Bolzano's logical system (Q2827263)

The book under review aims at a systematic consideration of B.\ Bolzano's logical thought as presented above all in Bolzano's \textit{Wissenschaftslehre} (1837). The logic is presented within the formal system of the predicate calculus with identity and choice operator, i.e., Hilbert's epsilon calculus. The author introduces his formal model of Bolzano's logic and its basic concepts (the Bolzanian conceptual universe), among them the central relation of \textit{having} which holds between objects and qualities. The author elaborates the system by stepwise increasing complexity, from ideas and propositions to the ``symbolic level'', removing first limitations in the theory of ideas and propositions, taking a symbolic stance, i.e., a position that acknowledges that ideas and propositions ``are also objects and hence possible references of ideas'' (p. x). Chapter 5 deals with inferences, Chapter 6 with higher level systems, ``characterized by the assumption that qualities are objects, too'' (p. 232). Chapter 8 is devoted to etiology, i.e., the doctrine of the consecutivity (\textit{Abfolge}) of truths, i.e., the relation between grounds and consequences. Topics of the last two chapters are the theory of knowledge with the basic epistemological notions of ``having as material'' (\textit{Stoff}) and ``having as content'' (\textit{Inhalt}), and semiotics. The volume closes with appendices on the epsilon calculus with definitory expansions (A), a discussion of specific axioms (general axioms, comprehension axioms) (B), aggregates with the different relations of inclusion and membership (C), unity and multiplicity (D), antinomies (E), and real numbers (F).