Deflationism and The Gödel Phenomena - Reply to Tennant Jeffrey Ketland 1. Introduction Neil Tennant (Tennant 2002) has recently replied to an argument given by Stewart Shapiro (Shapiro 1998) and myself (Ketland 1999) concerning the incompatibility of the deflationary conception of truth with the Gödelian incompleteness phenomena in mathematics. Call this argument the Reflection Argument, since it turns on the truth- theoretic justification of reflection principles. 1 The Reflection Argument concerns the substantiality of the notion of truth. To introduce the idea, consider the soundness statement, All theorems of Peano arithmetic (PA) are true. By Gödel’s Second Incompleteness Theorem, this single statement is deductively stronger than the whole theory PA, at least if PA is consistent. For PA does not imply the consistency statement Con(PA), while the soundness statement ‘All theorems of PA are true’ does imply Con(PA) (modulo disquotation axioms for truth). But surely if we accept PA and we also grasp the notion of truth, we see that we should accept ‘All theorems of PA are true’. This shows that accepting the axioms and rules (and thus theorems) of PA is logically weaker than accepting ‘All theorems of PA are true’. There is a logical difference between accepting each theorem of PA and accepting the single reflective proposition that each theorem of PA is true. 2. The Reflection Argument In order to answer Tennant’s reply, it is necessary to rehearse in detail the arguments given by Shapiro and myself. The reason is that Tennant misconstrues the central points of the argument that Shapiro and I gave. Tennant introduces a so-called ‘semantical argument’, and in this connection he cites Kleene, Dummett and others. It should be stressed that this ‘semantical argument’ is quite different from the arguments given by Shapiro and myself. Our argument concerned the justification of the reflective principle ‘All theorems of S are true’, given that one already accepts a mathematical theory S. It also concerns the consequent justification of weaker reflection principles of the form Prov S (  ϕ  ) → ϕ, given acceptance of S. Such principles are logical consequences of ‘All theorems of S are true’, given the disquotation scheme, and are a weaker way of expressing in the language of S that anything provable in S is true. Shapiro and I argue that the justification for reflection principles involves the notion of truth. Tennant, however, provides no response to this justification given by Shapiro and myself. Tennant seems, in part, to be worried that the global reflection principle ‘All theorems of S are true’ contains a truth predicate and a reflection principle like Prov S (  ϕ  ) → ϕ does not. It is hard to believe that this could be considered of significance, since we are concerned with the justification of these principles, and not their conceptual content. Of course, Prov S (  ϕ  ) → ϕ is equivalent to Prov S (  ϕ  ) → T(  ϕ  ), if we have a disquotational truth predicate. 1 Hartry Field in his interesting reply (Field 1999) to Shapiro calls it the ‘Conservativeness Argument’.