Reference patterns of paradox

• Applicant: Professor Dr. Hannes Leitgeb, since 9/2018
• Subject Area: Theoretical Philosophy
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 289567880

In this project we aim to take a fresh look at the logical (concept- or property-theoretic) and semantic paradoxes. These paradoxes seem to result from certain vicious reference patterns. Our goal is to determine the source of paradox by analyzing their referential patterns in graph-theoretic terms and to devise new axiomatic theories of properties (within classical first-order logic) based on that analysis. The graph-theoretic approach is motivated, on the logical side, by Bertrand Russell's view that every property has a range of significance, i.e., a collection of arguments to which the property can be meaningfully applied, and, on the semantic side, by Hans Herzberger's view that every sentence has a domain, i.e., a collection of objects that the sentence refers to. Our program can be understood as an explication and vindication of Gödel's statement that we may assume every property to be significant everywhere except for certain "singular points" (which we want to determine as part of the project). We expect to conclude this project with a uniform solution (within classical first-order logic) to the logical and semantic paradoxes.

• DFG Programme: Research Grants
• Co-Investigator: Dr. Thomas Schindler
• Ehemalige Antragstellerin: Dr. Lavinia Picollo, until 8/2018