Formal methods as a counterbalance to intuitions in philosophy.

Recent discussions on the role of intuitions in philosophical methodology often oppose, on the one hand, proponents of a radical skepticism towards intuitions as reliable sources of philosophical insight to, on the other hand, zealous defendants of their epistemic value for philosophy. But (as is so often the case) the right place for intuitions within philosophical investigation might be somewhere in between these two positions. Intuitions do have a role to play in philosophical investigations, but they must be neither the unique kind of raw material taken as a starting point, nor the single ultimate test for the accuracy of a philosophical theory. In other words, philosophical theorizing must have some degree of autonomy vis-à-vis intuitions.

What kind of methodology can ensure this relative autonomy of theories with respect to intuitions? In this talk, I suggest that formal methods are particularly suitable to counterbalance the weight of intuitions in philosophical investigations. This is because at the very heart of the epistemology of formal methods lies the idea of inferential moves not requiring any insight or ingenuity. Such moves can be iterated to form very long arguments, the conclusions of which are often not to be foreseen by intuition alone. That is to say, formal methods used in philosophy can reveal ‘hidden truths’ that might otherwise be inaccessible.

To illustrate this observation, I present an analysis of the role formal methods play for the methodology of physics. The analysis will focus on the interplay between experimental data and (formal-mathematical) theories by means of the following two case-studies: Maxwell’s theory of electromagnetism, and Einstein’s special theory of relativity. In both cases, the use of the mathematical formalism yielded predictions that were at first highly counterintuitive, but which were then confirmed experimentally. I propose that an analogy between the methodology of physics thus described on the one hand, and philosophical methodology on the other, can shed light on the interplay between intuitions and formal methods in philosophy. This suggests a model of philosophical investigation that may be understood as a sophisticated version of the old but still topical idea of a reflective equilibrium.