Course Syllabus: This course, while providing a philosophical and historical account of how non-Euclidean geometries were discovered, deals with some important methodological and historical problems of geometry such as the possibility of methodology of non-empirical sciences, continuity and progress in geometry with special emphasis on case studies in geometry.
Course Content: The discovery of non-Euclidean geometries has a long and complicated history. The predominant account of this discovery claims that this history is a linear compilation of geometrical results and should be best understood as a sequence of foundational studies. Moreover, it does not deal with the issues of rationality geometrical progress and revolutions in the history of geometry. So it has some weakness to represent faithfully what went on when such a discovery came about. An historical-cum-methodological account of this discovery shall be offered in terms of methods employed by geometers in problem-solving, the characterization of geometrical language, problems and theories, and the intentions of geometers themselves. Euclid’s and Saccheri’s works will be studied as case studies.
Pre-Requisites: Some familiarity with logic and the philosophy and history of science.
Written Work, Oral Presentation and Examination: tba.