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Bolzano's Logical System$
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Ettore Casari

Print publication date: 2016

Print ISBN-13: 9780198788294

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198788294.001.0001

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Elementary Level (B): Propositions

Elementary Level (B): Propositions

(p.62) 3 Elementary Level (B): Propositions
Bolzano's Logical System

Ettore Casari

Oxford University Press

This chapter develops the theory of propositions, beginning with the consideration of propositions of the form ‘A has b’ that are defined to be true if and only if to every object referred to by A there belongs a quality referred to by b. Particular attention is devoted to the ways in which complex propositions are generated. After this, the famous ‘theory of variation’ is developed, which allows the introduction of the fundamental distinction between the material and formal dimensions of truth and so, besides the distinction between analytic and synthetic truth, also the theory of the formal relations among propositions: compatibility, derivability (and its specifications: exact and redundant) equivalence, subordination, independence, exclusion, reciprocal exclusion, contradictoriness, contrariety, integration (absolute and conditioned). The chapter ends with the exposition of the ‘logical-inductive’ Bolzanian theory of probability.

Keywords:   true proposition, variation, analytic and synthetic truth, compatibility, derivability, probability

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