Ideals of Proof 2008 – 2011

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The Ideals of Proof Program is an interdisciplinary project supported by the Agence Nationale de la Recherche, together with its associated Chair D’Excellence and hosted by the following institutions :

  • Université Nancy 2 / LHSP – Archives Henri Poincaré (UMR CNRS 7117)
  • Université Paris Diderot – Paris 7 / Département d’Histoire et Philosophie des Sciences / RESHEIS (UMR CNRS 7596)
  • Collège de France / Chaire de philosophie du langage et de la connaissance (Jacques Bouveresse)
  • University of Notre Dame

The term ‘ideals’ in the title is used in two senses. The first concerns the aims and virtues of proof considered as justificative norms for mathematical practice generally. The second concerns the use of so-called “ideal” elements or methods as means of pursuing these aims.

Ideals in the first sense include not only such traditional standards as rigor, certainty, apriority, purity and explanatory gain, but also such systematic virtues as (various types of) completeness, closure, efficiency and freedom. Generally speaking, we want to improve our understanding of why such conditions and constraints as have figured as ideals of proof in the history of mathematics have so figured and whether they are truly deserving of such regard.

Ideals in the second sense include such things as the introduction of “infinites” (both large and small), imaginary and complex numbers in algebra and analysis, the use of Kummer ideals in number theory and the use of points, lines and planes at infinity in projective geometry.

The Archive for Mathematical Sciences and Philosophy has recorded the following events within the Ideals of Proof Program and made them available on this subsite at the request of Prof. Mic Detlefsen, Holder of the ANR Chair D’Excellence and Director of the IP Program, and his colleagues responsible for the administration of the Program The recordings listed below can also be found within the chronological listing of all recordings made by the Archive within the individual years 2008 – 2011. In addition to official IP Events, some additional events in the History and Philosophy of Mathematics involving IP Fellows, or otherwise of closely related interest have also been included.

PAGE UNDER CONSTRUCTION

 

 

2008 RECORDINGS of Events in Ideals of Proof Program and Chaire D’Excellence plus closely related events in History and Philosophy of Mathematics in Paris

 

The first meetingof the Philosophy of Mathematics Seminar organized by Ivahn Smadja at the Department of History and Philosophy of Science of Université Paris Diderot – Paris 7, took place on January 11th 2008. Detailed information about the seminar are available here.

The following Sessions and talks in this Seminar were recorded and can be listened to by clicking on the links in the monthly chronology of recordings in the Archive :

Professor Michael (Mic) D etlefsen, Chaire D’Excellence, Ideals of Proof Program gave two inaugural lectures for the IP project at Université Nancy 2 and Université Paris Diderot – Paris 7. The Nancy lecture took place on January 30th 2008, at 17:00, Campus Lettres et Sciences Humaines, room G 04 (flyer available here).The first meeting of the IP research seminar in Nancy took place on February 1st, 2008 at Université Nancy 2, Campus Lettres et Sciences Humaines, room A-104. [read more] Unfortunately this seminar was not recorded.

February 8th 2008 : Inaugural Session of Chair D’Excellence ANR “Ideals of Proof”

Place: Université Paris 7, Bâtiment « Halle aux Farines », Hall AB, 2nd floor, Amphi 2A – 2, rue Marguerite Duras, Paris 13ème.

An Inaugural Symposium on Proof and Inference took place on February 8th 2008 at Université Paris 7, Bâtiment « Halle aux Farines », Hall AB, 2nd floor, Amphi 2A – 2, rue Marguerite Duras, Paris 13ème. It featured a lecture by Dag Prawitz on “The Validity of Inference” and a lecture by Prof. Michael Detlefsen on “Varieties of Completeness” (flyer available here).

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to recording of Invited Lecture by Prof.. Dag PRAWITZ (Theoretical Philosophy, Stockholm) “On The Validity of Inference”

For his overheads :

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to Prof. DETLEFSEN’s Inaugural Lecture : “On Ideals of Purity of Proofs : The Examples of Kronecker and Dedekind : Their Debate on the Proper Object of Arithmetical Investigation”

Click here for his Overheads

February 22nd, 2008

ENS : Seminaire Riemann : Part 1 : Christian HOUZEL : The Two Fundamental themes of Poincare’s (1895) Memoir on Analysis Situs :

a) The Definition of Poincare Duality and of an Algebraic Variety

b) The Notion of the Fundamental Group of A Space and Its Role in Topology

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to recording of Prof. HOUZEL’s Talk

Part 2 : Patrick POPESCU-PAMPU (Univ. Paris 7) : Les Notions de Variete Chez Poincare

Click here for link to recording of Prof. POPESCU-PAMPU’s Talk

Total length of recording : 3 hours 15 minutes 21 seconds. Windows media Audio File 23.2 MB bitrate 16kbps

The Second meeting of the IP research seminar in Nancy took place on February 26th 2008 at The Université Nancy 2, Campus Lettres et Sciences Humaines, room Jules Vuillemin, J-303, 16:30. [read more]

The Third meeting of the IP research seminar in Nancy took place on March 7th, 2008 at Université Nancy 2, Pôle Lorrain de Gestion, room 020, 16:30. [read more]

Thursday March 20th, 2008

Institut Henri Poincare History of Mathematics Seminar :

A Survey Talk by Christian HOUZEL : An Introductory Survey of The Early History of Category Theory circa. 1946 – 1965

Click here for link to recording of Prof. HOUZEL’s Talk

April 11th, 2008 REHSEIS/ENS Workshop in Series “Seminaire Riemann” on “The Reception of Relativity”

Talk 1 by Scott WALKER : “Minkowski and the Scandal of Spacetime”

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for link to recording of Part 1 of Scott WALKER’s Talk

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for Link to Part 2 of his Talk plus Q&A Session

Click here for Link to File (File 20) of Overheads of talk by Scott Walker at 11th April 2008 ENS Workshop : Hermann Minkowski and the Scandal of Spacetime

Talk 2 : Jan LACKI (CNRS/REHSEIS) : The Logical Empiricist Reception(s) of Relativity Theory

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for link to the recording of Jan LACKI’s Talk (Incomplete)

Talk 3 : Alex AFRIAT (Urbino) : Mach’s Principle, Conservation Principles and Substantival Space-Time

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for link to recording of Alex AFRIAT’s Talk

 

April 14th, 2008

Talk by Renaud CHORLAY at REHSEIS Workshop/Colloque of 14th April 2008 on the notion of a function (A Study of the notion of a function from the 18th to the early 20th Century)

Darbour and Weierstrass’s critique of Cauchy’s account of limits, maxima and convergence : A probe for exploring the transition from the framework of the theory of magnitudes to the modern understanding of the notion of function in the course of the 19th Century.

