Mathematical Fixtures

Abstract

The pluralist sheds the more traditional ideas of truth and ontology. This is dangerous, because it threatens instability of the theory. To lend stability to his philosophy, the pluralist trades truth and ontology for rigour and other ‘fixtures’. Fixtures are the steady goal posts. They are the parts of a theory that stay fixed across a pair of theories, and allow us to make translations and comparisons. They can ultimately be moved, but we tend to keep them fixed temporarily. Apart from considering rigour of proof as a fixture, I discuss fixed models, invariant notions and fixed information about objects across theories. There are other fixtures, but it is enough to start with these.