On the tension between Tarski's nominalism and his model theory (definitions for a mathematical model of knowledge)

The nominalistic ontology of Kotarbinski, Slupecki and Tarski does not provide any direct interpretations of the sets of higher types which play important roles in type theory and in set theory. For this and other reasons (to be explained below) I will interpret those theories as descriptions of some finite structures which are actually constructed in human imaginations and stored in their memories. Those structures will be described (mathematically defined) in this lecture. They are hinted by the idea of Skolem functions and Hilbert's epsilon-symbols, and they constitute a finitistic modification of Tarski's concept of a model. They suggest also a form of the evolutionary process which leads to the development of human intelligence and language. (C) 2003 Published by Elsevier B.V.