Mathematical Sciences Seminar - Why be interested in incompleteness anyway?
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
The incompleteness results discovered in the 1930s precipitated a change in mathematical and philosophical outlooks concerning the practice of Mathematics. In particular, these discoveries writ large the impossibility of proving the self-consistency of arithmetic, and had profound implications for our understanding of proof and its relation to mathematical truth. Subsequently, these incompleteness results raise the question of whether or not, now the fact of incompleteness is known, it is fruitful to continue to study the phenomenon. In this paper I argue that incompleteness is a worthwhile topic of inquiry for both mathematical and philosophical reasons. First, the notion illuminates several core philosophical concepts (including truth and its relation to proof). Second, incompleteness results enable us to avoid pursuing doomed research programmes. Third, the study of incompleteness phenomena has resulted in the development of constructions of independent mathematical interest. Finally, the detailed study of different principles has led to a deeper understanding of how mathematical structures interrelate.
Contact name:
Department of Economics, Mathematics and Statistics