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to recording of Renaud Chorlay’s Talk : Windows media Audio File 5.86 MB bitrate 16kbps Duration : 49 mins 18 seconds

April 15th, 2008

Talk to Seminaire Categories en Physique : Salle Malevich Batiment Condorcet University Paris 7 by J-J. SZCZECINIARZ

Covariance and Invariants in GR and Theories of Spacetime Structure in general : Is General Covariance the same thing as Background Independence ?

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of Jean-Jacques SZCZECINIARZ’s Talk : Duration : 1 hour 38 minutes 03 seconds File size : 11.6 MB

April 16th, 2008 ; REHSEIS Workshop on Philosophy of Mathematics : Title “Visions of Mathematical Reality and Accounts of Mathematical Practice” (Organiser ; Ivahn SMADJA)

Talk 1 by David CORFIELD : Narratives and Visions of Mathematical Rationality : With observations on the Program of Categorification and some remarks about ideas of Grothendieck concerning the Algebraisation of Notions of Space and of geometric notions in general.

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to recording of David CORFIELD’s Talk : Duration 1 hour 30 minutes 11 seconds

Talk 2 : Jamie TAPPENDEN : On the Objectivity of the Notion of Mathematical Natural Kinds

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to recording of Jamie TAPPENDEN’s Talk : Duration 1 hour 50 minutes 57 seconds

Third Talk : Jose FERREIROS : Details to be added.

April 17th, 2008 :

IHP 4:00 pm : Christian HOUZEL : Poincare et le Continu : Poincare, The Continuum and Types of Continuity.

Click here for link to recording of Christian HOUZEL’s Talk : 1 hour 48 minutes 16 seconds

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edited version with enhanced sound

 

May 4th – May 8th 2008

Marcus Giaquinto (University College, London) visited the project team from May 4th to May 8th 2008 , and lectured in Nancy (May 5th to 6th 2008 workshop on ‘Visual Reasoning in Mathematics and the A Priori‘) and in Paris (May 7th, 2008 at The Riemann Seminar, Ecole Normale Supérieure, 45, rue d’Ulm, salle Dussane, 17H00:19H00).

Title: “Synthetic a priori knowledge in geometry: recovery of a Kantian Insight”.

Both Marcus Giaquinto’s Lectures were recorded and can be listened to Here.

Click here to listen to recording of his Talk in Nancy

Click here to listen to recording of his Talk in Paris

May 9th 2008

ENS Salle Weil : Seminaire RIEMANN on Sophus Lie, Groups and Algebra

Talk 1 : Joel MERKER : Axioms for Groups, Mobility of Pairs of Points and Foundations of Geometry (in Lie and in Poincare)

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to recording of Joel MERKER’s Talk : Duration 1 hr 18 mins 27 seconds

Talk 2 of 9th May 2008 : ENS Salle Weil Seminaire RIEMANN on Sophus Lie, Groups and Algebra : Benoit TIMMERMANS : Quelques Etapes de L’Histoire de La representation des Groupes

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to recording of Benoit TIMMERMAN’s Talk : Duration 1 hr 18 mins 30 seconds

Talk 3 of 9th May 2008 : ENS Salle Weil Seminaire RIEMANN on Sophus Lie, Groups and Algebra : Frederic BRECHENMACHER (Univ. of Artois-Picardy) : The “Algebras” of Lie and The development of Algebra : The story of a complex relationship (1876 – 1907)

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to recording of Frederic BRECHENMACHER’s Talk : Duration 1 hr 27 mins 45 seconds

May 23rd 2008

ENS : Seminaire Riemann : Felix Klein and The Erlangen Program and Its Legacy (i)

Talk 1 by David ROWE : From Line Geometry to Relativity Theory : The (Multiple) Broader Context(s) of Klein’s Erlangen Program.

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of David ROWE’s Talk : Duration : 1 hour 33 mins 02 seconds

Talk 2 by Jim RITTER : The Renewal and Enlargement of the Erlangen Program as the framework for understanding strategies for the Unification of Physics in the 1920s

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to recording of Jim RITTER’s Talk : Duration : 1 hour 34 minutes 06 seconds

 

June 9th–13th 2008 : International Workshop on Mathematical Understanding Univ Paris 7.

An International Workshop on ‘Mathematical Understanding’ organized by Prof. Ivahn Smadja (University Paris-Diderot and REHSEIS) and jointly sponsored by the Département Histoire et Philosophie des Sciences – Université Denis Diderot, REHSEIS and the Ideals of Proof Project.

For more information see: http://www.histnet.cnrs.fr/research/sfhst/spip.php?article217

This workshop was intended to contrive a fruitful confrontation between studies of conceptually rich history of mathematics and themes in the philosophy of mathematics. Taking into account some historical background, notably some of the overarching viewpoints and programs which emerged in the 19th and 20th centuries : (geometrization, algebraization, arithmetization, …), the aim was to shed light on various epistemic, cognitive and logical aspects of mathematical knowledge. Different approaches were studied in the setting of particular historical case studies and then brought into relation to general philosophical questions and approaches involving logical and formal tools.

