Never trust an unsound theory

• Lajevardi and Salehi, in “There may be many arithmetical Gödel sentences”, argue against the use of the definite article in the expression “the Gödel sentence”, by claiming that any unsound theory has Gödelian sentences with different truth values. We show that their Theorems 1 and 2 are special cases (modulo Löb's theorem and the first incompleteness theorem) of general observations pertaining to fixed points of any formula, and argue that the false sentences of Lajevardi and Salehi are in fact not Gödel sentences.

Subject headings

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

HUMANIORA  -- Filosofi, etik och religion -- Filosofi (hsv//swe)

HUMANITIES  -- Philosophy, Ethics and Religion -- Philosophy (hsv//eng)

Keyword

fixed points

Gödel sentences

soundness

truth

Publication and Content Type

ref (subject category)

art (subject category)