  We propose a distinction between the physical and the mathematical parts of
gauge field theories. The main problem we face is to uphold a strong and
meaningful criterion of what is physical. We like to call it "Field's dilemma",
referring to Hartry Field's nominalist proposal which we consider to be
inadaequate. The resolution to the dilemma, we believe, is implicitly provided
by the so-called fiber bundle formalism. We shall demonstrate, in detail, that
the bundle structure underlying modern quantum and gravitational gauge field
theories allows for a genuine distinction between the physically significant
and the merely mathematical parts of these theories.
