Mathematical Games

Is resolving mathematical problems a game for you? If so, here are some games.

Aimez-vous faire des jeux mathématiques? Voici deux jeux (faciles) pour commencer...


First Game/Premier jeu:
*Feeding 10 animals required 56 biscuits. The set of animals are composed by cats and dogs. A dog eats 6 biscuits and a cat eats 5 biscuits. Amongst the animals, how many are dogs and how many are cats?

*Il faut 56 biscuits pour nourrir 10 animaux. Ces animaux sont des chats et des chiens. Un chat mange 5 biscuit et un chien en mange 6. Combien y a-t-il de chats et de chiens?


Second Game/Second jeu:
*A man sells big and tiny birds. A big bird costs twice the price of a tiny one. A woman is buying 5 big and 3 tiny birds. If she had bought 3 big and 5 tiny birds, she would have save $200. How much each birds costs?

*Un marchand vend des gros et des petits oiseaux. Un gros oiseau coûte le double d'un petit oiseau. Une cliente achète 5 gros oiseaux et 3 petits oiseaux. Si elle avait acheté 3 gros et 5 petits oiseaux, alors elle aurait économisé 200€. Quel est le coût de chaque oiseau?

Solutions coming soon!
Solutions à venir!

Rorty Debates with Donald Davidson

I invite you to watch a discussion with american pragmatist philosopher Richard Rorty and analytic philosopher Donald Davidson.

Vous trouverez ici une discussion avec Richard Rorty et Donald Davidson (65 mn).



La London School of Economics propose des entretiens qui réunissent des philosophes importants. Voici le débat entre Richard Rorty et Donald Davidson (Il faut dérouler un peu la page pour en trouver le descriptif).


The London Schools of Economics has a very interesting panel of interviews with great philosophers. Here you can watch the debate between Richard Rorty and Donald Davidson.

La Bêtise en Philosophie, suite: un humour intelligent (Einstein)/Nonsense against humour (Einstein)

Contrary to postmodernists who think very highly of themselves, with no humour at all, we can find very competent researchers with a lot of humour:

À l'inverse des postmodernes qui se prennent très au sérieux, voici un exemple de dérision de la part d'une personne compétente:

"At the end of a lecture given by Einstein at Washington, a spectator, quite naively, asked a question:
-Please, would you tell us the difference between theory and practice?
-Theory is when we know all there is to know about something but nothing works. Practice is when everything works, but nobody can tell why and how. But, here, today, we combine theory and pratice: nothing works and nobody can tell why."
(The translation and all the mistakes are mine)

"Au terme d'une conférence donnée à Washington, une personne dans l'assistance questionne un peu naïvement Albert Einstein:
-Quelle est la différence entre la théorie et la pratique?
-La théorie, c'est quand on sait tout et que rien ne fonctionne. La pratique, c'est quand tout fonctionne et que personne ne sait pourquoi. Mais ici, nous avons réuni théorie et pratique: rien ne fonctionne et personne ne sait pourquoi."

Jean Piat et Patrick Wajsman, Vous n'aurez pas le dernier mot! Petite anthologie désinvolte des plus belles réparties, Albin Michel, Paris, 2006. D'autres paroles mémorables et drôles/other good phrases (in french only): ici.

Philosophy of Mathematics Conference

The philosophy department at New York University will be hosting a conference on the Foundations of Mathematics, in April (10-12) of 2009.


List of Speakers:

John Burgess (Princeton University)
Haim Gaifman (Columbia University)
Joel Hamkins (City University of New York)
Kai Hauser (Humboldt-Universität Berlin)
Peter Koellner (Harvard University)
Stewart Shapiro (Ohio State University)
Stephen Simpson (Pennsylvania State University)
William Tait (University of Chicago)
Neil Tennant (Ohio State University)
W. Hugh Woodin (University of California, Berkeley)

Patricia Churchland interviews E. O. Wilson

Vous trouverez ici un entretien entre Patricia Churchland et E. O. Wilson.

I invite you to watch an interview of prof. E. O. Wilson by Patricia Churchland.

Patricia Churchland (née en 1943), professeur à l'UCSD (University of California, San Diego), s'entretient avec E. O. Wilson (né en 1929), professeur au Department of Organismic and Evolutionary Biology, Harvard University, biologiste et environnementaliste. Il s'agit d'un extrait du documentaire réalisé par Sophie Bensadoun et Pierre Faye, Vues de l'esprit.

Patricia Churchland, UCSD Professor, is interwiewing Pellegrino University Research Professor in Entomology for the Department of Organismic and Evolutionary Biology at Harvard University and conservationist E. O. Wilson. This is an excerpt of Sophie Bensadoun and Pierre Faye documentary Vues de l'esprit.




