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
According to formalism a mathematician is not concerned with mysterious meta-physical entities but with mathematical symbols themselves. Mathematical entities, on this view, become mere sensible signs. However, the price that has to be paid for this move looks to be too high. Mathematics, which is nowadays considered to be the queen of the sciences, thus turns out to be a content-less game. That is why it seems too absurd to regard numbers and all mathematical entities as mere symbols. T e aim of our paper is to show the reasons that have led some philosophers and mathemati¬cians to accept the view that mathematical terms in a proper sense do not refer to anything and mathematical propositions do not have any real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science.