A Substitutional Theory

Abstract

Considering later developments in the field, two aspects of Bolzano’s semantics are particularly significant: his definition of Ableitbarkeit and his definition of “logical analyticity”. The first — Bolzano’s attempt at an analysis of statements of the form ‘if…, then…’ — has often been compared to Tarski’s notion of logical consequence, and as we will see in Chapter 6, there are good reasons to maintain the comparison. The second anticipates the Quinean definition of logical truth and will be discussed in some detail in the next chapter. Both notions are common themes in the literature. Yet, important features of both have been neglected. Consequently, their role in Bolzano’s theory has often been misunderstood with the upshot that crucial aspects of Bolzano’s theory as a whole have been completely overlooked. The concern that is at the core of virtually every discussion of Bolzano’s substitutional method is that the latter does not deliver the kind of results one would reasonably expect when it comes to defining analyticity and consequence and, in particular, that it does not account for the kind of epistemic and metaphysical necessity those notions are assumed to carry with them.