In this paper we deal with the problem, whether number is a property of external things. It is divided into three parts. Firstly Mill’s empiristic concept of natural numbers is summarized, then Frege’s arguments against this conception are put forth and finally viewpoints of some contemporary analytical philosophers (first of all G. Kessler), who reject Frege’s critique, are set out. Kessler and his followers in fact revive the abandoned theory of Mill., V tomto článku se zabýváme problémem, zda je číslo majetkem vnějších věcí. Je rozdělena do tří částí. Nejprve je shrnut Millmův empirický koncept přirozených čísel, pak jsou uvedeny Fregeovy argumenty proti tomuto pojetí a nakonec jsou vytyčena stanoviska některých současných analytických filozofů (především G. Kesslera), kteří Fregeovu kritiku odmítají. Kessler a jeho následovníci ve skutečnosti oživují opuštěnou teorii mlýna., and Prokop Sousedík ; David Svoboda
In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.