 

Monday 9 June 2008

9h30-11h00 : Jeremy Gray (Open University London) : « Understanding [and] Riemann surfaces »

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to recording of Jeremy Gray’s Talk : Size 10.8 Mb : 1 hr 31 mins 23 seconds

Click here for his Overheads

11h15-12h45 : Karine Chemla (CNRS Rehseis) : « Understanding while proving the correctness of algorithms. Reflexions based on ancient Chinese sources »

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to recording of Karine CHEMLA’s Talk : Size 13.00 Mb : 1 hr 49 mins 40 seconds

14h30-16h00 : Alain Michel (Université d’Aix-Marseille) : « La théorie de la mesure: origines et prolongements »

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to recording by Alain MICHEL : Size 10,2 Mb ; 1 hr 25 mins 54 seconds

16h15-17h45 : Renaud Chorlay (Université de Paris 8 – Rehseis)

« Making sense of it with structures : the mathematical (and philosophical) background to Charles Ehresmann’s work »

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to Renaud Chorlay’s Talk : Size : 12.5 Mb ; 1 hr 45 mins 39 seconds

18h00-19h30 : Andrei Rodin (Université Denis Diderot de Paris 7)

«Category theory, Mathematical Structuralism & Mathematical Hermeneutics»

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to Recording of Andrei Rodin’s Talk. Requires addition of digitalised audiotape back-up for last part of Talk

 

Tuesday 10 June 2008

14h00-15h30 : Ken Manders (University of Pittsburgh) : « On Mathematical Understanding »

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to recording of Ken MANDERS Talk : Size 9.80 Mb : 1 hr 22 mins 24 seconds

15h45-17h15 : Catherine Goldstein (CNRS, Institut de Mathématiques, Paris 6)

« Charles Hermite, Mathematical Understanding and Mathematical Nature »

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of Catherine GOODSTEIN’s Talk : Size 10.9 Mb ; 1 hr 32 mins 13 seconds

Click here for link to File 21 : .pdf of Contents and other information on Book : The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae, edited by Catherine Goldstein, Norbert Schappacher and Joachim Schwermer, Berlin, Heidelberg, New York: Springer, 2007, (available at http://www.springer.com)

This File provides Background to Talk by Catherine GOLDSTEIN « Charles Hermite, Mathematical Understanding and Mathematical Nature » (see above)

Click here for link to File 22 : .pdf of VERSION PRELIMINAIRE, texte prévu pour l’ouvrage La justification en mathématiques, éd. D. Flament et P. Nabonnand : Un arithméticien contre l’arithmétisation : les principes de Charles Hermite This file provides Background to Talk by Catherine GOLDSTEIN « Charles Hermite, Mathematical Understanding and Mathematical Nature » (see above)

Click here for links to 3 Files (Files 23 – 25) : dvi files of overheads of Talk by Catherine GOLDSTEIN « Charles Hermite, Mathematical Understanding and Mathematical Nature » (see above)

17h30-19h00 : Ivahn Smadja (Université Denis Diderot Paris 7) « Diverging Thrusts. Contrasting Insightful Plasticity with Articulate Embeddings »

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of Ivahn SMADJA’s Talk : Size 10.9 Mb ; 1 hr 31 mins 46 seconds

Wednesday 11 June 2008

9h30-11h00 : Jeremy Avigad (Carnegie Mellon) : « The role of the diagram in Euclid‘s Elements »

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of Jeremy AVIGAD’s Talk : Duration : 1 hr 51 mins 55 seconds : 13.3 Mb

11h15-12h45 :  Philippe Nabonnand (Université de Nancy 2) « La polémique entre Poncelet et Von Staudt : comprendre la dualité »

Click here for link to recording of Philippe Nabonnand’s Talk : Size 10.9 Mb : 1 hr 18 mins 58 seconds

14:30-16:00 : Gerhard Heinzmann (Université de Nancy 2)  « Mathematical Comprehension and Intuition »

Click here for link to recording of Gerhard HEINZMANN’s Talk : Size 10.2 Mb : 1 hr 13 mins 49 seconds

16h15-17h45 : Mark Steiner (University of Jerusalem) : « Getting more out of mathematics than we put in: the case of complex numbers and their generalizations »

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to recording of Mark STEINER’s Talk ; Duration 1 hr 29 mins 21 seconds

18:00-19:30 : Michel Paty (CNRS Rehseis) : « La Structure du rationnel dans l’invention de la theorie de la relativite et de la theorie quantique »

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of Michel PATY’s Talk : Size 10.7 Mb : 1 hr 17 mins 37 seconds.

 

Wednesday 11 June 2008 :

Seminar on Historical and Epistemological Approaches to the Study of Mathematical Concepts ; IHP (Institut Henri Poincare) 14:00 hrs

Talk by Michel SERFATI (Convenor of Seminar) : Marshal Stone : Ideals and Duality : Stone’s contributions to the conceptual transformation of notions of algebraic structure 1920 – 1950 and the role of his work in the genesis of Category theory.

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of Michel SERFATI’s Talk and sunsequent discussions : Duration : 1 hr 45 mins 37 seconds

 

Thursday 12 June 2008 : List of recordings of June 9th–13th 2008 : International Workshop on Mathematical Understanding (continued)

9h30-11h00 : Jan von Plato (University of Helsinki) « A combinatorial view of mathematical proofs »

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of Jan von PLATO’s Talk : Duration : 1 hour 29 mins 09 seconds

11h15-12h45 : Joël Merker (ENS Ulm, DMA & LATP) « Insights towards the speculative thought of formal computation »

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of Joel MERKER’s Talk : Duration : 1 hour 24 minutes 30 seconds

14h30-16h45 : Andrew Arana (Kansas State University) & Mic Detlefsen (University of Notre-Dame)« Purity and Understanding »

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of Talk by Andrew ARANA and Mic DETLEFSEN : Duration : 2 hours 5 minutes 43 seconds

17h-18h30 : Jean-Jacques Szczeciniarz (Université Paris 7) : « Le Galoisisme de Grothendieck »

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of Jean-Jacques SZCZECINIARZ’s Talk : Duration : 11.5 Mb : 1 hr 23 minutes 30 seconds

Click here for File (File 34) of Overheads of JJ Szczeciniarz’s Talk.

