Cyrille Imbert

Scientific models need to be investigated if they are to provide valuable information about the systems they represent. Surprisingly, the epistemological question of what enables this investigation has hardly been investigated. Even authors who consider the inferential role of models as central, like Hughes or Bueno and Colyvan, content themselves with claiming that models contain mathematical resources that provide inferential power. We claim that these notions require further analysis and argue that mathematical formalisms contribute to this inferential role. We characterize formalisms, illustrate how they extend our mathematical resources, and highlight how distinct formalisms offer various inferential affordances.

This paper shows that, under certain reasonable conditions, if the investigation of the behavior of a physical system is difficult, no scientific change can make it significantly easier. This impossibility result implies that complexity is then a necessary feature of models which truly represent the target system and of all models which are rich enough to catch its behavior and therefore that it is an inevitable element of any possible science in which this behavior is accounted for. I finally argue that complexity can then be seen as representing an intrinsic feature of the system itself.