Invariance, symmetry and meaning

The role of the concept of invariance in physics and geometry is analysed, with attention to the closely connected concepts of symmetry and objective meaning. The question of why the fundamental equations of physical theories are not invariant, but only covariant, is examined in some detail. The las t part of the paper focuses on the surprising example of entropy as a compl ete invariant in ergodic theory for any two ergodic processes that are isom orphic in the measure-theoretic sense.