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Advances in Modal Logic's Workshop, 9-12 September 2008, Nancy, France

Advances in Modal Logic is an initiative aimed at presenting an up-to-date picture of the state of the art in modal logic and its many applications. The initiative consists of a conference series together with volumes based on the conferences.

The conference is the main international forum at which research on all aspects of modal logic is presented. The Advances in Modal Logic Initiative was founded in 1995 and the first AiML Conference was held in 1996 in Berlin, Germany. Since then the AiML Conference has been organised on an bi-annual basis with previous meetings being held in 1998 in Uppsala, Sweden, in 2000 in Leipzig, Germany (jointly with ICTL-2000), in 2002 Toulouse, France, in 2004 in Manchester, UK, and in 2006 in Noosa, Australia.

In 2008, Advances in Modal Logic will be organized by LORIA, le Laboratoire Lorrain de Recherche en Informatique et ses Applications (Lorraine Laboratory of IT Research and its Applications), in Nancy, France.


1) Invited speakers at AiML-2008 will include the following:

Mai Gehrke, Radboud Universiteit Nijmegen: "Using duality theory to export methods from modal logic".
Abstract: The rich theory of modal logic includes many powerful results and tools relating relational semantics and syntactic deduction. Mathematically, this may be seen as duality results and methods and these are pertinent in a much wider setting. The algebraic theory of canonical extensions, which formulates the canonical model construction of modal logic in an algebraic and widely available setting, has developed substantially over the last decade and this is the required 'Rosetta Stone' for translating the theorems, tools, and problems of modal logic to a wider setting. In this talk we give an introduction to this theory and illustrate the exportation with examples in substructural logic and the theory of finite semigroups and regular languages.

Guido Governatori, NICTA, Australia: "Labelled modal tableaux".
Abstract: Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This talk consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. In the second and third part we concentrate on a particular labelled tableaux system called KEM using free variable and a specialised label alebra. Specifically in the second part we show how labelled tableaux (KEM) can account for different types of logics (e.g., non-normal modal logics and conditional logics). In the third and final part we investigate the relative complexity of labelled tableaux systems and we show that the uses of KEM's label algebra can lead to speed up on proofs.

Agi Kurucz, King's College London: "Axiomatising many-dimensional modal logics".
Abstract: Many-dimensional propositional modal logics (multi-modal logics having productsof Kripke frames among their frames) have been studied in both pure modal logic and in computer science applications. They are also connected to algebras of relations in algebraic logic and to finite variable fragments of modal and intermediate predicate logics. In this talk we give a survey of axiomatisation problems for many-dimensional modal logics, discuss important techniques, and present some new results.

Lawrence Moss, Indiana University: "Relational syllogistic logics, and other connections between modal logic and natural logic".
Abstract: Syllogistic logics and modal logics share a number of features: they are both families of logics, both typically use relational semantics, both tend to be decidable, and both are motivated by the need to capture interesting fragments of reasoning. Despite the similarities, there is far less technical work on syllogistic logics than on modal logics. This talk will provide modal logicians with a look at much of the technical work on the other side, including: completeness theorems for some logics obtained via representations of orthoposets (rather than boolean algebras), connections to boolean modal logics, and the computational complexity of several logics (work done with Ian Pratt-Hartmann). People are interested in modal logic for many reasons; some of those reasons could also suggest an interest in this other work.

Michael Zakharyaschev, Birkbeck College: "Topology, connectedness, and modal logic".
Abstract: This talk presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (low-dimensional) Euclidean spaces.


2) The following papers has been accepted for the conference.

Marta Bilkova, Alessandra Palmigiano and Yde Venema, "Proof systems for the coalgebraic cover modality".
Tim French and Hans van Ditmarsch, "Undecidability for arbitrary public announcement logic".
Rajeev Gore, Linda Postniece and Alwen Tiu, "Cut-elimination and proof-search for bi-intuitionistic logic using nested sequents".
Rajeev Gore and Revantha Ramanayake, "Valentini's Cut-elimination for Provability Logic Resolved".
Jens Ulrik Hansen, Thomas Bolander and Torben Brauner, "Many-Valued Hybrid Logic".
Andreas Herzig and Francois Schwarzentruber, "Proof-theoretic properties of logics of individual and group agency".
Savas Konur, "An Interval Logic for Natural Language Semantics".
Clemens Kupke, Alexander Kurz and Yde Venema, "A complete coalgebraic logic".
Antti Kuusisto, "A Modal Perspective on Monadic Second-Order Alternation Hierarchies".
Yavor Nenov and Dimiter Vakarelov, "Modal Logics for Mereotopological Relations"
Martin Otto and Robert Piro, "A Lindstrom Characterisation of the Guarded Fragment and of Modal Logic With a Global Modality".
Ilya Shapirovsky, "PSPACE-decidability of Japaridze's Poly-modal Logic".
Timofei Shatrov, "On the intermediate logic of open subsets of metric spaces".
Viorica Sofronie-Stokkermans, "Locality and subsumption testing in EL and some of its extensions".
Yoshinori Tanabe, Koichi Takahashi and Masami Hagiya, "A decision procedure for alternation-free modal mu-calculi"
Tero Tulenheimo, "Modal Logic of Time Division"
Sara L. Uckelman, "Three 13th-century views of quantified modal logic".


