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Philosophical and Mathematical Correspondence between Gottlob Frege and Bertrand Russell in the years 1902-1904. Some Uninvestigated Topics

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Besler G.

Folia Philosophica

2016

tom 35

Abstract Although the connections between Frege’s and Russell’s investigations are commonly known (Hylton 2010), however, there are some topics in the letters which do not seem to have been analysed until now: 1. Paradoxes formulated by Russell on the basis of Frege’s rules: a) „»ξ can never take the place of a proper name« I false proposition when ξ is a proposition”; b) “A function never takes the place of a subject”. A solution of this problem was based on reference/sense theory and on distinction between the first- and second-level names (Frege). 2. The inconsistency in Frege’s system may be avoided by introduction of: a) a new kind of objects called quasi-objects (Frege); b) logical types (Frege and Russell); c) mathematics without classes (Russell); d) some restrictions on domain of function (Frege). 3. Since an inconsistency is connected with a class what is class? In one of the letters Frege compared a class to a chair which is composed of atoms. It seems to be similar to collective understanding of a set (Stanisław Leśniewski). 4. Russell doubted that the difference between sense and reference of expressions is essential. Hence, Frege found some additional reasons to distinguish them: semiotic, epistemological, from identity, from mathematical practice. This discussion can be seen as a next step in developing the theory of description by Bertrand Russell.

Gottlob Frege o liczbie. Przyczynek do określenia roli, jaką dla filozofów pełni historia matematyki

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Besler G.

Zagadnienia Filozoficzne w Nauce

2013

nr 53

133-164

In this paper I will focus on Frege’s six crucial claims on numbers. I begin with indicating the reasons for his interest in this topic and conclude with a reflection on the role of the history of mathematics in the practice of philosophy. Frege believed that the study on numbers is a common task for both philosophers and mathematicians. In this article, priority is given to the philosophical aspect.