Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot’s account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today’s debate: (1) the relationship between empirical and (...) mathematical thought experiments and (2) the question of whether mathematical thought experiments can play a justificatory function in proofs. The main corollary of this analysis is that Piaget’s interpretation is seriously flawed and insufficiently appreciative of important theses of Goblot’s account. First, Goblot can be easily defended against Piaget’s main criticism, and second, Goblot developed ideas about mathematical thought experiments that still deserve attention. (shrink)

Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot’s account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today’s debate: (1) the relationship between empirical and (...) mathematical thought experiments and (2) the question of whether mathematical thought experiments can play a justificatory function in proofs. The main corollary of this analysis is that Piaget’s interpretation is seriously flawed and insufficiently appreciative of important theses of Goblot’s account. First, Goblot can be easily defended against Piaget’s main criticism, and second, Goblot developed ideas about mathematical thought experiments that still deserve attention. (shrink)

With reference to an already existing and relatively widespread use of the expression in question, mathematical “thought experiments” (“TEs”) involve mathematical reasoning in which visualisation plays a relatively more important role. But to ensure an unambiguous and consistent use of the term, certain conditions have to be met: (1) Contrary to what has happened so far in the literature, the distinction between logical-formal thinking and experimental-operational thinking must not be ignored; (2) The separation between the context of discovery and the (...) context of justification is to be rejected, at least in one of the main senses in which it was defended by the logical empiricists and Popper (this excludes any position which, ascribing to mathematical TEs only a heuristic role, regards them an intermediate step to attain more traditional forms of rigour); (3) The distinction between mathematical TEs and formal proofs must be regarded as one of degree, and not as a qualitative one, although this distinction may be used in a de facto way for particular or local purposes. (shrink)