What does gödel's second theorem say

Philosophia Mathematica 9 (1):37-71 (2001)

Michael Detlefsen
University of Notre Dame
We consider a seemingly popular justification (we call it the Re-flexivity Defense) for the third derivability condition of the Hilbert-Bernays-Löb generalization of Godel's Second Incompleteness Theorem (G2). We argue that (i) in certain settings (rouglily, those where the representing theory of an arithmetization is allowed to be a proper subtheory of the represented theory), use of the Reflexivity Defense to justify the tliird condition induces a fourth condition, and that (ii) the justification of this fourth condition faces serious obstacles. We conclude that, in the types of settings mentioned, the Reflexivity Defense does not justify the usual ‘reading’ of G2—namely, that the consistency of the represented theory is not provable in the representing theory.
Keywords Gödel  Gödel's incompleteness theorems  Gödel's second incompleteness theorem  Hilbert-Bernays derivability conditions  Löb's derivability conditions  representing metamathematical notions
Categories (categorize this paper)
DOI 10.1093/philmat/9.1.37
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,878
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
2004 Summer Meeting of the Association for Symbolic Logic.Wolfram Pohlers - 2005 - Bulletin of Symbolic Logic 11 (2):249-312.

Add more citations

Similar books and articles


Added to PP index

Total views
110 ( #62,331 of 2,319,040 )

Recent downloads (6 months)
18 ( #35,693 of 2,319,040 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature