James Robert Brown

RésuméDans leur livre récent, George Lakoff et Rafael Núñez se livrent à une critique naturaliste soutenue du platonisme traditionnel concernant les entités mathématiques. Ils affirment que des résultats récents en sciences cognitives démontrent qu'il est faux. En particulier, ils estiment que la découverte que la cognition mathématique s'appuie pour une large part sur les métaphores conceptuelles est incompatible avec le platonisme. Nous montrons ici que tel n'est pas le cas. Nous examinons et rejetons également quelques arguments philosophiques que formulent Lakoff et Núñez contre le platonisme. Enfin, nous lions leur hostilité au platonisme à certaines opinions sur les ramifications politiques de celui-ci. Pour conclure, nous faisons valoir que ces opinions sont sans fondements et présentent une image distordue des dimensions politiques du platonisme.

Most disciplines make use of thought experiments, but physics and philosophy lead the pack with heavy dependence upon them. Often this is for conceptual clarification, but occasionally they provide real theoretical advances. In spite of their importance, however, thought experirnents have received rather little attention as a topic in their own right until recently. The situation has improved in the past few years, but a mere generation ago the entire published literature on thought experiments could have been mastered in a long weekend. Now the subject is beginning to flourish. Given the relative newness of the field, it might be useful to have several examples at one’s finger tips, so a number of great ones will be described. Attention will also be drawn outside physics and philosophy. In mathematics there is something analogous to thought experiments -- visual reasoning and picture proofs. I will look briefly at this class of thought experiments and try using them to make a case for possibly settling the continuum hypothesis. After this, I will return to thought experiments in the sciences and propose an account of how they work. Finally, I will end with a sketch of a topic I am currently working on, a kind of progress report which, I hope, will be an inducement to others.