On the Explanatory Role of Correspondence Truth

An intuitive argument for scientific realism suggests that our successes in predicting and intervening would be inexplicable if the theories that generate them were not approximately true. This argument faces many objections, some of which are briefly addressed in this paper, and one of which is treated in more detail. The focal criticism alleges that appeals to success cannot deliver conclusions that parts of science are true in the sense of truth-as-correspondence that realists prefer. The paper responds to that criticism, in versions proposed by Michael Williams, Michael Levin, and, especially, Paul Horwich, by arguing that critics typically stop at a shallow level of psychological explanation. If we probe more deeply we discover a genuine explanatory role for correspondence truth.     

On Interpreting Chaitin's Incompleteness Theorem

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.     

Correspondence

The American Journal of Psychoanalysis -