Ideals of Proof 2008 – 2011
Click here for homepage of Ideals of Proof program
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.
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- Summaries & Lecture Notes of the Talks (made available by Ideals of Proof program)
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).
Click here for link to recording of Invited Lecture by Prof.. Dag PRAWITZ (Theoretical Philosophy, Stockholm) “On The Validity of Inference”
For his overheads :
Click here to listen 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
Click here for link 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”
Click here for link to recording of Part 1 of Scott WALKER’s Talk
Click here 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
Click here 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
Click here 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.
Click here to listen 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 ?
Click here for link to recording 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.
Click here for link 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
Click here for link 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
Click here for 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)
Click here for link 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
Click here for link 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)
Click here for link 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.
Click here for link to recording 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
Click here to listen 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 »
Click here for link 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 »
Click here for link 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 »
Click here for link 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 »
Click here for Link 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»
Click here for link 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 »
Click here to listen 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 » Click here for link to recording 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 »
Click here for link to recording 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 »
Click here for link to recording 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 »
Click here for link 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 »
Click here for link to recording 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.
Click here for link to recording 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 »
Click here for link to recording 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 »
Click here for link to recording 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 »
Click here for link to recording 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 »
Click here for link to recording 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 »
Click here for link 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 »
Click here for link 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 »
Click here for link 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»
Click here for link to recording 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
Click here 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
Click here for link to Recording of First Part of Marcus GIAQUINTO’s Talk
Click here for link to Recording of Second Part of his Talk.
Click here 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
Click here for link to recording of Ken MANDERS Talk
Talk 4 : Hourya BENIS-SINACEUR (Paris) : Practices and Styles in Mathematics
Click here for link to recording of this Talk
Click here 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
Click here for link to recording of Benoit TIMMERMANS Talk ; Duration : 1 hour 23 mins 08 seconds
Talk 2 : Michael BEANEY : (York) : Conceptions of Analysis in Early Analytic Philosophy
Click here for link to recording 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
Click here for link 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
Click here for link to Recording 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
Click here for link 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
Click here for link 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
Click here for link 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.
Click here for link 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
Click here for link 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
Click here for link 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
Click here for link to recording 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)
Click here for link to recording of Renaud CHORLAY’s Talk
22nd January 2009 : 2nd IP Fellows Seminar
Andrei RODIN : How Mathematical Concepts Get their Bodies : The Example of Forcing
Click here for link to recording of Andrei Rodin’s Talk
Click here for link to recording of discussion/Q&A Session following his Talk.
Professor Augustin RAYO :
Click here for recording of Professor RAYO’s Talk
Click here for recording 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
Click here for link to recoring of Sebastian MARONNE’s Talk
Click here for his Overheads
Session II : 11:15 – 12:45 : Oliver SCHAUDT :
Abstraction and Ideation : A Constructivist Approach to the Nature of Mathematical Concepts
Click here for link to recording of Oliver SCHAUDT’s Talk
Session III (Focus Session) 14:00 – 15:30 : Paul McCALLION :
Ideal Numbers –vs- Numerical Properties
Click here for link to recording of Paul McCALLION’s talk and subsequent discussion
Session IV (Focus Session) 15:45 – 17:15 : John MUMMA :
Contentful reasoning and Rigor in Elementary Geometry
Click here for link to recording of John MUMMA’s Talk and subsequent discussion
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
Click here for link to recording of David RABOUIN’s Talk
and here for link to recording of Discussion/Q&ASession following his Talk
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
Click here for link to recording of Belhoste’s Talk
Talk by Karine Chemla (Part) 22 mins 32 seconds
Click here for link to recording of Karine Chemla’s Talk.
Karine Chemla and B. Belhoste Joint Talk on Poncelet’s use of Ideal Elements : Discussion Session after Lunch : 28 minutes 11 seconds
Click here for link to recording of Discussion Session following Joint Talk of Chemla and Belhoste
Talk by Brice HALIMI : Ideal Elements and Extensions : The Case of Nonstandard Set Theory : 1 hour 21 mins 47 seconds
Click here for link to recording of Brice HALIMI’s Talk
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
Click here for link to discussions after his Talk
Click here for his Overheads
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 here for link to recording of JJ Szczeciniarz’s Talk.
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
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 here for link to Recording of Jacqueline Boniface’s Talk.
