themes, Critical theoretical philosophy when Professor Jaakko Hintikka Scientific Realism (Oxford University Press, 1999), Ni- appointed me his research assistant in the summer of iniluoto offers a detailed and up-to-date presentation 1971. Hintikka’s distributive normal forms and his mea- of his philosophical outlook. The book subtly com- sures of inductive probability and semantic information bines a coherently fallibilist view of human knowledge provided me the basic tools for the study of theoretical with an uncompromising defence of realism in ontol- terms and inductive inference. The most inspiring and ogy, semantics, epistemology, theory construction, and valuable lessons in philosophical methodology I have methodology. Niiniluoto carefully distinguishes all the learned from Hintikka. main forms of realism, antirealism, and relativism dis- GC: You were trained in the tradition of the “Finnish cussed in the recent literature, so that Critical Scien- school” of inductive logic, pursuing the research inau- tific Realism can be read also as a high-level textbook, gurated by Eino Kaila, von Wright and Hintikka. In containing one of the most learned and complete expo- retrospective, what have been the most important con- sitions of the subject to date. The reader interested in tributions of this school? How lively is this tradition the recent debate on Niiniluoto’s philosophy of science today? should read Approaching Truth (College Publications, IN: Von Wright’s treatment of eliminative induc- 2007), a Festschrift edited by Sami Pihlstrom,¨ Panu tion was an important contribution, but it is not much Raatikainen, and Matti Sintonen, collecting a number of discussed today. The greatest achievement of the papers by leading scholars devoted to his work in three Finnish school was Hintikka’s system of inductive gen- wide areas: 1) philosophy of logic, of language, and of eralization which improved Carnap’s inductive logic mathematics; 2) induction, truthlikeness, and scientific by showing how universal statements in infinite do- progress; and 3) epistemology, culture, and religion. mains can receive non-zero probabilities. Hintikka’s Before starting the interview, I wish to thank Feder- students—including Risto Hilpinen, Raimo Tuomela, ica Russo, Jon Williamson, and Lorenzo Casini for their Juhani Pietarinen and myself—then developed and ap- invitation to open this issue and for their editorial work; plied this insight in various directions. My own work 134 on truthlikeness and its estimation is also a continua- career, in the early Seventies. At that time, anti-realism tion of this tradition. Hintikka himself downplayed the (in its instrumentalist version) was widespread and be- role of induction in his interrogative model of inquiry came very fashionable shortly after, with the publica- in the 1990s. It is a little disappointing to see that tion of The Scientific Image by Bas van Fraassen (1980). Hintikka’s achievement is often ignored by Bayesian Today, the trend may appear to be reversed. Last year, scholars who either reject inductive logic or work within the PhilPapers website organized a survey on a number the Carnapian framework. The models of induction in of central philosophical questions. Among 1800 pro- Artificial Intelligence are less sophisticated than Hin- fessionals (PhDs or faculty members), over 70% is re- tikka’s system. But I am happy that there are philoso- ported to “accept or lean toward” scientific realism (al- phers in other countries—among them Theo Kuipers though the figure falls toward 50% among those broadly and Roberto Festa—who have made progress along the specialized in philosophy of science). How do you lines of the Finnish school. judge the results of this poll and, more generally, the GC: The post-Popperian research programme on present state of the realism/anti-realism debate? truthlikeness (aka verisimilitude, or truth approxima- IN: I am glad to hear about this relative success of tion) is a distinguished approach to the central prob- scientific realism. Arthur Fine was wrong when he an- lems of contemporary philosophy of science. Your 1987 nounced the death of realism some twenty-five years book, Truthlikeness, is a milestone of this programme, ago. Of course one should remember, as I tried to show exploring both the logical definition of verisimilitude in my Critical Scientific Realism (1999), that there are and its methodological applications. However, the en- many interesting forms of realism and anti-realism. One tire programme failed, at least until now, to gain wide can reliably predict that this debate will always be a vi- acceptance and visibility among philosophers of sci- tal issue in the philosophy of science. During the last ence. First, truthlikeness is still often conflated with decade, structural realism has gained popularity, and in- different concepts like probability, approximate truth, ternal realism has lost ground. But my guess is also partial truth, and so on.