 Friday 13 June 2008

9h30-11h00 : Paolo Mancosu (University of Berkeley) : « Understanding, Explanation and Unification »

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to recording of Paolo MANCOSU’s Talk : Duration : 1 hour 30 minutes 01 second

11h15-12h45 : Stewart Shapiro (Ohio State University) : « An ‘i’ for an i. Reference and indiscernibility »

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to recording of Stewart SHAPIRO’s Talk : Duration : 1 hour 27 minutes 04 seconds

14h30-16h00 : Marco Panza (CNRS, Rehseis) : « From the naturals to the reals using abstraction »

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   to recording of Marco PANZA’s Talk : Duration : 1 hour 33 minutes 18 seconds

16h15-17h45 : José Ferreiros (University of Sevilla) : «Conceptual understanding, logical consistency, and mathematical existence»

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  of Jose FERREIROS’ Talk : Duration : 1 hour 27 minutes 08 seconds

End of Section on June 9-13 Workshop on “Mathematical Understanding

Tuesday 17th June 2008 : An International Workshop in Seville, Spain on “Mathematical Practices”

Talk 1 by Mario SANTOS-SOUSA (Madrid) : The Shape of Number

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for link to recording of this Talk (Last part of Talk and Q&A and Discussions only)

Talk 2 : Marcus GIAQUINTO (London) : Synthetic A Priori Knowledge in Geometry : The Recovery of A Kantian Insight

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for link to Recording of First Part of Marcus GIAQUINTO’s Talk

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for link to Recording of Second Part of his Talk.

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for link to Recordings of Q&A and Discussion Session following Marcus Giaquinto’s Talk.

Talk 3 : Ken MANDERS (Pittsburgh) : Descartes Transformation of Geometrical Reasoning

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for link to recording of Ken MANDERS Talk

Talk 4 : Hourya BENIS-SINACEUR (Paris) : Practices and Styles in Mathematics

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for link to recording of this Talk

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for Link to Discussion Period and Q&A Session after Talk

 

October 10th – 31st 2008 : Prof. Mic Detlefsen gave a series of four lectures during October at the École Normale Supérieure (ENS), 45, Rue d’Ulm, Paris.

The title of the lectures was: “In Search of Formalism”.

Lecture I: Friday, October 10, 2008, 16h00-18h00, Salle Cavaillès

Lecture II: Friday, October 17, 2008, 16h00-18h00, Salle Cavaillès

Lecture III: Friday, October 24, 2008, 16h00-18h00, Salle Cavaillès -

Lecture IV: Friday, October 31, 2008 16h00-18h00, Salle des Actes.

 

October 29th 2008 : The fall IP Fellows Seminar took place in Nancy (University Nancy 2, Campus Lettres et Sciences Humaines, room G-04), October 29th. 2008 The program was as follows: Session I (10h30-12h00):

Paul McCallion (IP Fellow), “Ideality and the integers” -

Session II (13h30-15h00): Fabien Schang (IP Fellow), “An abstract object in logic: logical value, and its philosophical import”

Session III (15h15–16h45): John Mumma (IP Fellow), “The real and the ideal in complex projective space”

 

December 10th 2008

Seminaire “Philosophie des Mathematiques” REHSEIS/University Paris 7 : 1 Day Workshop “Conceptual issues in Analysis”

Talk 1 : Benoit TIMMERMANS (V.U. Brussels) : An Analysis of the Typologies of Analysis

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  of Benoit TIMMERMANS Talk ; Duration : 1 hour 23 mins 08 seconds

Talk 2 : Michael BEANEY : (York) : Conceptions of Analysis in Early Analytic Philosophy

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  of Michael BEANEY’s Talk : Duration : 2 hours 7 mins 50 seconds

December 15th – 16th 2008 :

A Workshop on “Geometrical Thinking” in Nancy (Université Nancy 2, Amphithéâtre Maison des Sciences de l’Homme Lorraine), took place on December 15th – 16th 2008. Program and abstracts are available on this page.

The Talks at this Workshop were recorded and can be listened to below, together with an additional lecture delivered by Profesor Jeremy GRAY on the morning of December 17th 2008

Recordings of Talks at IP Workshop on Geometrical Thought Univ of Nancy 2 15th – 16th December 2008

December 15th 2008 Day 1 of Meeting :

Talk 1 : Jeremy GRAY (Open University UK) : On the Nature of Geometrical Thought : The Case of Minimal Surfaces

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 to the Recording of Jeremy GRAY’s Talk : 1 hour 04 minutes 06 seconds : 117 MB

Click here for his overheads

15th December 2008 Talk 1 Part II (Discussions following Talk) : 1 hour 00 minutes 15 seconds : 110 MB

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  of Discussions following Jeremy GRAY’s Talk

Talk 2 : Michael HALLETT (McGill University) : Geometry and Number in The Thought of Hilbert 1891 – 1905

Plus Following Discussions

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  to Recording of Michael HALLETT’s Talk : 2 hours 22 minutes 16 seconds : 260 MB

Talk 3 :  Douglas JESSEPH (University of Southern Florida) :   “The Very Soul of Mathematics” : The Mathematical Lectures of Isaac Barrow and The Theory of Ratio and Quantity in the 17th Century

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 to recording of Douglas JESSEPH’s  Talk : 1 hour 57 minutes 20 seconds :  Track 44  : 214 MB

16th December 2008 Day 2 of Meeting

Talk 1 :   Mary DOMSKI (Phil. Univ of New Mexico)  :  Kant on The Imagination and Geometrical Certainty

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 to recording of Mary DOMSKI’s Talk :  1 hour 47 mins 25 seconds  : 196 Mb

TALK 2 :  Victor PAMBUCCIAN (State University of Arizona)

Elementary Geometries, Groups and Fields : Resemblances and Differences between Geometric and Algebraic Standpoints.

