Model Selection in Science: The Problem of Language Variance

Recent solutions to the curve-fitting problem, described in Forster and Sober ([1994]), trade off the simplicity and fit of hypotheses by defining simplicity as the paucity of adjustable parameters. Scott De Vito ([1997]) charges that these solutions are ‘conventional’ because he thinks that the number of adjustable parameters may change when the hypotheses are described differently. This he believes is exactly what is illustrated in Goodman’s new riddle of induction, otherwise known as the grue problem. However, the ‘number of adjustable parameters’ is actually a loose way of referring to a quantity that is not language dependent. The quantity arises out of Akaike’s theorem in a way that ensures its language invariance.