What is it about?
Gottlob Frege's system of logic is inconsistent, due to the Russell-Zermelo paradox. However, some subsystems of Frege's theory are consistent. We provide finitistic consistency proofs of these systems.
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Why is it important?
The consistent subsystems of Frege's inconsistent theory were suspected to be very weak, in the sense that they cannot really formalize usual mathematics. Our finitistic consistency proofs confirmed these suspicions in a rigorous manner.
Perspectives
For a long time, I thought about giving finitistic consistency proofs of certain subsystems of Frege's inconsistent theory (these subsystems were known to be consistent by infinitary methods). The problem was how to deal with the term-forming operator characteristic of Richard Heck's subsystems. Together with my co-author Luís Cruz-Filipe, we finally were able to produce this paper.
Fernando Ferreira
Universidade de Lisboa
Read the Original
This page is a summary of: The Finitistic Consistency of Heck’s Predicative Fregean System, Notre Dame Journal of Formal Logic, January 2015, Duke University Press,
DOI: 10.1215/00294527-2835110.
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