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The Birth of Formal Sciences: History and Philosophy of the Relation Between Logic and Mathematics
Last Updated: 2026-02-05 15:40:51
Abstract
Formal 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.
Objective
During 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
Content
Knowledge 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.
General Information
- Language
- English
- Levels
- DS , DR , MSC
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | The Birth of Formal Sciences: History and Philosophy of the Relation Between Logic and Mathematics |
|
2 h weekly |
Offered In
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GESS Science in Perspective (Only the courses listed below will be recognized as "GESS Science in Perspective" courses. Further below you will find courses under the category "Type B courses Reflections about subject specific methods and content" as well as the language courses. During the Bachelor’s degree Students should acquire at least 6 ECTS and during the Master’s degree 2 ECTS. Students who already took a course within their main study program are NOT allowed to take the course again.)
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Type B: Reflection About Subject-Specific Methods and Contents (Subject-specific courses: Recommended for bachelor students after their first-year examination and for all master- or doctoral students. Students who already took a course within their main study program are NOT allowed to take the same course again. All these courses are listed under the category “Typ A”, this means, every student can enroll in these courses.)
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Doctoral Department of Humanities, Social and Political Sciences (More Information at: )