Talk 2 : Frédéric Brechenmacher (Université d’Artois, LML, EA 2462)
« Articulations entre arithmétique et algèbre chez Kronecker »
1 hr 28 mins 39 seconds : Click here for link to recording of F. Brechenmacher’s Talk
(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
Click here for recording of talk
and here for recording of following discussions
Talk 2 : Dag PRAWITZ : Conflicting Intuitions regarding Deductive Proof
Click here for recording of talk
and here for recording of following discussions
Day 2 : 16th April 2009 :
Talk by Rafael NUNEZ : Towards the Cognitive Foundations of Mathematical Reasoning and Proof
Click here for recording of talk
and here for recording of following discussions
Talk by Walter SIEG : Uncovering Aspects of the Mathematical Mind
Click here for recording of talk
and here for recording of following discussions
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
Click here for link to recording of Steve AWODEY’s Talk
Click here for Overheads
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 here for link to Recording of Colin McLARTY’s Talk.
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 here for link to recording of Alex PASEAU’ Talk
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 here for link to Recording of Prof. COHEN-TANNOUDJI’s Talk
Track 24 : Renaud CHORLAY (IP Fellow) : En Quel Sens Veblen et Whitehead Fondent-Ils La Gometrie Differentielle ? : 1 hour 35 minutes 57 seconds : Click here for link to recording of Renaud CHORLAY’s Talk
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 : Click here for link to Recording of Juliet FLOYD’s Talk
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.
Click here for link to Prof. Detlefsen’s Fourth College de France Lecture
and Here for recording of discussion/Q&A Session following this Lecture
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
Click here for link to recording of Richard PETTIGREW’s Talk : Track 28 : 1 hour 18 minutes 06 seconds
Talk 4 : (4th June PM) : Ken MANDERS : Poncelet’s Uniform Treatment of Euclidean Geometry
Click here for link to recording of Ken MANDERS Talk : Track 29 : 1 hour 15 minutes 54 seconds
Talk 5 by Sabetai UNGURU (Tel Aviv) : The 4-line locus in Apollonius’s Conics : Geometry and Algebra
Click here for link to recording of Sebatai UNGURU’s Talk : Track 30 : 1 Hour 18 minutes 32 seconds
Talk 5 : Victor PAMBUCCIAN : Existence and Constructions in Axiomatic (1st Order) Geometry
Click here for link to recording of Victor PAMBUCCIAN’s Talk : Track 31 : 1 hour 17 minutes 47 seconds
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 ?
Click here for link to recording of Geoffrey HELMANN’s Talk : Track 32 : 1 hour 23 minutes 22 seconds
Talk 3 : Jaako HINTIKKA : The Ontology of Geometry : Nominalistic, Set-Theoretic or Epistemic ? Ontological Shifts in Logic and Geometry.
Click here for link to recording of Jaako HINTIKKA’s Talk.
Talk 4 : Mic DETLEFSEN : Construction, Figures and Proof
Click here for link to recording of Mic DETLEFSEN’s Talk
Talk 5 : Jan Van PLATO : The Point of Intuitionistic Geometry
Click here for link to recording of Jan Van PLATO’s Talk : Track 35 : 1 hour 00 minutes 27 seconds
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?
Click here for link to recording of Paola CANTU’s Talk : Track 36 : 1 hour 17 minutes 11 seconds
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 ?
Click here for link to recording of Mathieu HUSSON’s Talk : Track 37 : 1 hour 12 minutes 33 seconds
Talk 3 : Carla Rita PALERMINO : Galileo on The Ontological Status of Mathematical Entities
Click here for link to recording of Carla Rita PALERMINO’s Talk : Track 38 : 1 hour 31 minutes 42 seconds
Talk 4 : Sebastien MARONNE: Pascal and The Ontology of Infinite Objects in Geometry
Click here for link to recording of Sebastian MARONNE’s Talk. Track 39 : 1 hour 14 minutes 25 seconds
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)
Click here for link 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
Click here for link to recording of Ivahn SMADJA’s Talk. Track 41 : 1 hr 07 mins 30 seconds
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
Click here for link to recording of Jamie TAPPENDEN’s Talk : Track 42 : 1 hr 23 mins 40 seconds
Session II
14h30-15h45 : Andrew ARANA, Department of Philosophy, Kansas State : Purity and the identity of problems
Click here for link to recording of Andrew ARANA’s Talk : Track 43 : 1 hr 9 mins 16 seconds
15h50-17h05 : Mathias SHIRN, Seminar für Philosophie, Logik und Wissenschaftstheorie, Universität München
Frege’s philosophy of geometry
Click here for link to recording of Mathias SCHIRN’s Talk : Track 44 : 1 hr 19 mins 38 seconds
17h10-18h25 Wilfrid HODGES, Herons Brook, Sticklepath, Okehampton, Devon EX20 2PY, England
The literal meanings of statements in mathematical textbooks
Click here for link to recording of Wilfrid HODGES Talk : Track 45 : 1 hr 12 mins 36 seconds
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?