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 to recording of Victor PAMBUCCIAN’s Talk : Duration :  1 hour 35 minutes 34 seconds  Track 46  :  174 MB

TALK 3  (Part 1): Henk BOS (Universities of Utrecht and Aarhus)

The Early Modern Tradition of Problem Solving (Late 16th – early 17th Century) as the Context for new ideas about the Nature of Geometry

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to recording of Part 1 of Henk BOS’s Talk :   1 hour 29 minutes 54 seconds   Track  47  : 164 MB

TALK 3 (Part 2)   : Henk BOS (Universities of Utrecht and Aarhus)  :  The Early Modern Tradition of Problem Solving (Late 16th – early 17th Century) as the Context for new ideas about the Nature of Geometry

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 to recording of Last Part of Talk plus following Discussions  Duration :  45 minutes 33 seconds

End of section of recordings of Nancy Workshop on Geometrical Thinking

—oOo—

December 17th  2008 :  Additional Talk at Archives Henri Poincare Nancy 2 :  Talk in Series : Grandes Conferences des Archives Poincare

Jeremy GRAY (Centre for the History of The Mathematical Sciences, Open University UK)

Poincare and Complex Function Theory

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of this Talk  (First Part of Talk Missing)  :  1 hour 25 minutes 8 seconds  Size : 19.8 Mb

End of 2008 Recordings

 

2009 RECORDINGS of Ideals of Proof and related Events

January 22nd 2009 Ideals of Proof Fellows Seminar

The Second 2009 IP Fellows Seminar took place in Paris, Thursday, January 22nd 2009 Ecole Normale Supérieure, Salle Dussane. The Special guest speaker was Prof. Agustin Rayo (Philosophy, MIT). The program is available here.

22nd January 2009 : 2nd IP Fellows Seminar

First Talk by Renaud CHORLAY : “Ways out of the Grey”

Size 1.65 GB Bitrate 1411 Kbps (Wave Sound File – Highest Quality sound reproduction)

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22nd January 2009 : 2nd IP Fellows Seminar

Andrei RODIN : How Mathematical Concepts Get their Bodies : The Example of Forcing

1 hour 17 minutes 44 seconds

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Professor Augustin RAYO :

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 of discussions following his Talk.

Other speakers at this IP Fellows Workshop were unfortunately not recorded.

 

 

February 27th 2009 : The Third IP Fellows Seminar at 9h30 in Salle17B of the Halle aux Farines building on the Grands Moulins Campus of University Paris 7 -Diderot. The program is available here.

 

February 27th 2009 : 3rd IP Fellows Workshop. Session I 9:30 – 11:00 : Sebastian MARONNE :

Ideal Elements and Projective Geometry in Modern Mathematics

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Session II : 11:15 – 12:45 : Oliver SCHAUDT :

Abstraction and Ideation : A Constructivist Approach to the Nature of Mathematical Concepts

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Session III (Focus Session) 14:00 – 15:30 : Paul McCALLION :

Ideal Numbers –vs- Numerical Properties

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Session IV (Focus Session) 15:45 – 17:15 : John MUMMA :

Contentful reasoning and Rigor in Elementary Geometry

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MARCH 5th 2009 : A joint Ideals of Proof-REHSEIS workshop on the Topic of “Ideal Elements in Mathematics” took place in Paris on Thursday, March 5th, 2009, at 9h30 The program is available here.

The following Talks in this Workshop were recorded :

5th MARCH 2009 :REHSEIS 1 Day Workshop

Talk by David RABOUIN on Leibniz on Infinitesimals

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Joint Talk by Karine CHEMLA Chemla and B. Belhoste (Main part) 1 hour 20 mins 57 seconds

Part i) Belhoste on Poncelet’s ideal Elements in Geometry : Between Carnot and Chasles

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Talk by Karine Chemla (Part) 22 mins 32 seconds

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Karine Chemla and B. Belhoste Joint Talk on Poncelet’s use of Ideal Elements : Discussion Session after Lunch : 28 minutes 11 seconds

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Talk by Brice HALIMI : Ideal Elements and Extensions : The Case of Nonstandard Set Theory : 1 hour 21 mins 47 seconds

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Click here for Overheads

Talk by Ivahn SMADJA : Kronecker on Ideal Numbers and Mathematical Substance :

1 hour 43 minutes 58 minutes

Click here for link to Ivahn Smadja’s Talk

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20th March 2009 : Seminaire RIEMANN Ecole Normale Superieure : Working Group on the Reception of Riemann’s Work

(Not an IP Event, but IP Fellows regularly take part)

Talk 1 by JJ SZCZECINIARZ : The Reading of Rieman, esp. the 1854 Habilitationschrift, in Spivak’s Texts on Differential Geometry

2 hours 18 minutes 18 seconds : Click

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20th March 2009 : Seminaire RIEMANN ENS : Working Group

Talk 2 by Francois CHARGOIS : Hermann Weyl’s 1919 Re-reading of Riemann (1854)

2 hours 14 minutes 54 seconds

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RECORDINGS OF Seminaire Riemann 27th March 2009

« Kronecker, Algèbre, géométrie algébrique, arithmétique »

Talk 1 Jacqueline Boniface (Université de Nice)

« Concept et calcul chez Kronecker »

1 hr 21 mins 23 seconds : Click

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Talk 2 : Frédéric Brechenmacher (Université d’Artois, LML, EA 2462)

« Articulations entre arithmétique et algèbre chez Kronecker »

1 hr 28 mins 39 seconds : Click

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(The Following cancelled his Talk : Erwan Penchèvre (CHSPAM, Université Paris 7)

Kronecker et sa méthode d’élimination )

 

April 15th – 16th 2009 : Ideals of Proof/Chaire D’Excellence Research Group Workshop on the Ideas of Proof Theory

The Ideals of Proof Chaire d’Excellence Research Group sponsored a two day workshop on April 15th and April 16th 2009 in Paris on The Fundamental Idea of Proof Theory. in the Salle Dussane of the Ecole Normale Supérieure (45 rue d’Ulm, Paris 75005). The program is available here.

