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# Séminaire – Histoire et Philosophie des Mathématiques

## February 5 @ 9h00 - 17h30

**“The Mathematizazion of Nature in the 16th and 17th Centuries” day**

Organisation : Vincenzo de Risi

**Programme**

9:30-10:30

**David M. Miller **(Auburn University), *Catena’s ‘Third Kind of Thing’ in the Quaestio de Certitudine*

10:45-11:45

**Álvaro Bo** (Academy Vivarium Novum, Rome), *Mathematising the unmathematical : Alessandro Piccolomini on the (im)possibility of a quantified science of nature*

12:00-13:00

**Michela Malpangotto** (Centre Jean Papin, Paris), *A revolution before Copernicus. The precopernican astronomy issued from Georg Peurbach’s Theoricae novae planetarum (15th-17th c.)*

14:30-15:30

**Sophie Roux** (École Normale Supérieure, Paris), *Mathematics and Natural Philosophy in Descartes and in the Reception of Descartes*

15:45-16:45

**Robert DiSalle** (University of Western Ontario), *The metaphysics and method of Newton’s Mathematical Principles*

*Résumé* :

Newton’s *Principia* was among the first examples, and eventually an ideal model, of what we now mean by “mathematical physics.” It is a challenge to understand, therefore, the view of some of his contemporaries that this work was only mathematics, and not physics at all. The explanation that is nearest to hand is that Newton’s approach set aside the pursuit of causal explanations : his contemporaries, dedicated to one or another form of the “mechanical philosophy,” would not recognize as a physical theory any mathematical account that, like Newton’s, provided no causal mechanism to explain its mathematical principles. Certainly some of Newton’s own remarks about the mathematical character of his work, and his disavowal of inquiry into the cause of gravity, seem to invite such an interpretation. But this interpretation falsely suggests an abandonment, at the very commencement of mathematical physics, of the very idea of physical understanding in favour of mathematical precision and predictive success. This is very far from Newton’s view of his work, its relation to the mechanical philosophy, and its actual and potential achievements. On the contrary, Newton considered his use of mathematics in physics to be a new and indispensable method for identifying, and understanding, the action of physical causes.

Few of Newton’s contemporaries grasped the radical novelty of his mathematical method, and this explains some of the difficulties they had in grasping the metaphysical implications of his method. Huygens, in particular— arguably the most accomplished representative of the mechanical philosophy— articulated an ideal of physical explanation and the ways in which Newton’s theory fell short of the ideal. His own theory of gravity was meant to show the conceptual clarity and explanatory power of mechanistic principles. By comparing Huygens’ mechanical method with Newton’s mathematical method, we can see why Newton’s method providing insights into the metaphysics of causation that were hidden from the mechanistic view. In the subsequent evolution of physics, it was the Newtonian conception, properly understood, that illuminated the power of mathematical physics as a means of understanding causes as well as a tool for predicting effects. Newton’s method also shed light on fundamental philosophical problems concerning the applicability of mathematics to the world, including questions about the nature of empiricism and realism regarding mathematical theories, that have preoccupied philosophers even in the realm of post-Newtonian physics.

Organization Vincenzo de Risi

**Salle : **Salle 628 (6è étage, bâtiment Olympes de Gouges)