How do We Know that the Godel Sentence of a Consistent Theory Is True?
G. Sereny · Philosophia Mathematica · 2011
Some earlier remarks Michael Dummett made on Gödel’s theorem have recently inspired attempts to formulate an alternative to the standard demonstration of the truth of the Gödel sentence. The idea underlying the non-standard approach is to treat the Gödel sentence as an ordinary arithmetical one. But the Gödel sentence is of a very specific nature. Consequently, the non-standard arguments are conceptually mistaken. In this paper, both the faulty arguments themselves and the general reasons underlying their failure are analysed. The analysis reveals the true nature of the epistemological relation between the Gödel sentence and its numerical instances.