### A discourse on epistemology, height and language

The formalism I presented so far has avoided the issue of choosing the free parameters in the model, namely the height function and the measure \( \mu \). I said that given an underlying logic we can use the notion of complexity to get a canonical height map, but this map, obviously, is only canonical in a specific signature/language. If we change the language of our theory to add new symbols for some additional operations which already exist in the theory, thus reducing their complexity, we have a more powerful language which can express more ideas in lower complexity. However, by doing so we also lose a lot of information - we put different functions which may "ought to" be in different complexity classes together. In practice, this means there is a trade-off between the expressive power of a language and the information its complexity classes contain. It's important to note at this point that the asymptotic properties of the formalism do not depend on the specific cho…