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The Emergence of Mathematical Probability from the Perspective of the Leibniz-Jacob Bernoulli Correspondence

This paper moves out from a defined body of evidence, namely the correspondence between Gottfried Wilhelm Leibniz and Jacob Bernoulli, to see what light it casts on the emergence of mathematical probability in the late seventeenth and early eighteenth centuries. At many times during his life Leibniz repeated his recommendation that serious attention should be paid to developing a theory of probabilistic reasoning. In his Ars Con]ectandi (The Art ofConjecturing), Jacob Bernoulli tried to do just what Leibniz at many times recommended, but he did not finish the work before his death in 1705, partly because he lacked information about real-life situations. Although, when they discussed probability and what Bernoulli had accomplished and hoped still to do in letters written between April 1703 and April 1705, Leibniz and Bernoulli did not understand each other perfectly, nevertheless, when one looks more broadly in their writings, one sees that they were in fundamental agreement about their purposes: the new probability logic or the art of conjecturing was to playa role in a practical moral discipline and its problems were to be more like those of law than those of empirical science. Within this practical discipline, the role of mathematics was to supply a rigorous method of reasoning and, in particular, a way of insuring comprehensiveness and consistency when the complexity of the situation might otherwise overwhelm normal reason.