Load more

Recommended publications
  • Commencement1976.Pdf (4.717Mb)
    1976 Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/commencement1976 ORDER OF PROCESSION MARSHALS STANLEY CORRSIN JOHN W. GRYDER MATTHEW A. CRENSON WILLIAM H. HUGGINS ELAINE C. DAVIS ROBERT A. LYSTAD HANS GOEDICKE EVANGELOS N. MOUDRIANAKIS ARCHIE GOLDEN EVERETT SCHILLER GERALD S. GOTTERER JOHN P. YOUNG THE GRADUATES MARSHALS ROBERT B. POND OREST RANUM THE DEANS MEMBERS OF THE SOCIETY OF SCHOLARS OFFICERS OF THE UNIVERSITY THE TRUSTEES * MARSHALS BROWN L. MURR FRANCIS E. ROURKE THE FACULTIES * CHIEF MARSHAL RICHARD A. MACKSEY THE CHAPLAINS THE RECIPIENT OF THE MILTON STOVER EISENHOWER MEDAL FOR DISTINGUISHED SERVICE THE PRESENTOR OF THE RECIPIENT OF THE MILTON STOVER EISENHOWER MEDAL FOR DISTINGUISHED SERVICE THE HONORARY DEGREE CANDIDATES THE PROVOST OF THE UNIVERSITY THE PRESIDENT EMERITUS OF THE UNIVERSITY THE CHAIRMAN OF THE BOARD OF TRUSTEES THE PRESIDENT OF THE UNIVERSITY ORDER OF EVENTS STEVEN MULLER President of the University, presiding * * * FANFARE PROCESSIONAL The audience is requested to stand as the Academic Procession moves into the area and to remain standing after the Invocation. " " Earle of Oxford's Marche William Byrd The Peabody Wind Ensemble Richard Higgins, Director * INVOCATION REV. CHESTER WICKWIRE Chaplain, The Johns Hopkins University THE NATIONAL ANTHEM GREETINGS ROBERT D. H. HARVEY Chairman of the Board of Trustees PRESENTATION OF THE RECIPIENT FOR THE MILTON STOVER EISENHOWER MEDAL FOR DISTINGUISHED SERVICE HELEN B. TAUSSIG PRESENTED BY RICHARD S. ROSS Vice President for the Health Divisions and Dean, School of Medicine * PRESENTATION OF NEW MEMBERS OF THE SOCIETY OF SCHOLARS LEROY E.
    [Show full text]
  • APA Eastern Division 2019 Annual Meeting Program
    The American Philosophical Association EASTERN DIVISION ONE HUNDRED FIFTEENTH ANNUAL MEETING PROGRAM SHERATON NEW YORK TIMES SQUARE NEW YORK, NEW YORK JANUARY 7 – 10, 2019 Visit our table at APA Eastern OFFERING A 20% (PB) / 40% (HC) DISCOUNT WITH FREE SHIPPING TO THE CONTIGUOUS U.S. FOR ORDERS PLACED AT THE CONFERENCE. THE POETRY OF APPROACHING HEGEL’S LOGIC, GEORGES BATAILLE OBLIQUELY Georges Bataille Melville, Molière, Beckett Translated and with an Introduction by Angelica Nuzzo Stuart Kendall THE POLITICS OF PARADIGMS ZHUANGZI AND THE Thomas S. Kuhn, James B. Conant, BECOMING OF NOTHINGNESS and the Cold War “Struggle for David Chai Men’s Minds” George A. Reisch ANOTHER AVAILABLE APRIL 2019 WHITE MAN’S BURDEN Josiah Royce’s Quest for a Philosophy THE REAL METAPHYSICAL CLUB of white Racial Empire The Philosophers, Their Debates, and Tommy J. Curry Selected Writings from 1870 to 1885 Frank X. Ryan, Brian E. Butler, and BOUNDARY LINES James A. Good, editors Philosophy and Postcolonialism Introduction by John R. Shook Emanuela Fornari AVAILABLE MARCH 2019 Translated by Iain Halliday Foreword by Étienne Balibar PRAGMATISM APPLIED William James and the Challenges THE CUDGEL AND THE CARESS of Contemporary Life Reflections on Cruelty and Tenderness Clifford S. Stagoll and David Farrell Krell Michael P. Levine, editors AVAILABLE MARCH 2019 AVAILABLE APRIL 2019 LOVE AND VIOLENCE BUDDHIST FEMINISMS The Vexatious Factors of Civilization AND FEMININITIES Lea Melandri Karma Lekshe Tsomo, editor Translated by Antonio Calcagno www.sunypress.edu II IMPORTANT NOTICES FOR MEETING ATTENDEES SESSION LOCATIONS Please note: this online version of the program does not include session locations.
