The Liar Syndrome

SATS 3 (1):37-55 (2002)
Download Edit this record How to cite View on PhilPapers
This article examines the various Liar paradoxes and their near kin, Grelling’s paradox and Gödel’s Incompleteness Theorem with its self-referential Gödel sentence. It finds the family of paradoxes to be generated by circular definition–whether of statements, predicates, or sentences–a manoeuvre that generates the fatal disorders of the Liar syndrome: semantic vacuity, semantic incoherence, and predicative catalepsy. Afflicted statements, such as the self-referential Liar statement, fail to be genuine statements. Hence they say nothing, a point that invalidates the reasoning on which the various paradoxes rest. The seeming plausibility of the paradoxes is due to the fact that the same sentence may be used to make both the pseudo-statement and a genuine statement about the pseudo-statement. Hence, if a formal system is to avoid ambiguity and consequent seeming paradox, it requires some sort of disambiguator to distinguish the two statements. Gödel’s Theorem presents a further complication in that the self-reference involved is sentential rather than statemental. Nevertheless, on the intended interpretation of the system as a formalization of arithmetic, the self-referential Gödel sentence can only be an ambiguous statement, one that is both a pseudo-statement and its genuine double. Consequently, the conclusions commonly drawn from Gödel’s theorem must be deemed unwarranted. Arithmetic might well be formalized in a proper system that either excludes circular definition or introduces disambiguators
No keywords specified (fix it)
(categorize this paper)
PhilPapers/Archive ID
Upload history
Archival date: 2014-01-28
View other versions
Added to PP index

Total views
345 ( #15,331 of 55,929 )

Recent downloads (6 months)
12 ( #44,964 of 55,929 )

How can I increase my downloads?

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