Click here for link to recording of Paolo MANCOSU’s Talk : Track 46 : 1hr 24 mins 08 seconds
10h05-11h20 Karl-Georg NIEBERGALL, Institut für Philosophie, Humboldt Universität-Berlin
Assumptions of infinity in weak set theories and calculi of individuals
Click here for link to recording of Karl-Georg NIEBERGALL’s Talk : Track 47 : 1 hr 03 mins 33 seconds
11h25-12h40 Albert VISSER, Department of Theoretical Philosophy, Universiteit
Utrecht : Relativization and thinking modulo: How does it help us in theory reduction?
Click here for link to recording of Albert VISSER’s Talk : Track 48 : 1 hr 17 mins 02 seconds
Session IV
15h00-16h15 Michael POTTER, Faculty of Philosophy & Fitzwilliam College,
University of Cambridge : Classes as ideal elements and limitation of size
Click here for link to recording of Michael POTTER’s Talk : Track 49 : 55 mins 32 seconds
16h20-17h35 Michael (Mic) DETLEFSEN, Department of Philosophy, University of Notre
Dame & ANR, France : Freedom and creativity in mathematics
Click here for link to recording of Mic DETLEFSEN’s Talk : Track 50 : 1 hr 22 mins 28 seconds
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
Click here for link to recording of Sean WALSH’s Talk : Track 51 : 1 hour 16 minutes 10 seconds
Talk 2 : Andrew ARANA: The Geometric/Algebraic Distinction
Click here for link to Andrew ARANA’s Talk : Track 52 : 1 hour 25 minutes 10 seconds
Talk 3 : Walter DEAN : Informal Provability and Goedel’s Modal Interpretation of Intuitionism
Click here for link to recording of Walter DEAN’s Talk : Track 54 : 1 hour 6 minutes 14 seconds
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
Click here for link to recording of Introductory Remarks
Track 2 : Talk on the Concept Calculus by Prof. Harvey FRIEDMAN (Ohio State) plus following Questions and Discussions
Click here for Link to Recording of Prof. Friedman’s Talk
and here for Link to recording of following Discussions
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
Click here for link to recording of Volker HALBACH’s Talk
Talk 2 : Annika KANCKOS: Hilbert’s Second Problem : A Possible and necessary consistency proof
Click here for link to recording of Annika KANCKOS’s Talk
Plus further Track : 20 minutes 49 seconds only
Part of Questions and Discussions Session following Talk by Michael POTTER : More on Replacement
Click here for this recording
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
Click here for link to recording of Lecture 2 on Godel by Mic DETLEFSEN
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
Click here for link to recording of Lecture 3 on Godel by Mic DETLEFSEN
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
Click here for link to recording of Andrei RODIN’s Talk : 1 hour 15 minutes 13 seconds
Talk 2 : Henri Gallinon: The Ideal of Truth and Ideals of Proof
Click here for link to recording of Henri Gallinon’s Talk : 1 hour 13 minutes 11 seconds
Talk 3 : Davide Crippa: As simple as possible: Descartes´algebraic interpretation of Pappus´norm
Click here 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
Click here for link to Recording of Richard’s Talk.
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.
Click here to listen to the recording of Andrew ARANA’s Talk
Click here to listen to the recording of the following discussion/Q&A Session
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
Click here for link to recording of discussions and Q&ASession following his Talk. Click here for his overheads
Third Speaker : WalterDEAN : Models and Recursivity :
Click here for link to recording of Walter DEAN’s Talk. Click here for his overheads
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.
Click here to listen to a recording of Sean WALSH’s Talk
Click here for his overheads :
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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
Click here for link to recording of this Talk
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
Click here for link to recording of this Talk
For accompanying Overheads
Talk 3 : Samuel Levey: Leibniz’s analysis of Galileo’s paradox
Click here for link to recording of this Talk
For accompanying Overheads
10th March 2010
Talk 1 : Emily Grosholz: The Representation of Time in Galileo, Newton and Leibniz
Click here for link to recording of this Talk
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.
Click here for link to recording of this talk
Talk 4 : Mark Van Atten : Intuitionism as Phenomenology : A Critique of Rota.
Click here for link to recording of this talk
| 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 |
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