 Between 1703 to 1705 , Leibniz corresponded with Jakob after learning about his discoveries in probability from his brother Johann . Leibniz managed to provide thoughtful criticisms on Bernoulli 's law of large number , but failed to provide Bernoulli with de Witt 's work on annuities that he so desired . From the outset , Bernoulli wished for his work to demonstrate that combinatorics and probability theory would have numerous real @-@ world applications in all facets of society — in the line of Graunt 's and de Witt 's work — and would serve as a rigorous method of logical reasoning under insufficient evidence , as used in courtrooms and in moral judgements . It was also hoped that the theory of probability could provide comprehensive and consistent method of reasoning , where ordinary reasoning might be overwhelmed by the complexity of the situation . Thus the title Ars Conjectandi was chosen : a link to the concept of ars inveniendi from scholasticism , which provided the symbolic link to pragmatism he desired and also as an extension of the prior Ars Cogitandi . 
