Novembertagung

News from the SMF

2005-12-05T08:31:57Z

Dear all,
It was a pleasure to meet you all in Paris a month ago. I am getting back to you as I have some more practical information concerning the proceedings of the 16th Novembertagung.
The Soci�t� Math�matique de France is willing to publish the proceedings of the tagung in its publication "seminaires et congr�s" (see the website http://smf.emath.fr/en/Publications/SeminairesCongres/). The proceedings would be published as a special issue of this review usually devoted to mathematics (...)

History of mathematics session 3 & 4

2005-11-09T13:05:29Z

Movements in the history od XVIII-XXth century Mathematics sessions 1 & 2

2005-11-09T13:00:51Z

Philosophy of logic sessions 1& 2

2005-11-09T12:39:30Z

Post's machine

2005-11-09T12:37:45Z

In 1936 Turing gave his answer to the question “What is a computable number?” by constructing his now well-known Turing machines as formalisations of the actions of a human computor. Less well-known is the almost synchronous published result by Emil Leon Post, in which a quasi-identical mechanism was developed for similar purposes. In 1979 these Post “toy” machines were described in a little booklet, called “Post's machine” by the Russian mathematician (...)

Abstract Tendencies: The Recursive Thought of Alan Turing

2005-11-09T12:35:26Z

In order to prove that mathematics cannot be exhausted by a finite set of procedures, Alan Turing conceives, in 1936, of an abstract machine. The machine makes its debut in “On Computable Numbers with an application to the Entscheidungsproblem,” his first major mathematical paper. Turing uses this machine to reveal the potential excess that haunts a given system's meaning. By proving that his machine can always generate another number belonging to a seemingly complete set, he (...)

A not trivial intersection of logic and geometry: n-opposition theory

2005-11-09T12:31:41Z

Aristotle's square has long been the principal, very symbolic instance of the poor intersections between logic and geometry. This particular intersection (a geometrical square with logical implicative arrows and contradictory diagonals) is both poor and important : poor because for almost 2500 years it didn't seem to go any further in terms of formal (thus also geometrical) developments of itself (“logic is simpler and more fundamental than geometry”), important because it (...)

The Standard Interpretation of Higher-Order Variables in Modern Logic and the Concept of Arbitrary Function in Mathematics

2005-11-09T12:30:11Z

I propose to bring together two developments in the philosophy of mathematics that deal with closely related problems. The more recent development is that of the standard interpretation of higher-order variables in modern logic. The older development is that of the idea of an arbitrary function in mathematics. The common problem they deal with concerns the existence of infinite totalities. To show the connection between arbitrary functions and the standard interpretation, I shall first give (...)

New planets in the solar system 200 years ago

2005-11-09T12:26:06Z

The discovery of new planets and other celestial bodies in our solar system is discussed focusing on the end of the eighteenth and the beginning of the nineteenth century and on questions concerning names, terminology and classification concerning the newly discovered bodies. These years before and after 1800 also changed the picture of the history of astronomy and the history of the world. Whereas the bible was the main authority earlier, in the nineteenth century scientific investigations (...)

On proportions of proportions: one aspect of the application of mathematics to music in the seventeenth century

2005-11-09T12:24:29Z

During the seventeenth century a major change took place in the use of mathematics to describe musical pitch. Since antiquity musical intervals had been identified with numerical ratios, and ratios had been considered significantly distinct from simple numbers. One consequence of this was that since different ratios were mutually incommensurable, so were different musical intervals. A 'common measure' for intervals was desirable for musical purposes, but was generally held to be strictly (...)