3) Accepted Abstracts

Francesco Belardinelli, "Counterpart Semantics at work: an Incompleteness Result in Quantified Modal Logic".
Anna Chernilovskaya and Mai Gehrke, "Generalised Kripke semantics for the Lambek-Grishin calculus".
Stas Kikot, "An extension of Kracht's theorem to monadic inductive formulas".
Hans Lycke, "Inconsistency-Adaptive Modal Logics: Part I"
Larisa Maksimova, "Restricted interpolation in modal and superintuitionistic logics"
Sergio Marcelino, "An algebraic generalization of Kripke structures"
John McCabe-Dansted, "A Tableau for RoBCTL".
Jacob Vosmaer, "Compact Hausdorff modal algebras are image-finite Kripke frames".

An interview of Aldous Huxley

I invite you to watch an interview of The Brave new World's author Aldoüs Huxley made in the 1950's.

Vous trouverez ici un entretien télévisé datant des années 1950 avec Aldoüs Huxley, l'auteur du Meilleur des Mondes

Aldöus Huxley (1894-1863) y aborde Le Meilleur des Mondes et Island, du point de vue philosophique.

In this interview, A. Huxley (1894-1963) is talking about The Brave new World and Island.

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Post-scriptum:
Je n'ai pas réussi à l'heure actuelle à découvrir l'origine de cet entretien. Si vous aviez la moindre information, je serais très heureux de la découvrir.
I did not succeed to find the source of this interview. Could you please contact me or leave a comment if you have in your possession any information?

About Meaning and Language, Wilfried Sellars

Vous trouverez ici une discussion des problèmes liés à la signification et au langage faite par Wilfried Sellars.

I invite you to listen to an audio discussion about Meaning and Language by Wilfrid Sellars.

Ssswwwsssss, sur Youtube, nous fait découvrir un enregistrement audio (en Playlist) de Wilfried Sellars, où il discute des problèmes liés à la signification et au langage: On meaning and Language.
Ce document fait partie des Notre Dame University Archives (1963).
Sur la page de sssswwwsssss, d'autres entretiens très intéressants sont à découvrir.

Thanks to sssswwwsssss, we can listen to this interesting discussion of Philosophy of Language's problems by Wilfried Sellars: On meaning and language. This recording can be found at the Notre Dame University Archives. You should have a look at sssswwwsssss's interesting playlists.

On Meaning and Language (a)
On Meaning and Language (b)
On Meaning and Language (c)
On Meaning and Language (d)
On Meaning and Language (e)
On Meaning and Language (f)
On Meaning and Language (g)

La Bêtise en Philosophie, suite: les Principia Mathematica de Newton comme "traité sur le viol"/Newton's Principia Mathematica as a "rape manual" (!)

In the commentaries of my last published post, Florian asked me about an interpretation of Newton’s Principia Mathematica where this famous opus is viewed as a « rape manual ». I summarize all I know about this affair here.

Florian, dans les commentaires du billet précédent, m’a demandé si je connaissais une interprétation des Principia Mathematica de Newton qui l’envisageait comme un traité du viol. Voici ce que je sais sur cette affaire.

1) Féminisme et science/Science and Feminism:

Feminist Science-criticism tries to demonstrate that science is a discriminatory and patriarchist activity, through the demonstration that its supposed pioneers were sexists.

Le Feminist Science-criticism essaie de montrer que la science contemporaine est fondamentalement machiste, sexiste et patriarchale. Mais, étant donné qu’un nombre très réduit de ses représentants a les compétences nécessaires pour interpréter les textes scientifiques, la plupart se contente d’une analyse du moment considéré comme « fondateur » de la science moderne : le 17ème siècle.



2) La faute à F. Bacon/Bacon's fault :

There is a mistranslation in english from a latin text written by Francis Bacon : « I am come in very truth leading to you Nature with all her children to bind her to your service and make her your slave. » The original proposition is : Ego… revera naturam cum fetibus suis tibi addicturus et mancipaturus. » There is no sign of sexism in the latin proposition.

