1. 5th International Conference of the ESHS, November the 1st 2012
Scientific Generalization, Order and Compatibility between disciplines in Poincaré’s Thinking
Anne-Françoise Schmid
MinesParisTech, INSA de Lyon
5th International Conference of the ESHS, November the 1st 2012

2. Poincaré’s Philosophy of sciences
My aim is to manifest the originality of Poincaré’s philosophical thinking and its value for contemporary research
Poincaré’s philosophy has a lot of names and characterizations: nominalism, conventionalism, occasionalism, pragmatism, idealism, commodism, constructivism, etc.
The reason is that the philosophy of Poincaré is minimalist and oppose a resistance to philosophical speculation

3. The construction of this minimalism
This minimalism concerns in the same time the order of the discipline between mind and experience and the relations and scales between facts and philosophy
We will first describe the relations between disciplines with the concept of convention, and the second, the scale between facts and philosophy with the concept of metaphor

4. The relation between disciplines
In his philosophical writings, Poincaré put always in the same order: arithmetic, algebra, analysis, geometry, mechanics, mathematical physics, experimental physics;
This order is thought between the operations of mind and the possibility of their repetition
And the experience, who is the bound of scientific and brute fact
The convention is the link between theses two contraries

5. Characterization of the discipline
Each discipline is a different combination of mind and experience
In the center of the space delimited by mind and experience, is the place for convention (geometry and mechanics)
Convention is a link between disciplines
Convention is a waranty of the autonomy of scientific language

6. The scale between facts and generalizations
There are brute and scientific facts (against nominalism), experience put in relations the two
Science is generalization, but a generalization with “decomposition”.
The “decomposition” is first the distinction between sensible space and geometry
But, a scientific proposition reflects too a diversity of discipline, for example geometry and mechanics

7. Scale between generalizations, theories and philosophy
Generalizations are operators which warrant the rapport and the relative independence between facts and propositions This independence is certified by use of hypothesis Generalization is a way of invention, more than justification Theories are systems of generalization, but they are metaphorical A generalization out of the limits of scientific hypothesis and conditions conduct to philosophy

8. Construction of philosophy
The philosophy of science is constrained by two orders, the one between disciplines, the other between facts and the theories by the way of generalizations, hypothesis and conventions
A hypothesis has to be built in an ordered removal from the fact

9. Symptoms
Poincaré has a certain distrust for the theories, he did not build numerous theories, a theory of tides, a theory of relativity
The status of mechanics as a model for physics. It is possible to have several mechanics, but mechanics is necessary to link the relations between mathematics and physics. Poincaré knew very well modern physic, but he said: “Electrons are very light, the radium is very rare”

10. The effects of order
The constraints of the order on the philosophy of the sciences has that Poincaré identifies in a remarkable way philosophy of the sciences and the epistemology His philosophy reflects its scientific practice, which puts in relationship the disciplines of a very inventive way
Example: algebraic mechanics, who was first developed in Russia and Soviet Union, where interdisciplinarity was more normal as in France

11. Now
The multiplication of the disciplines makes not relevant a design so narrow of the scientific disciplines
It is necessary to open the space of sciences
But Poincaré indirectly had constructed a rigorous method for science between disciplines
A generalization is justified if she is compatible with the different disciplines she requiert

12. Poincaré’s criterium 1) Decomposition (near a generic position)
2) Hyper-compatibility between a problem and the various disciplines (Extension of knowledge)
The distinction between profane and scientific generalization is the sort of link between facts and generalization
In profane generalization, there is a continuity from fact to generalization.
In scientific generalization, this relation is stopped by compatibilities