# Mathematical Explanations and Emergence in the Physical Sciences

Maison des sciences de l'Homme, amphitheatre 220

4 rue Ledru

Clermont-Ferrand 63000

France

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**Subject:**

Mathematics has become essential to the understanding of natural phenomena in the physical sciences. The precise role(s) this status may play, is, however, fiercely debated in contemporary philosophy of science, whether or not one subscribes to the thesis of the "unreasonable effectiveness of mathematics", to use Eugene P. Wigner's famous expression. Lately, more and more attention has been given to the role of *idealizations* in introducing mathematics into the explanation of natural phenomena. Here, the purely mathematical explanation concerns only a more or less altered "simulacrum" of the phenomenon under consideration. In this case, the explanatory power that can be attributed to the mathematical reasoning raises even more questions.

This non-trivial relationship between the explanatory power of mathematics and the "faithful representation" of natural phenomena concerns, of course, the general problem of applicability of mathematics to empirical science. But, as proposed by various authors taking as an example the phase transitions or critical phenomena, this relationship allows equally to refresh the notoriously elusive question of emergence. By highlighting mathematical reasoning, whose explanatory power is anchored in a distortion of the phenomenon's physical constitution, is it possible to identify non-causal explanations "superimposed" on explanations reducing the phenomenon to its physical constitution?

**Schedule:**

9:00 Annick Lesne, CNRS, LPTMC Paris & IGMM Montpellier : “Renormalization approaches of critical phenomena: the emerging reality”

10:00 Quentin Rodriguez, Université Clermont Auvergne : “Universality in critical phenomena: How can we speak of emergent explanations?”

*11:00 Break*

11:15 Vincent Ardourel, CNRS, IHPST : “Phase transitions and infinite limits”

*12:15 Lunch break*

2:30 Marina Imocrante, CNRS, IHPST : “Mathematical inference to the best explanation: Reconciling a priority and revisability”

3:30 Chris Pincock, Ohio State University : “Which universal phenomena are emergent?”

*End of the day at 4:30.*

*Access information: **http://www.msh-clermont.fr/content/acc%C3%A8s-%C3%A0-la-msh-clermont*

*Further information: [email protected]*

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