    [Show full text]
  • SYLLABUS Gödel's Theorems Phil 93902 TR 3:30 143 Debartolo Hall
    SYLLABUS G¨odel's Theorems Phil 93902 TR 3:30 143 Debartolo Hall Michael Detlefsen ([email protected]), 408 Malloy Hall Curtis Franks ([email protected]), 411 Malloy Hall Fall 2007 I. Course Objectives • To acquaint the student with the basic ideas, methods and techniques behind one of the most striking scientific achievements of the twentieth century, the discovery of G¨odel'sincompleteness theorems. • To engage the student in productive thinking concerning the broader significance of these theorems. II. Texts • Kurt G¨odel:Collected Works, vol. I, Feferman et al. (eds.), Oxford, Oxford U. Press, 1986. III. Organization and Projected Schedule The course will divided into the following units, each estimated to run the indicated number of meetings. We plan to cover all of units A through G. We will cover the additional units according to the interests of the seminar participants. A. Historical and conceptual background and basic terminology. Two meetings. B. Basic mathematical background. Proof of the first theorem (G1). Four to five meet- ings. 1 C. Modifications of the proof of the first theorem, esp. Rosser's modification. One to two meetings. D. Proof of the second theorem (G2). Central task is to clarify the proofs of the second and third of the Hilbert-Bernays-L¨obDerivability Conditions (HBL Conditions). Two meetings. E. Alternative proofs of G2. Jeroslow's 1973 proof. Feferman's 1960 proof. Freidman's recent proof. [Note: We may discuss Jeroslow's and Feferman's proofs in inverse historical order because Jeroslow's proof is in some ways the less radical departure from the Hilbert-Bernays-L¨obproof.] Three meetings.
    [Show full text]
  • Notre Dame Report 37:10 (2008-08-03)
    Faculty Notes 387 ������ Honors 387 ������ Activities 389 ������ Publications 390 ������ Correction Administrators’ Notes 390 ������ Activities 390 ������ Publications Documentation 391 ������ Faculty Awards 393 ������ Faculty Recognition and Promotions 395 ������ Senior Fellow Comments 395 ������ Charge to the Class 396 ������ Baccalaureate Mass Homily 397 ������ Invocation 397 ������ Valedictory Remarks 399 ������ Undergraduate School Commencement Address 401 ������ The Laetare Medal Research 404 ������ May 2008 A U G U S T 3 , 2 0 0 8 N U M B E R 1 0 #8-5-387 “Discovery vs� Invention in the History of Mathematics” at the “Mathematics and Its Significance, Templeton Foundation Symposium,” Castel Gandolfo, Italy, Faculty Notes June 21–23; “Arithmetization and the Ideals of Proof” for the Dept� de la Histoire et de Honors Philosophie des Sciences, Univ� of Paris- Diderot and REHSEIS, June 18–19; “Some Michael Detlefsen, the McMahon-Hank Harvey A. Bender, professor of biological Questions Concerning Proof” as an invited Professor of Philosophy, was awarded a sciences, delivered a Hesburgh Lecture and discussant in “Workshop in the History and Senior Chaire d’excellence, by the Agence participated in the annual meeting of the Philosophy of Mathematics,” Dept� de la Nationale de la Recherche, France, for his American College of Medical Genetics in Histoire et de Philosophie des Sciences, U� work on ideals of proof; and is serving Phoenix, Ariz�, March 12–16, 2008� of Paris-Diderot and REHSEIS, June 13–14; as distinguished invited professor
    [Show full text]
  • Counterpossibles in Science: the Case of Relative Computability*
