Paradoxes in R. Dedekind's and G. Frege's Systems
Vol.15,No.1(2014)
This paper deals with two arithmetical systems -namely with the system presented by R. Dedekind and the system established by G. Frege - and with paradoxes there occurring - namely with the Burali-Forti paradox (the first formulation of modern paradox at all), the Cantor´s paradox and the Russell´s paradox. The main purpose is to show in what way are these paradoxes similar and that although these paradoxes occur in different systems, they have common features. On the basis of studying these systems and paradoxes and also ways out from these paradoxes, the author reached the conclusion that the investigated paradoxes arise from the same source, namely the problem of nonhierarchization.
In addition, the Appendix of this article presents the Burali-Forti paradox in the form that shows the historically authentic way of derivation of this paradox. There is also a short exposition of Russell´s paradox in the Appendix. It shows the paradox not only in the form presented by B. Russell but also in the G. Frege´s formulation.
The Burali-Forti paradox; Cantor’s paradox; Russell’s paradox; Dedekind; Frege; Russell
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