Formalism and Its Discontents: Mathematics and Wisdom in the European Enlightenment
Short Definition
“Formalism and Its Discontents” weaves a technical history of the development of calculus and mechanics during the eighteenth century into a rich account of debates over the exact sciences as sources of theoretical and practical wisdom. “Formalism and its Discontents”also, pursues a series of focused case studies of Enlightenment disputes over the value of formal reasoning for scientific knowledge, aesthetic standards, and practical moral reasoning.
Summary Points
- “Formalism and Its Discontents” weaves a technical history of the development of calculus and mechanics during the eighteenth century into a rich account of debates over the exact sciences as sources of theoretical and practical wisdom.
- Enlightenment debates focused on the power of the different sciences for learning to reason in everyday life.
- Great advocates of mathematics, Enlightenment savants worried about the epistemological and moral dangers should mathematics become too disconnected from the real world.
- “Formalism and its Discontents” pursues a series of focused case studies of Enlightenment disputes over the value of formal reasoning for scientific knowledge, aesthetic standards, and practical moral reasoning.
- Animation of the production of much new mathematics and physics throughout the eighteenth century.
- The production of these tools animated debate about how best to apply them to realizing the good of individuals alongside the common good.
- The empirical and analytical framework of “Formalism and its Discontents” bridges existing studies from the history of science, organizational research, and psychology concerning the importance of tacit knowledge in the practical wisdom of everyday moral, scientific, and artisanal activity.
- The project illustrates the dynamic power of tensions between formal and tacit dimensions of wisdom for producing innovative work in science, art, politics, and craft alike.
- For mathematics to contribute to developing the new wisdom at the core of the Enlightenment project, it needed to be more than a mere game; this constraint pushed mathematicians to develop new techniques to tie mathematics and formal reasoning to the physical world.
- Jones conducted a general survey of the relations between philosophy and
- where Kant insists that mathematics be understood largely as synthetic aprioristic and therefore not reducible to logic. With this Kant defended the creativity and non-triviality of mathematical reasoning and secured it against denunciations of it as mere formalism.
Text from Wisdom Institute
“Formalism and Its Discontents” weaves a technical history of the development of calculus and mechanics during the eighteenth century into a rich account of debates over the exact sciences as sources of theoretical and practical wisdom. Enlightenment debates focused on the power of the different sciences for learning to reason in everyday life. These debates provide powerful ways for questioning the gulf between modern theories of wisdom that see it as an expert system (thus primarily intellectual) and those that insist upon the need for the development of a wise personality, in which knowledge plays a necessary but far from sufficient role.
Formalism and Its Discontents: Mathematics and Wisdom in the European Enlightenment
Great advocates of mathematics, Enlightenment savants worried about the epistemological and moral dangers should mathematics become too disconnected from the real world. Such worries are at the center of major public debates in science, education, philosophy, and aesthetics at the heart of the European Enlightenment. Since these disputes deal with apparently disparate subject matters, such as differential equations, the nature of tonality, the origins of language, and the subjective preconditions for all knowing, they are traditionally, but quite wrongly, segregated into separate histories. “Formalism and its Discontents” pursues a series of focused case studies of Enlightenment disputes over the value of formal reasoning for scientific knowledge, aesthetic standards, and practical moral reasoning. Advocates of new mathematical techniques were seeking less to replace the traditional goals of wisdom than to provide new tools using mathematics to aid the fulfillment of those goals. The tension between new and old tools for gaining wisdom helped animate the production of much new mathematics and physics throughout the eighteenth century. In turn, the production of these tools animated debate about how best to apply them to realizing the good of individuals alongside the common good. To understand the texture of scientific developments during the Enlightenment, the project argues, we need to understand how such developments aided the creation and sustaining of wisdom. The empirical and analytical framework of “Formalism and its Discontents”bridges existing studies from the history of science, organizational research, and psychology concerning the importance of tacit knowledge in the practical wisdom of everyday moral, scientific, and artisanal activity. The project illustrates the dynamic power of tensions between formal and tacit dimensions of wisdom for producing innovative work in science, art, politics, and craft alike.
Stretching from Leibniz to Kant, and considering philosophy, mathematical practice, and aesthetic debates, the project shows how seriously mathematicians took critiques such as that offered by Denis Diderot: “The subject of the mathematician has no more existence in nature than that of the gamer. Both are just a question of convention.” For mathematics to contribute to developing the new wisdom at the core of the Enlightenment project, it needed to be more than a mere game; this constraint pushed mathematicians to develop new techniques to tie mathematics and formal reasoning to the physical world. Jones examined primarily the technical aspects of musical harmony and the mathematical treatment of vibrating strings; then he focused more on a deeper reexamination of the major philosophical reflections on mathematics and its connections to knowledge during the eighteenth century, especially Kant.
Jones conducted a general survey of the relations between philosophy and mathematics in the eighteenth century for a Routledge encyclopedia of eighteenth-century philosophy. Refracted through the lens of considering mathematics as a form of wisdom, this new concise account of the importance of mathematics for philosophy will serve to illuminate a number of debates and doctrines that have long perplexed students of the period. His study underscores the grounds for the resistance to overly formal methods as a model for philosophical reasoning and thus helps to illuminate the compelling reasons enlightenment thinkers largely eschewed the logical innovations of figures such as Leibniz and Saccheri. Appreciating this resistance will greatly illuminate a key section of one of the most important but refractory texts of the period, the transcendental aesthetic of the Critique of Pure Reason, where Kant insists that mathematics be understood largely as synthetic apriorist and therefore not reducible to logic. With this Kant defended the creativity and non-triviality of mathematical reasoning and secured it against denunciations of it as mere formalism. Kant’s perplexing doctrine makes maximal sense only if we take seriously demands that mathematics contribute to enlightenment and thus to the higher forms of wisdom of that enlightenment.
https://wisdomcenter.uchicago.edu/about/project-1-defining-wisdom