Mathematics against Uncertainty
To this inventory of virtues in quantification for astronomy, Laplace was later to add the merits of the calculus of probability. Chronologically, his Philosophical essay on the theory of probability falls in a dark period of his life, near what he thought was the end of his career in 1813. This third crisis brought him face to face with the
limits of mortality and the uncertainties of life. His bachelor son, an artillery officer and aide-de-camp of Napoleon in the Russian campaign, nearly lost his life; his only daughter died in childbirth, causing him to sink into a profound depression; and Napoleon, who had come to power as a force of stability, was leading the Empire to dissolution and France to surrender. One might easily expect in this essay a Pascalian cry of despair about the weakness of the human mind or a Stoic sense of fatalistic resignation. But Laplace's intellectual resilience and self-confidence prevailed to turn his essay into a remarkably optimistic piece worthy of comparison with his departed friend Condorcet's Sketch for an historical picture of the human mind .
In a tour de force, Laplace stands traditional worries about fortuity on their head and asserts his famous view of determinism at the outset. According to his philosophy, the world operates by immutable laws that we can begin to know by applying the calculus of probabilities to the phenomena we observe. His concern with this calculus came directly from a desire dating back to his youth to find a systematic way of moving from the gathering of observations to the statement of true laws of nature. He had invented (or perfected) a calculus of statistical inference that allowed him to estimate the likelihood that a particular configuration of events would lead to a subsequent arrangement known through observation. This a posteriori calculus, presented in a pioneering paper of 1774 he subsequently developed, promised to become a powerful tool for his natural philosophy. Philosophically, its power stemmed from capturing game theory from the domain of conjecture (chance), and turning it into a method for calculating likelihood (probability). The uncertainties of chance were replaced by the manipulable concept of degrees of likelihood, bringing the operation within the reach of the mathematician. As a technical tool, statistical inference was prized for helping natural philosophers to distinguish between likely and spurious causes, thus preventing them from lapsing into unfounded speculation. Systematic errors of observation attributable to instruments could thus be distinguished from those dependent upon human failings. Statistical inference also offered the possibility for treating problems of civic life—such as the differential birth rates for the two sexes, annuities,
sampling techniques, voting methods, and judicial decisions—in a rigorous and rational manner, bringing mathematical light to obscure social problems.
For Laplace, calculation was no mere scientific tool of limited significance. Its scope went far beyond the technical advantages it had already supplied for the progress of natural philosophy. Mathematization offered a central path to an enhanced epistemology that would progressively reduce the errors of human ways and permit the assertion of intellectual powers. Given enough evidence, and using the proper analytic tools provided by mathematicians, humans could conceivably attain the skills necessary to rival the Supreme Being. It is no accident that Laplace proclaimed the possibility of an ideal, supreme, but human calculator (an absolute Intelligence) in the only philosophical essay he devoted to a mathematical subject. For him, mathematization truly embodied the spirit of rationalism, the greatest virtue offered by the Age of Enlightenment.