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abstract bibtex

abstract bibtex

In 1848, few months before his death, Bernard Bolzano wrote a letter to his pupil Zimmermann explaining why \S 102 of his already published Wissenschaftslehre is mistaken. Berg has repeatedly expressed the view that, in this letter, Bolzano rejects wholesale his previous adherence to the Euclidean common notion V ``The whole is greater than its part'', thus reneging a significant part of his own work in the \textit\Gr\"ossenlehre\ and \textit\Paradoxien des Unendlichen\, and adopts one-to-one correspondence as a sufficient condition for equality of size. This interpretation of that letter has recently been questioned and discussed by several scholars (Mancosu, Rusnock, Sebestik, but also Trlifajova). While all of these scholars express scepticism of varying degrees towards Berg's conclusion, a fully fledged explanation of the tension between Bolzano's letter and his previous work on comparisons of size is lacking. In this paper, we join the fray of the Berg sceptics by advancing the modest thesis that, contra Berg, Bolzano does not reject CN5 for quantities in general, but, in favour of Berg, the concepts which are considered as governed by CN5 change, and this explains the tension between the 1848 letter and Wissenschaftslehre \S 102.

@unpublished{ginammi_bolzano_0-1, title = {Bolzano on sets}, abstract = {In 1848, few months before his death, Bernard Bolzano wrote a letter to his pupil Zimmermann explaining why {\textbackslash}S 102 of his already published Wissenschaftslehre is mistaken. Berg has repeatedly expressed the view that, in this letter, Bolzano rejects wholesale his previous adherence to the Euclidean common notion V ``The whole is greater than its part'', thus reneging a significant part of his own work in the {\textbackslash}textit\{Gr{\textbackslash}"ossenlehre\} and {\textbackslash}textit\{Paradoxien des Unendlichen\}, and adopts one-to-one correspondence as a sufficient condition for equality of size. This interpretation of that letter has recently been questioned and discussed by several scholars (Mancosu, Rusnock, Sebestik, but also Trlifajova). While all of these scholars express scepticism of varying degrees towards Berg's conclusion, a fully fledged explanation of the tension between Bolzano's letter and his previous work on comparisons of size is lacking. In this paper, we join the fray of the Berg sceptics by advancing the modest thesis that, contra Berg, Bolzano does not reject CN5 for quantities in general, but, in favour of Berg, the concepts which are considered as governed by CN5 change, and this explains the tension between the 1848 letter and Wissenschaftslehre {\textbackslash}S 102.}, author = {Ginammi, Annapaola and Bellomo, Anna}, year = {0}, }

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