Day 1 ; 15th April 2009

Talk 1 by Per MARTIN-LOF : Hilbert and the Notion of Naturality of Proofs

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Talk 2 : Dag PRAWITZ : Conflicting Intuitions regarding Deductive Proof

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Day 2 : 16th April 2009 :

Talk by Rafael NUNEZ : Towards the Cognitive Foundations of Mathematical Reasoning and Proof

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Talk by Walter SIEG : Uncovering Aspects of the Mathematical Mind

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April 30th 2009 Nancy : 4th IP Fellow Seminar

The fourth IP Fellows Seminar took place in Nancy on Thursday, April 30th 2009. The program is available here.

 

 

Wednesday 13th May 2009 : Special Joint Ideals of Proof – REHSEIS Workshop with 2 Invited Speakers

A joint Ideals of Proof-REHSEIS workshop took place on Wednesday, May 13th 2009 with Talks by Professor Steve AWODEY and Professor Colin McLARTY The program is available here.

Talk 1 by Steve AWODEY : Ideals and Proofs : Domain Extensions in Algebraic Set Theory and a category Theoretic Viewpoint on the Objects of A Theory of Proofs : 1 hour 37minutes 29 seconds

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Talk 2 by Colin McLARTY : What Does The Philosophy of Mathematics Gain From The Study of Contemporary Mathematics ? Plus following discussions.

1 hour 16 minutes 48 seconds : Click

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21st May 2009 :

Joint ENS /IHPST/REHSEIS Workshop with participation of IP Fellow Jeremy Avigad

Talk 1 : Jeremy AVIGAD (Carnegie-Melon) : Why Math is Hard (and How This Bears on the Objectivity of Normative Assessments of Mathematical Practice)

1 hr 51 mins 28 seconds : Click here for link to recording of Jeremy Avigad’s Talk

Talk 2 : Alex PASEAU (Oxford) : Hilbert, Godel, Instrumentalism and Inductive Evidence : 1 hour 49 mins 29 seconds : Click

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22nd MAY 2009 : Seminaire RIEMANN : ENS Salle Henri Cartan :

Talk 1 : Gilles COHEN-TANNOUDJI : Le Concept De L’Horizon de Realite Chez Ferdinand GONSETH : 1 hour 25 minutes 06 seconds : Click

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Track 24 : Renaud CHORLAY (IP Fellow) : En Quel Sens Veblen et Whitehead Fondent-Ils La Gometrie Differentielle ? : 1 hour 35 minutes 57 seconds : Click

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May 26th 2009 : An Ideals of Proof Workshop “Mathematical Knowledge, Sense and Content” with Juliet Floyd and Jeremy Avigad took place in Paris. The program is available here.

Talk 1 : Juliet FLOYD (Boston) : Wittgenstein, Godel and Turing :

1 hour 28 minutes 48 seconds :

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Talk 2 : Jeremy AVIGAD (CMU) : The Role of Proof in Modern Mathematics

1 hour 43 minutes 16 seconds : Click here for link to Recording of Jeremy AVIGAD’s Talk

 

June 3rd – 24th 2009 : “Proof, Creation and Freedom in Mathematics” :

A Series of 4 Invited Lectures by Prof. Michael Detlefsen’s (ANR Chair D’Excellence Ideals of Proof Program) at the Collège de France

3rd JUNE 2009 : 17:00 hrs / Lecture 1 : Creation, Freedom and Concept Introduction in Mathematics

Click here for Link to recording of This Lecture

June 10, 2009 17h00 hrs : Lecture 2 : Freedom and Consistency

Click here for Link to recording of Prof. Detlefsen’s Second College de France Lecture

June 17, 2009 17h00 hrs : Lecture 3 : Freedom and Fruitfulness

Click here for Link to recording of Prof. Detlefsen’s Third College de France Lecture

June 24th, 2009 : 10h00hrs. Lecture 4 : The End of Freedom.

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Location : Salle 2, Collège de France, 11 Place Marcelin Berthelot, 75005 Paris

4th – 6th JUNE 2009 : An International Colloquium entitled “ONTOLOGICAL SHIFTS IN GEOMETRY” Took place under the joint auspices of The Ideals of Proof Program and REHSEIS in The Seminar Room at Universite Paris 7

 

4th – 6th JUNE 2009 : IP/REHSEIS Joint Conference (Universite Paris VII)

ONTOLOGICAL SHIFTS IN GEOMETRY

4th June 2009 Day 1 of Conference on Ontological Shifts in Geometry

(Talk 1 : Introductory Address by Marco PANZA followed by Talk 2 : JOHN MUMMA : Relations in Geometrical Figures versus relations in Geometric Spaces)

Click here for link to recording of Marco PANZA’s Opening Address and John MUMMA’s Talk : Track 27 : 1 hour 49 minutes 07 seconds

Talk 3 : Richard PETTIGREW : Aristotle and Lawvere on the Ontology of Geometry

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Talk 4 : (4th June PM) : Ken MANDERS : Poncelet’s Uniform Treatment of Euclidean Geometry

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Talk 5 by Sabetai UNGURU (Tel Aviv) : The 4-line locus in Apollonius’s Conics : Geometry and Algebra

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Talk 5 : Victor PAMBUCCIAN : Existence and Constructions in Axiomatic (1st Order) Geometry

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5th JUNE 2009 ; Day 2 of Conference on Ontological Shifts in Geometry

Talk 1 : Michael RESNIK : on Structuralism and Geometry

Click here for link to recording of Michael RESNIK’s Talk

Talk 2 : Geoffrey HELMANN : Does Mathematical Geometry Need Ontology ?

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Talk 3 : Jaako HINTIKKA : The Ontology of Geometry : Nominalistic, Set-Theoretic or Epistemic ? Ontological Shifts in Logic and Geometry.

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Talk 4 : Mic DETLEFSEN : Construction, Figures and Proof

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Talk 5 : Jan Van PLATO : The Point of Intuitionistic Geometry

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June 6th 2009 Day 3 of Conference on Ontological Shifts in Geometry

Talk 1 : Paola CANTU : Did Grassmann’s Theory of Extensions (Extensive Quantities) produce an Ontological Shift in Geometry?

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Talk 2: Mathieu HUSSONN : Do The Geometrical terms used in the Work of Dietrich of Freiburg’s “De Coloribus” refer to Geometrical Concepts in anything like a modern sense ?

