Grounding in Bolzano and Normal Proofs

Antje Rumberg (University of Konstanz)

In my talk I will discuss Bolzano's theory of grounding (Abfolge) in the Wissenschaftslehre (1837) and the parallels between his concept of grounding and current notions of normal proofs. The relation Bolzano is most interested in is the relation between a truth and its immediate complete ground. Iterating those immediate grounding steps gives rise to grounding trees, which play a crucial role in Bolzano's theory of proofs as they correspond to explanatory proofs. Occasionally, similarities have been pointed out between Bolzano's grounding trees and cut-free proofs in Gentzen's sequent calculus. I will discuss those similarities and extend the comparison to normal natural deduction proofs and their role in proof-theoretic semantics in the tradition of Dummett and Prawitz, which I consider more fruitful. Discussing Bolzanian grounding trees against the background of current notions of normal proofs will shed light on Bolzano's concept of grounding as a proof-theoretic notion and on the interrelation between grounding and formal consequence relations in general.