On Nelson Goodman's final formulae for Primary Complexity

In the Structure of Appearance and in Problems and Projects, Nelson Goodman has constructed a theory of complexity whose elements are the predicates of a system. One of his main results is a closed formula to evaluate v[n-pl], the maximum complexity value of an n-place predicate. Up to this day no procedure has been found to reduce v[n-pl], i.e., to write it in terms of (n-1)-place predicates. In this article we propose elementary combinatorial algorithms to carry out such a reduction.