On interpreting Chaitin's incompleteness theorem

Journal of Philosophical Logic 27 (6):569-586 (1998)
Download Edit this record How to cite View on PhilPapers
The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental
Reprint years
PhilPapers/Archive ID
Revision history
Archival date: 2017-04-11
View upload history
References found in this work BETA
Computability and Logic.Boolos, George; Burgess, John; P., Richard & Jeffrey, C.
Computability and Logic.Boolos, George S.; Burgess, John P. & Jeffrey, Richard C.
Mathematical Logic.Shoenfield, Joseph R.

View all 15 references / Add more references

Citations of this work BETA
Propagation of Partial Randomness.Higuchi, Kojiro; Hudelson, W. M. Phillip; Simpson, Stephen G. & Yokoyama, Keita
Exploring Randomness.Raatikainen, Panu

View all 8 citations / Add more citations

Added to PP index

Total views
403 ( #9,948 of 47,363 )

Recent downloads (6 months)
45 ( #17,790 of 47,363 )

How can I increase my downloads?

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