Truthlikeness for Multidimensional, Quantitative Cognitive Problems

This book is concerned with the problem of applying the theory of verisimilitude to cognitive problems of a quantitative nature. Attention is mostly focused on hypotheses concerned with (physical or other) systems whose state can be represented with an element of a multidimensional state space, but hypotheses concerned with quantitative laws are also considered. The book provides a systematic introduction to the main contemporary forms of the theory of verisimilitude, including both proposed definitions of quantitative degrees of verisimilitude and proposed definitions of the relation 'closer to the truth than'. It shows why the quantitative measures that have been proposed earlier produce unacceptable results in the multidimensional case and, using the tools of geometric measure theory, works out alternatives for them in detail. In addition, the standard structuralist theory of science and the way in which the problems of approximation are dealt with in it are presented and evaluated critically.