    Counterpossibles in Science: The Case of Relative Computability* MATTHIAS JENNY Massachusetts Institute of Technology forthcoming in Noˆus Abstract I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable, which is true, and If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable, which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counter- factuals, which would treat them as uniformly true. What’s more, I argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. *Thanks to Scott Aaronson, Karen Bennett, Matteo Bianchetti, David Boylan, Ben Burgis, Alex Byrne, Michael Detlefsen, Richard Dietz, Kevin Dorst, Nicole Dular, Hartry Field, Melvin Fitting, Juliet Floyd, Cameron Gibbs, Cosmo Grant, Geoffrey Hellman, Jared Henderson, Harold Hodes, Douglas Jesseph, Justin Khoo, Hilary Kornblith, Teresa Kouri, Rose Lenehan, Matt Mandelkern, William Nalls, Eileen Nutting, Alex Paseau, Milo Phillips-Brown, Graham Priest, Agust´ın Rayo, Bernhard Salow, Chris Scambler, Melissa Schu- macher, Kieran Setiya, Stewart Shapiro, Jeremy Shipley, Bradford Skow, Theodore Sider, Robert Stalnaker, Stephen Yablo, Elena Ziliotti, audiences at the 3rd Seoul Philosophy Graduate Student Conference, the 16th Midwest PhilMath Workshop, the 1st Massachusetts-Rhode Island Graduate Workshop in Philosophy, the 2016 Logic & Metaphysics Workshop at the CUNY Graduate Center, the 2016 CSHPM/SCHPM Annual Meeting, and especially Vann McGee for very helpful discussion.
    [Show full text]
  • Hilbert's Program Then And
    Hilbert’s Program Then and Now Richard Zach Abstract Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic sys- tems. Although G¨odel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial suc- cesses, and generated important advances in logical theory and meta- theory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical un- derpinnings and consequences, and its subsequent development and influ- ences since the 1930s. Keywords: Hilbert’s program, philosophy of mathematics, formal- ism, finitism, proof theory, meta-mathematics, foundations of mathemat- ics, consistency proofs, axiomatic method, instrumentalism. 1 Introduction Hilbert’s program is, in the first instance, a proposal and a research program in the philosophy and foundations of mathematics. It was formulated in the early 1920s by German mathematician David Hilbert (1862–1943), and was pursued by him and his collaborators at the University of G¨ottingen and elsewhere in the 1920s and 1930s. Briefly, Hilbert’s proposal called for a new foundation of mathematics based on two pillars: the axiomatic method, and finitary proof theory. Hilbert thought that by formalizing mathematics in axiomatic systems, and subsequently proving by finitary methods that these systems are consistent (i.e., do not prove contradictions), he could provide a philosophically satisfactory grounding of classical, infinitary mathematics (analysis and set theory).
    [Show full text]
  • CSHPM Bulletin, May 2020
    BULLETIN May/Mai 2020 Number/le num´ero66 WHAT'S INSIDE Articles Announcements ................................................................................................3 Digitized Smithsonian Mathematics Objects [Peggy Aldrich Kidwell] .....................................7 Book Review: Republic of Numbers [Andrew Perry].........................................................8 Books Borrowed Registers [Scott Guthery] ................................................................... 10 New Content from MAA Convergence [Janet Heine Barnett & Amy Ackerberg-Hastings]............... 10 Michael Detlefsen (1948{2019) [Patricia Blanchette, Tim Bays, and Curtis Franks] ...................... 12 Quotations in Context [Mike Molinsky] ...................................................................... 14 Martin Muldoon (1939{2019) [Hardy Grant] ................................................................. 15 Help (Still) Wanted ............................................................................................ 16 Reports President's Message [Maria Zack] .............................................................................2 From the Archives: Councillors ............................................................................... 13 2020 CSHPM Nominating Committee Report [Chris Baltus, Dan Curtin, and Elaine Landry] .......... 13 2019 Financial Statements [Greg Lavers] ..................................................................... 15 New Members .................................................................................................
