Two jesuits against the indivisibles

International audienceThis chapter presents two opponents of indivisibles, both coming from the same intellectual background: the Society of Jesus. Their outlooks were somewhat different on the subject which interests us: while Father Antoine de Lalouvère (1600–1664) was firmly hostile to indivisibles, Father André Tacquet (1612–1160) accepted their use, but under serious restrictive conditions meant to prevent the risks of paralogisms. The question of knowing whether they only represented their own opinion or if they expressed that of their order can only be resolved after an exhaustive investigation into the publications and manuals written by the members of the order. But the example of Grégoire de Saint-Vincent, to whom both Father Tacquet and Father Lalouvère paid tribute, would tend to prove that the opinions amongst the Company were very varied and that, contrary to what Pascal says concerning probabilities, one cannot, at least for geometry, infer the opinion of the whole body from that of a few individuals without being reckless. However, as interesting as the criticisms opposed to indivisibles by these two Jesuits may be, the concessions that they were obliged to make on the subject, consciously or not, are even more significant of the progress this new method was making amongst geometricians