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Talk 3 : Carla Rita PALERMINO : Galileo on The Ontological Status of Mathematical Entities

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Talk 4 : Sebastien MARONNE: Pascal and The Ontology of Infinite Objects in Geometry

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June 25th and 26th 2009 : International Conference at Pont-Au-Mousson entitled

“The Imaginary, the Ideal and the Infinite in Mathematics.”

An Ideals of Proof Project jointly sponsored workshop with the TransCoop Project of the Alexander von Humboldt Stiftung

Speakers included Andrew Arana, Michael Detlefsen, Wilfrid Hodges, Paolo Mancosu, Felix Mühlhölzer, Karl-Georg Niebergall, Michael Potter, Matthias Schirn, Ivahn Smadja, Jamie Tappenden and Albert Visser. The program is available here. Location of Conference : Pont-A-Mousson

Recordings at PONT-A-MOUSSON MEETING Thursday 25th and Friday 26th June 2009

The Imaginary The ideal and The Infinite in Mathematics :

Thursday, June 25th

Session I

8h45-10h00 Felix MUHLOLZER Philosophisches Seminar, Georg-August Universität Göttingen.

Parsons on mathematical intuition and natural numbers

(missed opening of talk. Recorded last part plus discussions)

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to recording of F. MUHLHOLZER’s Talk : 40 mins 06 seconds :

10h05-11h20 Ivahn SMADJA, Département d’Histoire et de Philosophie des
Sciences, Université Paris-Diderot (Paris 7)

The discrete and the singular: Some Kroneckerian ideas about arithmetization

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11h25-12h40 : James TAPPENDEN, Department of Philosophy, University of Michigan

Branching at branch points: Interpretations of “Riemann surface” as a fork in the road to contemporary mathematics

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Session II
14h30-15h45 : Andrew ARANA, Department of Philosophy, Kansas State : Purity and the identity of problems

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15h50-17h05 : Mathias SHIRN, Seminar für Philosophie, Logik und Wissenschaftstheorie, Universität München

Frege’s philosophy of geometry

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17h10-18h25 Wilfrid HODGES, Herons Brook, Sticklepath, Okehampton, Devon EX20 2PY, England

The literal meanings of statements in mathematical textbooks

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Day 2 of Conference : June 26th 2009

Session III

8h45-10h00 Paolo MANCOSU, Department of Philosophy, University of California at Berkeley

Measuring the size of infinite sets of integers: Was Cantor’s conception of infinite number inevitable?

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10h05-11h20 Karl-Georg NIEBERGALL, Institut für Philosophie, Humboldt Universität-Berlin

Assumptions of infinity in weak set theories and calculi of individuals

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11h25-12h40 Albert VISSER, Department of Theoretical Philosophy, Universiteit
Utrecht : Relativization and thinking modulo: How does it help us in theory reduction?

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Session IV

15h00-16h15 Michael POTTER, Faculty of Philosophy & Fitzwilliam College,
University of Cambridge : Classes as ideal elements and limitation of size

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16h20-17h35 Michael (Mic) DETLEFSEN, Department of Philosophy, University of Notre
Dame & ANR, France : Freedom and creativity in mathematics

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 The IP Fellows’ Seminar September 8, 2009 from 10h30 to 17h15, at the Ecole Normale Supérieure (45, rue d’Ulm, 75005, Paris), Immeuble Rataud, salle INFO1. Program is available here.

Talk 1 : Sean WALSH : The Role of Interpretability Results in the Justification of Axioms

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Talk 2 : Andrew ARANA: The Geometric/Algebraic Distinction

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Talk 3 : Walter DEAN : Informal Provability and Goedel’s Modal Interpretation of Intuitionism

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October 19th 2009 :

Talk to Joint Ideals of Proof/REHSEIS Meeting by Prof. Harvey FRIEDMAN (Ohio State) : The Concept Calculus

Track 1 : Introduction by Andrew Arana

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Track 2 : Talk on the Concept Calculus by Prof. Harvey FRIEDMAN (Ohio State) plus following Questions and Discussions

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October 21st – 22nd 2009

The first Paris-Nancy PhilMath Workshop took place in Nancy October 21st-22nd 2009 co-organised by the Henri Poincare Archives, IHPST and REHSEIS and supported by the Ideals of Proof Project. Presentation and Program available here.

The speakers were as follows :

Paola Cantù: On Real and Ideal Elements in Mathematics
Harvey Friedman: Conceptus Calculus
Volker Halbach: Computational Structuralism
Annika Kanckos: Hilbert’s second problem: a possible and necessary consistency proof
proof
Michael Potter: More on Replacement
Davide Rizza: Discernibility by Symmetries
Stewart Shapiro: Structures and Logics: a Case for Relativism
Hourya Sinaceur: Objets mathématiques
Claudio Ternullo: Why did Cantor Believe in the Truth of the Continuum Hypothesis?
Sean Walsh: The Justification of Mathematical Induction

Due to a technical problem, only some Talks and parts of Talks on Day 2 October 22nd 2009 were recorded. These Talks can be heard by accessing the links below together with those overheads of speakers which are available

22nd October 2009 : 2 hours 59 minutes 16 seconds

Talk 1 : Volker HALBACH on Computational Structuralism

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Talk 2 : Annika KANCKOS: Hilbert’s Second Problem : A Possible and necessary consistency proof

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Plus further Track : 20 minutes 49 seconds only

Part of Questions and Discussions Session following Talk by Michael POTTER : More on Replacement

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Overheads and abstracts of the Talks and such other information as can be supplied by the speakers will be posted here in due course.

October 23rd – NOVEMBER 13th 2009

A Course of 4 Lectures by Prof. Mic DETLEFSEN, ANR Chair D’Excellence, Ideals of Proof Programme

At ENS Paris : Godel’s Theorems and Their Significance.

Click here for link to Announcement of Lectures, Short Abstract and other information

Lecture 1 October 23rd 2009 : Basics and Background : Salle de Conférences (46, rue d’Ulm) :

2 hours 15 minutes 17 seconds.

