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1 results

  • EARLY BOLZANO ON GROUND-CONSEQUENCE PROOFS

  • STEFANIA CENTRONE
  • Journal:
    Bulletin of Symbolic Logic / Volume 22 / Issue 2 / June 2016
    Published online by Cambridge University Press:
    05 July 2016, pp. 215-237
    Print publication:
    June 2016

  • In his early Contributions to a Better-Grounded Presentation of Mathematics (1810) Bernard Bolzano tries to characterize rigorous proofs (strenge Beweise). Rigorous is, prima facie, any proof that indicates the grounds for its conclusion. Bolzano lists a number of methodological constraints all rigorous proofs should comply with, and tests them systematically against a specific collection of elementary inference schemata that, according to him, are evidently of ground-consequence-kind. This paper intends to give a detailed and critical account of the fragmentary logic of the Contributions, and to point out as well some difficulties Bolzano’s attempt runs into, notably as to his methodological ban on ‘kind crossing’.