Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

Archibald Pitcairne’s medical writings are inspired by Newton’s Principia mathematica, as the Scottish physician assumed Newtonian physics as a model for scientific inquiry that should be applied to other branches of natural philosophy, including physiology and pathology. The ideal of a comprehensive mathematical science was very appealing to late seventeenth-century intellectuals, including physicians. This essay focuses on how Pitcairne tried to implement these ideas. In particular, I argue that Pitcairne’s medical thinking is based on three philosophical assumptions: first, a methodological (...) assumption, for which medical knowledge should be sought in the form of a deductive system; second, an epistemological assumption, that is, that our knowledge of physiological processes is sound only when we reduce them to a set of mathematical laws; and, third, an ontological assumption that identifies blood as the substance on which animal life most directly depends. I also suggest that such ideas should be studied against the backdrop of Pitcairne’s general mindset, including his personal sympathy for political conservativism. I further argue that his insistence on the reduction of natural processes to mathematical relations and his search for the universal order of nature also connect to his religious and political ideals. (shrink)

In biology the term “vitalism” is usually associated with Hans Driesch’s doctrine of the entelechy: entelechies were nonmaterial, bio-specific agents responsible for governing a few peculiar biological phenomena. Since vitalism defined as such violates metaphysical materialism, the received view refutes the doctrine of the entelechy as a metaphysical heresy. But in the early twentieth century, a different, non-metaphysical evaluation of vitalism was endorsed by some biologists and philosophers, which finally led to a logical refutation of the doctrine of the entelechy. (...) In this non-metaphysical evaluation, first, vitalism was not treated as a metaphysical heresy but a legitimate response to the inadequacy of mechanistic explanations in biology. Second, the refutation of vitalism was logically rather than metaphysically supported by contemporary biological knowledge. The entelechy was not a valid concept, because vitalists could neither formulate vital laws, nor offer convincing examples of experimental indeterminism. (shrink)