Click here for link to recording of Lecture 1 on Godel by Mic DELEFSEN

Lecture 2 : Friday 30th October 2009 : Salle de Conférences (46, rue d’Ulm) :

The Representation of Metamathematics : 1 hour 39 minutes 58 seconds

Theories of Representation and Metamathematics : Godel’s focal argument

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Lecture 3 : Friday 6 November 2009, Salle de Conférences (46, Rue d’Ulm):

Gödel’s Theorems and Hilbert’s Program : 1 hour 50 minutes 28 seconds

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Lecture 4 : November 13th 2009 : Salle INFO1 (45, Rue d’Ulm, Immeuble Rataud) :

Gödel’s Theorems and Mechanist Views of Mind : 1 hour 33 minutes 58 seconds

Click here for link to Lecture 4 on Godel by Mic DETLEFSEN

Monday 9th NOVEMBER 2009

The IP Fellows’ Seminar of November 9, 2009 from 09h00 to 17h15, at the Ecole Normale Supérieure, Salle Jules Ferry, 29 rue d’Ulm, 75005, Paris). Program is available here. All Talks

Talk 1 : Andrei Rodin: Renewing foundations plus following discussions

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Talk 2 : Henri Gallinon: The Ideal of Truth and Ideals of Proof

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Talk 3 : Davide Crippa: As simple as possible: Descartes´algebraic interpretation of Pappus´norm

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for link to recording of Davide CRIPPA’s Talk : 1 hour 5 minutes 40 seconds

Talk 4 : Richard Pettigrew: Prospects for a Foundation for Mathematics in Category Theory

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2010 RECORDINGS of Ideals of Proof Events and closely related events

 January 25 th 2010

IP Fellows’ Workshop in ENS (45, Ulm), Salle Dussane. 9 A.M. to 6 P.M.

Speakers : First Speaker : Andrew ARANA : The Complexity of Pure and Impure Proof

Abstract: It has often been claimed that pure proofs are less valuable than impure proofs because of the relative “difficulty” or “complexity” of pure versus impure proofs. Whatever advantages pure proof may have over impure proof would be countered by disadvantages if impure proof is systematically “easier” or “simpler” than pure proof. In order to evaluate this claim, it is helpful to identify precise measures of proof complexity for which the claim may be tested. In this talk we single out a “topological” measure of proof complexity studied in recent work by Alessandra Carbone, and evaluate the thesis for that measure.

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Click here for his overheads

Second Speaker : Jeremy AVIGAD : On Understanding, Formal Verification and The Philosophy of Mathematics

Click here for link to recording of Jeremy AVIGAD’s Talk

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Third Speaker : WalterDEAN : Models and Recursivity :

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Fourth Speaker : Sean WALSH : Weierstrass, Frege and Husserl on the Equality of Numbers

Abstract : From the early 1860s to the mid 1880s Weierstrass lectured on Introductory Compex Analysis once every two years. A persistent feature of his lectures was a long introductory section on the development of extensions of the natural number concept and the treatment of infinite sequences. This introductory section of Weierstrass’s Lectures was discused by both Frege and Husserl in their published and unpublished writings on the philosophy of arithmetic. In this talk I shall focus on contextualizing and evaluating the respective views of Weierstrass, Frege and Husserl on Hume’s principle and the equality of numbers.

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Click here for his overheads :

—oOo—

MARCH 8th – 10th 2010 : SPECIAL EVENT IN IDEALS OF PROOF PROGRAM

“Mathesis metaphysica quadam”: Leibniz, between Mathematics and Philosophy. The Ideals of Proof (IP) Project (ANR) and REHSEIS (UMR 7219, SPHERE)  Schedule is available here.

March 8th 2010

Talk 1 :  Herbert Breger: The substructure of Leibniz’s metaphysics

Click here for link to recording of this Talk

For accompanying Overheads

Tak 2 :  Michel Serfati: Mathematics, metaphysics and symbolism in Leibniz: the principle of continuity

Click here for link to recording of this Talk

For accompanying Overheads

Talk 3 :  Vincenzo De Risi: Leibniz’s studies on the Parallel Postulate

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For accompanying Overheads

9th March 2010

Talk 1 : Philip Beeley: In deliberationibus ad vitam pertinentibus. Method and Certainty in Leibniz’s Mathematical Practice

Talk 2 :  Richard Arthur: Leibniz’s Actual Infinite in Relation to his Analysis of Matter

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For accompanying Overheads

Talk 3 :  Samuel Levey: Leibniz’s analysis of Galileo’s paradox

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For accompanying Overheads

10th March 2010

Talk 1 :  Emily Grosholz: The Representation of Time in Galileo, Newton and Leibniz

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For accompanying Overheads

Talk 2 :  Eberhard Knobloch: Analyticité, équipollence et la théorie des courbes chez Leibniz

Click here for link to recording of this Talk

For accompanying Overheads

—oOo—

 

 

24th March 2010 :  8th IP Fellows’ Seminar Paris

The 8th IP Fellows’ Seminar will meet March 24, 2010 from 09h30 to 17h25, at the Ecole Normale Supérieure, salle Favard in the new building of the ENS, 46 rue d’Ulm, 75005, Paris. Program is available here.

 

Talk  1 : Jean-Baptiste JOINET : Negation – From Ideality to Interaction

Click here for link to recording of this talk

Talk 2 : Dirk SCHLIMM : Pasch’s Ideal ofProof

Click here for link to recording of this talk

Talk 3 : Irina STARIKOVA : Intuition, Visualization, Geometric Shifts and Proofs.

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Talk 4 : Mark Van Atten : Intuitionism as Phenomenology : A Critique of Rota.

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8th IP Fellows’ Seminar Jean-Baptiste Joinet: Negation: from ideality to interaction
Dirk Schlimm: Pasch’s ideal of proof
Irina Starikova: Intuition, Visualization, Geometric Shifts & Proofs’
Mark van Atten: Intuitionism as phenomenology: a critique of Rota

—oOo—