abstract bibtex

In the eighteenth century, the German mathematician and philosopher Christian Wolff famously claimed that all sciences should apply the so-called mathematical method. Interpreters (e.g. Frängsmyr 1975; Friedman 1992; Zammito 2002) typically identify Wolff's mathematical method with the traditional axiomatic ideal of science, i.e. the tenet that a proper science should have an axiomatic structure. In this paper we argue against this identification. We show that several eighteenth-century authors who did reject the mathematical method in science did so while retaining the axiomatic ideal of science - which suggests that the two should not be identified. We argue that in the eighteenth century the expression 'the mathematical method' designated a specific take on the traditional axiomatic ideal of science, and that it is this specific take that was targeted by critics, not the axiomatic ideal of science tout court. In order to substantiate our claims, we rely on information from a corpus of approximately 700 eighteenth-century books on logic and philosophy in German and Latin, processed using a novel method building upon the mixed one (qualitative, quantitative and computational) introduced by Betti et al (2019). In keeping with the latter, we claim that historical-interpretive claims should rely on a corpus which is as large as possible, and employ precisely defined annotation schemes to capture differences and similarities between various conceptions in a way which is as accountable as possible. We supplement the method with a new explicitly defined procedure of book-centered corpus building for historians of philosophy which is as objective and accountable as possible. Our results should be understood as part of a longer-term ambition of making historico-interpretive investigations more scientific, i.e., controlled, explicit, and as objective as possible

@article{van_den_berg_spread_nodate, title = {The {Spread} of the {Mathematical} {Method} in {Eighteenth}-{Century} {Germany}: {A} {Quantitative} {Investigation} [ongoing]}, abstract = {In the eighteenth century, the German mathematician and philosopher Christian Wolff famously claimed that all sciences should apply the so-called mathematical method. Interpreters (e.g. Frängsmyr 1975; Friedman 1992; Zammito 2002) typically identify Wolff's mathematical method with the traditional axiomatic ideal of science, i.e. the tenet that a proper science should have an axiomatic structure. In this paper we argue against this identification. We show that several eighteenth-century authors who did reject the mathematical method in science did so while retaining the axiomatic ideal of science - which suggests that the two should not be identified. We argue that in the eighteenth century the expression 'the mathematical method' designated a specific take on the traditional axiomatic ideal of science, and that it is this specific take that was targeted by critics, not the axiomatic ideal of science tout court. In order to substantiate our claims, we rely on information from a corpus of approximately 700 eighteenth-century books on logic and philosophy in German and Latin, processed using a novel method building upon the mixed one (qualitative, quantitative and computational) introduced by Betti et al (2019). In keeping with the latter, we claim that historical-interpretive claims should rely on a corpus which is as large as possible, and employ precisely defined annotation schemes to capture differences and similarities between various conceptions in a way which is as accountable as possible. We supplement the method with a new explicitly defined procedure of book-centered corpus building for historians of philosophy which is as objective and accountable as possible. Our results should be understood as part of a longer-term ambition of making historico-interpretive investigations more scientific, i.e., controlled, explicit, and as objective as possible}, author = {van den Berg, Hein and Betti, Arianna and Oortwijn, Yvette and Parisi, Maria Chiara and Wang, Shenghui and Koopman, Rob}, }

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