First Degree Entailment, Symmetry and Paradox

• Authors: Restall Greg
• Languages of publication: EN

Abstracts

EN

Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment (FDE) is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts (and there seems to be no very good reason to prefer gaps over gluts or gluts over gaps if you’re happy with FDE), then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How is the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle – an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected.

Keywords

EN

first degree entailment; paradox; symmetry; models; theories

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2017
• Volume: 26
• Issue: 1
• Pages: 3–18

Dates

published

2017-03-15

online

2016-10-19

Contributors

author

Restall Greg

• Philosophy Department The University of Melbourne

References

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Identifiers

DOI

10.12775/LLP.2016.028