Theories of truth based on four-valued infectious logics

Logic Journal of the IGPL 28 (5):712-746 (2020)
Download Edit this record How to cite View on PhilPapers
Abstract
Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems.
Keywords
No keywords specified (fix it)
PhilPapers/Archive ID
SZMTOT
Upload history
Archival date: 2018-03-15
View other versions
Added to PP index
2018-03-15

Total views
195 ( #25,653 of 55,807 )

Recent downloads (6 months)
37 ( #21,125 of 55,807 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.