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Accueil du site > Archives > Séminaires : Septembre 2008–Juillet 2012 > Programmes des séminaires 2009-2010 > Tappenden PhilMath Workshop

Tappenden PhilMath Workshop

Jamie Tappenden (University of Michigan, Ann Arbor) is visiting Professor at Paris Diderot University this term.

He will run a twice-weekly research seminar in philosophy of mathematics. The unifying theme of the seminar will be "styles of mathematical practice in the nineteenth century". Professor Tappenden’s sessions will principally draw from his forthcoming book Philosophy and the Origins of Contemporary Mathematics : Frege and his Mathematical Context to appear with Oxford University Press.

Jamie Tappenden (Université du Michigan, Ann Arbor) est professeur invité à l’Université Paris Diderot ce semestre. Il dirigera un séminaire de recherche en philosophie des mathématiques (en anglais, à raison de deux seances par semaine en général). Le thème unificateur du séminaire sera "styles de mathématiques au XIXe siècle". Plusieurs séances seront fondées sur le livre de Prof. Tappenden : Philosophy and the Origins of Contemporary Mathematics : Frege and his Mathematical Context à paraître chez Oxford University Press.

Sessions will be conducted in English and will be held at
Université Paris Diderot-Paris,
Bâtiment Condorcet
4, rue Elsa Morante,
75013 Paris.
Access

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May 27th, 2010

Location : Room 483A-Malevitch, 14h-17h

J. Tappenden (University of Michigan)
"Frege as Historical Mathematician and Philosopher : Some guidelines" Frege poses special challenges for the historian of philosophy and logic. Much of the relevant archival material is lost, and his intellectual environment was in many ways unlike what we tend to find with philosophers from the past. This session is aimed at spelling out some of the basic facts that can be ascertained about Frege’s intellectual mileu and what we can learn about Frege from them.
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May 31st, 2010

Location : Room 646A-Mondrian, 14h-17h

J. Tappenden (University of Michigan)
"Frege as Historical Mathematician and Philosopher : Some guidelines" (2)

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June 7th, 2010

Location : Room 646A-Mondrian, 14h-17h

Jamie Tappenden and Danielle Macbeth (University of Michigan and Haverford College)
Professors Tappenden and Macbeth will discuss the idea of "fruitful concepts" in nineteenth century mathematics, especially in Frege’s writings and in Frege’s philosophical environment. Prof. Tappenden’s discussion will draw from the relevant sections of his book, Professor Macbeth’s will draw from a paper entitled "Diagrammatic Reasoning in Frege’s Begriffsshrift" (MACBETH PAPER NOW AVAILABLE : It can be downloaded from the link at the bottom of this page (click on icon on left)

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June 10th, 2010

Location : Room 483A-Malevitch, 14h-17h

J. Ferrieros (Madrid/Univ. de Sevilla) :
Dedekind’s Logicism PAPER NOW AVAILABLE - IT CAN BE DOWNLOADED FROM THE LINK AT THE BOTTOM OF THIS PAGE (click on icon on right)

J. Carter (Syddansk Universitet - Odense DK) :
Understanding, representations and visualisation

Carter presentation abstract :
In a recent paper J. Tappenden (2005) addresses the topic of understanding in connection with naturalness of definitions, fruitfulness and visualization. The underlying motive for this discussion is to obtain a philosophical description of the “mathematical revolution initiated by Riemann in the nineteenth century”. This talk shall primarily address the topic of understanding and visualization.By understanding is meant to ‘understand why’ a certain result holds. It is also assumed that understanding why a result holds may lead to new results. We start by discussing a number of descriptions of understanding from mathematics education. The first is by R. Duval who claims that understanding consists of the ability to shift between different semiotic registers. Underneath Duval’s theory lies a Platonic conception of mathematical objects that we will argue is problematic. Instead it will be argued that it is more appropriate to talk of mathematical practice as dealing with representations in different contexts. This is more in line with a description of understanding due to Ajdukiewicz, according to which ‘a person understands an expression if on hearing it he directs his thoughts to anobject other than the word in question’. We shall discuss this description in the light of some examples where one understands expressions by representing them by certain pictures or diagrams. We discuss first what it takes for a representation to further understanding of the represented and, second, why it is that these diagrams are fruitful. Finally we investigate whether these answers are useful in the context of Riemann’s work.

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June 17th, 2010

Location : Room 483A-Malevitch, 14h-17h

Andrew Arana (Kansas State University) :
Analytic and Synthetic Methods in Nineteenth Century Geometry

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June 23rd, 2010 (Note : Wednesday this week, not Monday

Location : Room 646A-Mondrian, 14h-17h

Colin Mclarty (Case Western Reserve, Cleveland USA)
Emmy Noether’s First Great Mathematics, and the Culmination of First- phase Logicism, Formalism and Intuitionism.

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June 24th, 2010

Location : Room 483A-Malevitch, 14h-17h

Jamie Tappenden and Marco Panza ; with participation by Jeremy Gray and Umberto Bottazzini (University of Michigan ; Open University/Warwick ; Milano)
Discussion of the Riemann and Weierstrass chapters from the forthcoming Jeremy Gray and Umberto Bottazzini history of nineteenth century complex analysis ; Professors Gray and Bottazzini will attend to participate in the discussion ; each will read a brief presentation of core ideas from the chapter.

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June 28th, 2010


Location : Room 646A-Mondrian, 14h-17h

Mic Detlefsen (University of Notre Dame (USA)
Symbolic and Formal Methods in Nineteenth Century Algebra

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July 1st, 2010

Location : Room 483A-Malevitch, 14h-17h

Jamie Tappenden and Ivahn Smadja (University of Michigan and Rehseis Paris-Diderot)
In the first half of the session Professor Tappenden will discuss Hilbert’s early lectures on the foundations of geometry and Frege’s reactions, with a brief transitional observation on a scholarly puzzle concerning Frege and Minkowski’s geometry of numbers in connection with Hilbert’s foundations of geometry. In the second half of the session, "Local Axioms in Disguise : Did Hilbert Really Dismiss Diagrams ?" Professor Smadja will discuss Hilbert’s assessment of Minkowski’s geometry of numbers.
A version of Prof. Smadja’s paper is available here :
http://halshs.archives-ouvertes.fr/...

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July 5th, 2010

Location : Room 646A-Mondrian, 14h-17h

Karine Chemla and Jean Paul Van Bendegem (Rehseis Paris-Diderot and Vrije Universiteit Brussel)
Simplicity in Chasles and Monge ; The first hour of the session will be covered by Professor Tappenden, devoted to background framing information on C19 geometry, including a discussion of Jeremy Gray’s Worlds out of Nothing.
In the final hour Professor van Bendegem will discuss beauty as an aspect of mathematical method.
Description :
No one doubts that mathematicians experience beauty in their mathematical practices. In this lecture I will concentrate on the role of aesthetics in mathematical proofs and propose a model to evaluate this beauty. In addition I want to defend the thesis that these considerations form an integral part and an essential ingredient of mathematical development.

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