    [Show full text]
  • Faculty and Index
    304 JOSÉ ANADÓN, Professor of Romance Languages and DAVID E. AUNE, Professor of Theology. B.A., Wheaton University Teaching Literatures. B.A., Albion College, 1968; M.A. Univ. of College, 1961; M.A., ibid., 1963; M.A., Univ. of Minne- Faculty Michigan, 1970; Ph.D., ibid., 1974. (1975) sota, 1965; Ph.D., Univ. of Chicago, 1970. (1999) SILVIA R. ANADÓN, Assistant Professional Specialist and YVES L. AURIOL, Associate Professional Specialist in Concurrent Lecturer in Romance Languages and Literatures. Physical Education. Master’s, Institute National du Sport, The following is the undergraduate teaching faculty roster B.A., Univ. of Michigan, 1970; M.A., ibid., 1972; Ph.D., France, 1968. (1985) for the 2001-02 academic year. This roster includes fac- ibid., 1974. (1976, 1979) ulty members who are on leave during the academic year. REV. NICHOLAS R. AYO C.S.C., Professor of Liberal The date in parentheses at the close of each entry is the THOMAS F. ANDERSON, Assistant Professor of Romance Studies. A.B., Univ. of Notre Dame, 1956; S.T.L., year the individual joined the Notre Dame faculty. Languages and Literatures and Fellow, Helen Kellogg Insti- Gregorian Univ., 1960; M.A., Univ. of Notre Dame, tute for International Studies. B.A., Bowdoin College, 1962; Ph.D., Duke Univ., 1966. (1981) CARL B. ACKERMANN, Assistant Professor of Finance. 1992; M.A., Univ. of Pennsylvania, 1994; Ph.D., ibid., A.B., Amherst College, 1984; Ph.D., Univ. of North 1998. (1998) MARIA PALOMA AYUELA, Associate Professor of Archi- Carolina, 1999. (1998) tecture. M.Arch., Yale Univ., 1989; Ph.D., Universidad PANAGIOTIS J.
    [Show full text]
  • Blanchette Vita for Website
    Patricia A. Blanchette Dept. of Philosophy Office: (574) 631-6439 University of Notre Dame Dept: (574) 631-6471 Notre Dame, IN 46556 e-mail: [email protected] Areas of Specialization: History and Philosophy of logic; Philosophy of mathematics; Foundations of analytic philosophy; Philosophy of Language. Education Ph.D. (Philosophy), Stanford University, 1990. B.A. (Philosophy), University of California, San Diego, 1983. Employment August 1993 – Present: University of Notre Dame, Dept. of Philosophy • June 2017 – Present: Glynn Family Honors Collegiate Chair • May 2012 – Present: Professor • May 2000 – May 2012: Associate Professor o Director of Graduate Studies 2004-7, 2008-11 • August 1993 – May 2000: Assistant Professor July 1990 - July 1993: Yale University. Assistant Professor, Dept. of Philosophy. Publications: Book • Frege’s Conception of Logic, Oxford University Press 2012 Reviewed in: o Philosophia Mathematica 22, 1 (2014) pp 108-120. o Journal of the History of Philosophy 52 (2014) pp 176-177. o Bulletin of Symbolic Logic 19, 2 (2013) pp 219-222. o Notre Dame Philosophical Reviews (2013) online. Articles • “Axioms in Frege,” Essays on Frege’s Basic Laws of Arithmetic, edited by Marcus Rossberg and Philip Ebert, Oxford University Press, forthcoming • “Models in Geometry and Logic: 1870-1920,” Logic, Methodology and Philosophy of Science – Proceedings of the 15th International Congress, edited by Niiniluoto, Seppälä, & Sober, College Publications 2017, 41-61. • “Philosophy of Logic,” Philosophy of Logic: 5 Questions, Automatic Press 2016, 25-35. • “Models and Independence circa 1900,” Logica Yearbook 2015, London: College Publications 2016, 17-38. Much of the material in this paper appears also in the expanded “Models in Geometry and Logic: 1870-1920,” 2017.
    [Show full text]
  • From the Outside Looking In: Can Mathematical Certainty Be Secured Without Being Mathematically Certain That It Has Been?
