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Logicism and Paradox (II)

(Original title: Logicizmus a paradox)
Organon F, 2005, vol. 12, No 2, pp. 121-140.
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This is a sequel to my article devoted to the development of Fregean logi-cism. The first part dealt with its „rise and fall“, i. e. its initial success in ana-lyzing the concept of number and its subsequent fall at Russell’s antinomy. In the course of the previous article we did not (have to) leave the area of the classical Fregean research. On the contrary, Russell’s paradox and its analy-sis bring us now to the second part of the whole story – the (alleged) resurrec-tion of the logistic idea in the works of Crispin Wright and George Boolos. We find ourselves in the middle of a neo-Fregean – structuralistic – approach based on the techniques of modern model-theoretical logic and (meta)mathe-matics. We do not want to criticize it yet, but only present some of the most important results such as the consistency of Hume’s Principle or categoricity of Frege’s (and Peano’s) second-order arithmetic.

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