We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order Logic.Expand

The foundational crisis is a celebrated affair among mathematicians and it has also reached a large nonmathematical audience. A well-trained mathematician is supposed to know something about the… Expand

The aim of this paper is to offer a brief presentation of the approach to the analysis of mathematical knowledge that I am developing in a forthcoming book entitled “Mathematical Knowledge and the… Expand

La theorie des ensembles emergea au XIX e siecle et fut la base des mathematiques. La notion d'ensemble est analysee a travers les travaux de Riemann (B.) et Dedekind (R.), en discutant le langage et… Expand

This paper gives a detailed analysis of the scientific interaction between Cantor and Dedekind, which was a very important aspect in the history of set theory during the 19th century. A factor that… Expand

The celebrated “creation” of transfinite set theory by Georg Cantor has been studied in detail by historians of mathematics. However, it has generally been overlooked that his research program cannot… Expand