Ableitbarkeit and Abfolge

Abstract

Bolzano’s conception of what it is for a conclusion to follow from a set of premises has been a popular topic in recent scholarship as well as in more general work on logical consequence — (cf. van Benthem 1985, 2003; Etchemendy 1990; Siebel 1996, 2002; Tatzel 2002). Most commentators agree that Bolzano’s account fails, and my position is not essentially different.1 However, Bolzano’s views are both more complex and more interesting than one might assume. Bolzano’s account of consequence comprises not one but three distinct aspects: his conception of Ableitbarkeit (1837, §155), his conception of statistical inference (1837, §161) and his conception of Abfolge (1837, §162). On the one hand, the notion of Ableitbarkeit delivers a sophisticated and plausible semantic account of truth-preservation, and his generalisation of it to an account of statistical inference is also worthy of consideration. On the other hand, Bolzano’s attempt at a definition of Abfolge constitutes the basis of an account of a priori knowledge (see Chapter 8) that remains underappreciated and of a theory of justification and demonstration (Chapter 7) whose interest has been noticed by some authors, and in some cases even vindicated.