Subtle Truths. A formal investigation into Deflationism and Conservativeness

Dissertation, University of Torino - Italy (2010)

Andrea Strollo
NanJing University
At the end of the nineties some authors (Leon Horsten, Stewart Shapiro and Jeffrey Ketland) worked out a fairly technical argument against deflationary theories of truth. In a nutshell, deflationism, it was argued, is committed to conservativeness by the the claim that truth is not a substantial notion, a conservative theory (under the light of certain logico-mathematical facts) can not be an adequate theory of truth, therefore deflationism is an inadequate theory of truth. Beside the apparent simplicity of this argument, it hides a lot of subtle questions and problems and it is a very sophisticated argument. Deflationists attempted to reply in different ways to the argument but the general impression is that, so far, they have not been able to find a good solution. Deflationism does really seem to be condemned to be an inadequate theory. This work is divided in three main parts. The first part is a very general survey where the study of the notion of truth is introduced. In Chapter One we sketch philosophical theories of truth comparing more traditional approaches to deflationism; we briefly survey the history of deflationism and then we try to find a general characterization of it. In the second Chapter the notion of truth is considered under a formal approach and some important and simple axiomatic theories of truth are sketched. The second part join the philosophical and the formal approach to truth together into the debate over deflationism and conservativeness. In Chapter Three we introduce the notion of conservativeness and we give some example of its application both to logical and to philosophical matters. Then we spell out the argument from conservativeness and we discuss it in order to get a precise requirement that deflationary theories are supposed to satisfy. In Chapter Four we focus on deflationist replies to the argument from conservativeness and we discuss each solution. The third and last part is the core of the work, it consists in a more technical study of some presuppositions of the debate: we want to take a step backward and to compare the two major claims of deflationism - the centrality of T-sentences and the logical function of the truth predicate - with conservativeness. Many of the results used here are due to other logicians and philosophers and are available in literature yet, the originality consists in a critical consideration of such results under the light of the conservativeness of truth. More original reflections can be found in Chapter Seven and in particular in the conclusive Chapter Eight, where the proposal is completely new, at least as far as I know. In Chapter Five we compare T-sentences with the empty base theory and in Chapter Six we analyse in what measure a deflationary theory can be really conservative over a theory of syntax. The result would be quite serious for a deflationist. In Chapter Seven we compare conservativeness with the logical function of the truth predicate. We will get the unpleasant result that the truth predicate is not able to serve the logical function in no sense without loosing conservativeness at the same time. In Chapter Eight we draw some conclusion and we sketch a reformulation of the conservativeness requirement. This new requirement, we will argue, makes justice to the claim of the unsubstantiality of truth and at the same time it does not condemn deflationism to death. In this way, we will be able also to clarify what is the exact role of truth in sentential quantification, showing that this role is really innocent and unsubstantial. The unsubstantiality of deflationary truth, though, will not force deflationism into an inadequate theory of truth.
Keywords Deflationism  Truth  Conservativity
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