Observation and Mathematics

Weighing Experience: Experimental Histories and Francis Bacon's Quantitative Program

“…64 Domski builds on an early, seminal article by Thomas Kuhn, who famously identified two separate traditions to have stood at the cradle of modern science. 65 Kuhn's thesis was particularly innovative because it moved away from the accepted line of explanation, which substantially viewed modern science as an evolution of the methods of what Kuhn called the classical physical sciences of astronomy, statics, and geometric optics.…”

“…Rather, he rejected both because he thought that no system so complex, abstract, and mathematical could contribute to either the understanding or the control of nature 67 However, as Domski suggests, [u]pon closer examination of the system of sciences that Bacon urged natural philosophers to establish, we find that he does not demand that astronomy relinquish its use of mathematics, or more generally, that the mixed mathematical sciences relinquish their use of abstraction and idealization. Rather, what he demands is that the mathematical treatment of nature, and of heavens in particular, be grounded on and informed by the findings of natural history 68 In general, as Graham Rees has also pointed out, Bacon did not reject the use of mathematics in the so-called mixed sciences. Instead, he was careful in stating its subordinate character with respect to experiments and natural histories: Bacon's point is that we must be careful to put mathematics in its proper place, as a tool that can be used to investigate certain domains of nature after a proper natural history and physics has been established.…”

“…71 According to Domski, there is evidence that a similar stance was adopted by several later authors associated with the Baconian tradition, and Robert Boyle in particular. 72 If this new analysis is correct, what is the place of the Baconian program of experientia literata in this larger history? In my discussion of quantification in experientia literata, I have tried to document how the "weighing of experience" was mostly connected to the efficacy of operations.…”