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.