Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

851-0170-00L  The Birth of Formal Sciences: History and Philosophy of the Relation Between Logic and Mathematics

SemesterSpring Semester 2020
LecturersJ. L. Gastaldi
Periodicitynon-recurring course
Language of instructionEnglish


AbstractFormal knowledge, such as mathematics and logic, has a singular capacity to resist historical critique. But what if formality itself had a history - a recent birth and a foreseeable decline? In this course, we will explore this hypothesis by critically assessing the novel relationship between mathematics and logic that emerged in the 19th century, forging our notion of formal.
ObjectiveDuring the course, students will be able to:
-Acquire a general perspective on the history of formal logic
-Review relevant aspects of the history of modern mathematics
-Obtain philosophical and historical tools for critically assessing the status of formal sciences
-Develop a critical understanding of the notion of formal
-Discuss the methodological capabilities of historical epistemology
ContentKnowledge reputed to be formal, such as mathematics and logic, has a singular capacity to resist historical critique. Indeed, from a traditional perspective, a historical account of a purely formal statement, like a theorem, can hardly do more than show the inevitable path that led to its evident and thenceforth everlasting truth. But what if formality itself had a history - a relative recent birth and a foreseeable decline? In this course, we will explore this hypothesis by critically assessing the conditions, impact and limits of the novel relationship between mathematics and logic that emerged in the 19th century, forging both the modern notion of formal and the subsequent epistemological status of formal sciences. After discussing the difficulties of a historical (or archaeological, in the sense that M. Foucault gives to this term) approach to formal knowledge, we will present the principal historical circumstances providing the conditions for an unprecedented association between logic and mathematics. This will give us the means to undertake the detailed study of that association, within the context of the most prominent attempts to provide formal deductive languages in the 19th century: those of George Boole and Gottlob Frege. Finally, we will address the limitations manifested by those projects at the turn of the 20th century, putting them into perspective to assess the transformation our notion of formal is experiencing as a result of the proliferation of computational practices.