Il y a une traduction anglaise fautive d’un texte latin de F. Bacon, dans laquelle il est question de réduire à l’esclavage la Nature (cet aspect est absent du texte latin) : « I am come in very truth leading to you Nature with all her children to bind her to your service and make her your slave. » (dans Récusation des doctrines philosophiques et autres opuscules).


3) Le raisonnement des féministes est le suivant/Statements of the feminists:

a) Feminists try to show that 17th science is sexist and suppose that all that is true for this century is true for our time.
Ils/elles étendent les caractéristiques historiques de la science du 17ème s à celle d’aujourd’hui.

b) They try to demonstrate that the sexist/rape metaphors is a key to methodological and theoretical aspects in sciences.
Ils/elles tentent de démontrer que cette métaphore a autant d’importance que n’importe quelle autre métaphore dans le processus des découvertes scientifiques.


4) Science and rape/Les Sciences et le viol :

Sandra Harding is one the most famous feminists historians of sciences and epistemologists and she is the one who tries to demonstrate those statements:

Ce n’est pas Luce Irigaray, mais Sandra Hardings qui s’est chargée de tenter de démontrer ces thèses :

« Francis Bacon appealed to rape metaphors to persuade his audience that experimental method is a good thing »
« ...(these sexual meanings) are central to the ways scientists concepualize both the methode of inquiry and models of nature »

Harding, Sandra, Whose Science ? Whose Knowledge ? Thinking from Women’s Lives, Cornell University Press, 1991, Ithaca, pp 43-44.


5) Introduction de Newton dans le débat/Principia Mathematica as a « rape manual » :

Sandra Harding is also the author of the interpretation of the Principia mathematica as a « rape manual » :

Newton fut mentionné, encore une fois, par Harding. Croyant qu’on pouvait extrapoler à tous les « fondateurs » des propositions de ce type, elle s’est attaquée à Newton. Voilà la citation exacte :

« Traditional historians and philosophers have said that these (rape and torture) metaphors are irrelevant to the real meanings and referents of scientific concepts… But when it comes to reagarding nature as a machine, they have a quite different analysis : here, we are told, the metaphor provides the interpretations of Newton’s mathematical laws : it directs inquirers to fruitful ways to apply his theory… But if we are to believe that mechanistic metaphors were a fundamental component of the explanations the new science provided, why should we believe that the gender metaphors were not ? A consistent analysis would lead to the conclusion that understanding nature as a woman indifferent to or even welcoming rape was equally fundamental to the interpretations of these new conceptions of nature and inquiry. Presumably these metaphors, too, had fruitful pragmatic, methodological, and metaphysical consequences for science. In that case, why is it not as illuminating and honest to refer to Newton’s laws as « Newton’s rape manual » as it is to call them « Newton’s mechanics » ? »

Hardings, Sandra, The Science question in Feminism, Cornell University Press, Ithaca, 1986, pp. 113.

Je laisse à chacun le soit de tirer des leçons de ce texte absurde. Je n’insisterai que sur un seul aspect : Hardings commet une erreur de raisonnement importante en faisant une « genesis fallacy », car elle conclut du fait que les représentations présupposées par les méthodes de recherche scientifique sont sexistes (admettons qu’elle ait raison pour l’argument), que les produits de la science sont eux-mêmes sexistes.

La Bêtise en Philosophie

Deux extraits soigneusement choisis:

• « (L)’équation E=Mc2 est-elle une équation sexuée ? Peut-être que oui. Faisons l’hypothèse que oui dans la mesure où elle privilégie la vitesse de la lumière par rapport à d’autres vitesses dont nous avons vitalement besoin. Ce qui me semble être une possibilité de la signature sexuée de l’équation, ce n’est pas directement ses utilisations par les armements nucléaires, c’est d’avoir privilégié ce qui va le plus vite (…). »

Luce Irigaray, « Sujet de la science, sujet sexué ? » (pp 95-121), in Sens et place des connaissances dans la société, Paris, Centre national de la recherche scientifique, p 110.

• « Nos systèmes complexes, métastatiques, virals, voués à la seule dimension exponentielle (que ce soit celle de l’instabilité ou de stabilité exponentielle), à l’excentricité et à la scissiparité fractale indéfinie ne peuvent plus prendre fin. Voués à un intense métabolisme, à une intense métastase interne, ils s’épuisent en eux-mêmes et n’ont plus de destination, plus de fin, plus d’altérité, plus de fatalité. Ils sont justement voués à l’épidémie, aux excroissances sans fin du fractal, et non à la réversibilité et à la résolution parfaite du fatal. »

Jean Baudrillard, L'Illusion de la fin, Galilée, Paris, 1992, p 160.
(Si quelqu'un est capable de déchiffrer cet extrait, je serais heureux qu'il me communique ses résultats.)