John Searle has argued that functions owe their existence to the value that we put into life and survival. In this paper, I will provide a critique of Searle’s argument concerning the ontology of functions. I rely on a standard analysis of functional predicates as relating not only a biological entity (e.g., the heart), an activity that constitutes the function of this entity (e.g., pumping blo...

Let (E,A) be a set system consisting of a finite collectionA of subsets of a ground set E, and suppose that we have a function φ which maps A into some set S . Now removing a subset K from E gives a restriction A(K̄) to those sets of A disjoint from K, and we have a corresponding restriction φ|A(K̄) of our function φ. If the removal of K does not affect the image set of φ, that is Im(φ|A(X̄)) = Im...

Many neural networks can be derived as optimization dynamics for suitable objective functions. We show that such networks can be designed by repeated transformations of one objective into another with the same xpoints. We exhibit a collection of algebraic transformations which reduce network cost and increase the set of objective functions that are neurally implementable. The transformations in...

Objectives . A frequently used method for obtaining Pareto-optimal solutions is to minimize a selected quality index under restrictions of the other indices, whose values are thus preset. For scalar objective function, global minimum sought that contains restricted indices as penalty terms. However, landscape such function has steep-ascent areas, which significantly complicate search minimum. T...