In contrast to the more modern applied mathematics, mixed mathematics did not necessarily presuppose a prior and independent mathematical theory to be applied to various subject matters. Classical probability theory had no existence independent of its subject matter, viz. the beliefs and conduct of reasonable men. As Laplace put it in a famous passage, mathematical probability was in essence “only good sense reduced to a calculus” (Laplace,  1951, p. 6).(Gigerenzer et al. 1990, p.13)
Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.(Laplace, 1814, p.4)
Gigerenzer, G., Porter, T., Swijtink, Z., Daston, L., Beatty, J. and Kruger, L. (1990) The Empire of Chance. Cambridge University Press.
Laplace, P. S. (1814) A Philosophical Essay on Probabilities. Translated by F. W. Truscott and F. L. Emory. [link]