Mathematics and Metabasis: “Mathematical” Models in Early Modern Civil Sciences

Mikhailovski, Alexander Sergeevich
Graduate Student, the School of Philosophy of the Faculty of Humanities, Research Assistant Fellow, the Poletayev Institute for Theoretical and Historical Studies in the Humanities, HSE University, Moscow, Russia
amihaylovskiy@hse.ru

Abstract
Social and historical sciences, however quantitative they may be (economics), are generative of problems concerning unambiguous application and interpretation of mathematical models. Unique achievement of contemporary curriculum of “analytical philosophy” concerns generation and development of formal models in epistemology, epistemology of social and economic sciences included. Employment of formal-logic semantical models in decision theory and game theory became a vehicle for the development of theories of action in social sciences since Otto Neurath, Hans Reichenbach and Ludwig von Mises in Germany; Kenneth Arrow, Amartya Sen and John Rawls in English-speaking academy.
Fruitful contemporary projects of logical-semantical “formalization” of social and economic action based on achievements in formal semantics and mathematical logic, however, are not the first instances of attempts on “mathematization” of social knowledge. Erhard Weigel, Samuel Pufendorf’s teacher, ascribes to every (juridical) “person” some moral quantity in his juridical ontology of “persons” and “things.” If some “person” is engaged in criminal activity, then negative number should be ascribed to that person (Arithmetische Beschreibung der Moral-Weißheit von Personen und Sachen, 1674). Herman Konring, one of the main proponents of Early Modern “statistical” knowledge, employs arrays of historical data for his probabilistic (“statistical”) inferences on the most prudent action in various policies. Jesuit moral theology develops complex models for “probable” contingent mass-phenomena. Gottfried Achenwall is both one of leading figures in XVIII-century German “science of natural right” and a prominent statistician and “empirical” researcher of politics and economy.  
On the other hand, consider employment of classical Hobbesian and Lockean “state-of-nature” arguments in contemporary game-theoretic modelling. Why informal Early Modern arguments remain productive of a number of potential formalizations and, nevertheless, are not reduced to these formalizations. I believe that these questions can be explicated by a careful consideration of Early Modern mathematical milieu, where “civil sciences” of Hobbes, Locke and Konring were embedded. Dissemination of Cavalieri’s “method of indivisibles” and its various “metaphysical” interpretations, algebraic (analytic) revolution of XVI–XVII centuries, flourishing projects of new “sciences of nature”, have all contributed to the unique conditions for metabasis, epistemic “transfer” of geometrical and “mathematical” models to other fields of knowledge, from physics to biology, medicine and rhetoric. Analysis of connections of “mathematical” and “social” knowledge in Early Modernity can be instructive even for the perspectives of interdisciplinary interactions of social-historical and formal sciences in contemporary settings. 

Keywords: Early Modern Civil Sciences, Early Modern Mathematics, Maker's Knowledge Principle, State of Nature, Moralization of Modalities