The paper deals with the problem whether the number is a property or an object. The authors are convinced that from the logical point of view the number is an object, but from the ontological point of view the number is a special kind of property (briefly spoken the property of a system or a structure). and Prokop Sousedík, David Svoboda
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 the positivists, all our knowledge is based on experience which is the foundation not only of every empirical science, but also of those disciplines that are usually considered to be a priori. The paper consists of two main parts. Firstly, a positivist concept of number defended by J. S. Mill is presented; secondly, it is shown how this conception can settle some objections coming from apriori-oriented philosophers. Mill’s theory of number is interesting for at least two historical reasons. It is developed in connection with a relatively rich scholastic logic which is why its methodology is similar to the contemporary philosophy of language; it is indispensable for an appropriate comprehension of the concept of number that was proposed by Mill’s most famous opponent G. Frege., Podle pozitivistů jsou všechny naše znalosti založeny na zkušenostech, které jsou základem nejen každé empirické vědy, ale také těch oborů, které jsou obvykle považovány za a priori . Příspěvek se skládá ze dvou hlavních částí. Nejprve je prezentován pozitivistický koncept počtu obhajovaných JS Millem; Za druhé, je ukázáno, jak tato koncepce může vyřešit některé námitky z apriori-orientovaných filozofů. Millova teorie čísel je zajímavá alespoň ze dvou historických důvodů. Je rozvíjena v souvislosti s relativně bohatou akademickou logikou, proto je její metodika podobná současné filosofii jazyka; je nepostradatelné pro vhodné pochopení pojmu čísla, který navrhl nejslavnější oponent ml. G. Frege., 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.