Methodological imperfection and formalizations of scientific activity

Any mathematical formalization of scientific activity allows for imperfections in the methodology that is formalized. These can be of three types, dirty, rotten, and dammed. Restricting mathematical attention to those methods that cannot be construed to be imperfect drastically reduces the class of objects that must be analyzed, and related all other objects to these more regular ones. Examples are drawn from empirical logic.