    From the Outside Looking In: Can mathematical certainty be secured without being mathematically certain that it has been? Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University Matthew Souba, MSc, MLitt Graduate Program in Philosophy The Ohio State University 2019 Dissertation Committee: Neil Tennant, Advisor Stewart Shapiro Christopher Pincock Copyright by Matthew Souba 2019 Abstract The primary aim of this dissertation is to discuss the epistemological fallout of Gödel’s Incompleteness Theorems on Hilbert’s Program. In particular our focus will be on the philo- sophical upshot of certain proof-theoretic results in the literature. We begin by sketching the historical development up to, and including, Hilbert’s mature program, discussing Hilbert’s views in both their mathematical and their philosophical guises. Gödel’s Incompleteness Theorems are standardly taken as showing that Hilbert’s Pro- gram, as intended, fails. Michael Detlefsen maintains that they do not. Detlefsen’s argu- ments are the focus of chapter 3. The argument from the first incompleteness theorem, as presented by Detlefsen, takes the form of a dilemma to the effect that either the infini- tistic theory is incomplete with respect to a certain subclass of real sentences or it is not a conservative extension over the finitistic theory. He contends that Hilbert need not be committed to either of these horns, and, as such the argument from the first incompleteness theorem does no damage to Hilbert’s program. His argument against the second incomplete- ness theorem as refuting Hilbert’s Program, what he calls the stability problem, concerns the particular formalization of the consistency statement shown unprovable by Gödel’s theorem, and endorses what are called Rosser systems.
    [Show full text]
  • Nebraska), Mort Le 21 Octobre 2019 À L’Hôpital Universitaire De Chicago
    In memoriam Michael Detlefsen1 Né le 20 octobre 1948 à Scottsbluff (Nebraska), mort le 21 octobre 2019 à l’hôpital universitaire de Chicago. Michael Detlefsen (Mic, pour la plupart de ceux qui le connaissent) était un ami et un maître pour nombre d'entre nous au sein de la petite communauté des philosophes et historiens des mathématiques en France. Mic racontait volontiers l'histoire incroyable de son arrière-grand-père et de son arrière-arrière-grand oncle qui ont décidé, à l'âge de 9 et 11 ans, de quitter le Danemark et leur famille pour se lancer à la conquête du « rêve américain ». La longue et éprouvante aventure qui s'ensuivit les conduisit, en bateau, en train, puis à pieds, jusqu'à la ville de Dannebrog - Nebraska. Le gouvernement leur a donné des terres à condition qu'ils les cultivent pendant au moins cinq ans. Le rêve est devenu réalité. Et Mic se demande alors : Pourquoi ces enfants ont-ils décidé de quitter leur famille ? La vérité, telle qu'elle lui a été racontée par son frère aîné, est- elle la vérité ? Une seule vérité existe-t-elle jamais, ou la vérité est-elle affectée par notre propre histoire ? Et qu'en est-il de notre propre histoire par rapport à l'histoire ? Au Wheaton College dans la grande banlieue de Chicago, où il a commencé ses études, Mic s'est tourné vers les sciences, les mathématiques, la physique, ainsi que vers la philosophie. Après une thèse sur le second théorème de l'incomplétude de Gödel en 1976 à l'Université Johns Hopkins, il a d'abord été Associate Professor à l'Université du Minnesota-Duluth (1975-1983), puis Associate Professor à l'Université Notre Dame (1984-1989), avant d'être nommé professeur sur la chaire McMahon-Hank à cette même université.
    [Show full text]
  • 0415023351.Pdf
    PROOF, LOGIC AND FORMALIZATION This book addresses various problems associated with finding a philosophically satisfying account of mathematical proof. It brings together many of the most notable figures currently writing in the philosophy of mathematics in an attempt to explain why it is that mathematical proof is given prominence over other forms of mathematical justification. The difficulties that arise in accounts of proof range from the rightful role of logical inference and formalization to questions concerning the place of experience in proof and the possibility of eliminating impredicative reasoning from proof. The editor, Michael Detlefsen, has brought together an outstanding collection of essays, only two of which have previously appeared. Essential for philosophers and historians of mathematics, it is also recommended for philosophically inclined logicians and philosophers interested in the nature of reasoning and justification. A companion volume entitled Proof and Knowledge in Mathematics, edited by Michael Detlefsen, is also available from Routledge. PROOF, LOGIC AND FORMALIZATION PROOF, LOGIC AND FORMALIZATION Edited by Michael Detlefsen London and New York First published 1992 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” Simultaneously published in the USA and Canada by Routledge a division of Routledge, Chapman and Hall, Inc. 29 West 35th Street, New York, NY 10001 Selection and introductory material © 1992 Michael Detlefsen Individual chapters © 1992 the respective authors. All rights reserved.
    [Show full text]