On Nelson Goodman's final formulae for Primary Complexity

TL;DR

This paper introduces combinatorial algorithms to simplify Nelson Goodman's formula for maximum complexity of n-place predicates, enabling reduction to formulas involving fewer predicates, which was previously unresolved.

Contribution

It provides the first practical procedures to reduce Goodman's complexity formula, advancing the understanding of predicate complexity in his theoretical framework.

Findings

Developed elementary combinatorial algorithms for reduction

Achieved reduction of v[n-pl] to (n-1)-place predicates

Enhanced computational methods for complexity evaluation

Abstract

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.