Citations of:
Add citations
You must login to add citations.


This paper is an exposition of some recent results concerning various notions of strength and weakness of the concept of truth, both published or not. We try to systematically present these notions and their relationship to the current research on truth. We discuss the concept of the Tarski boundary between weak and strong theories of truth and we give an overview of nonconservativity results for the extensions of the basic compositional truth theory. Additionally, we present a natural strong theory of (...) 

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over (...) 

We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic. 

One of the popular explications of the deflationary tenet of ‘thinness’ of truth is the conservativeness demand: the declaration that a deflationary truth theory should be conservative over its base. This paper contains a critical discussion and assessment of this demand. We ask and answer the question of whether conservativity forms a part of deflationary doctrines. 

Deflationists argue that ‘true’ is merely a logicolinguistic device for expressing blind ascriptions and infinite generalisations. For this reason, some authors have argued that deflationary truth must be conservative, i.e. that a deflationary theory of truth for a theory S must not entail sentences in S’s language that are not already entailed by S. However, it has been forcefully argued that any adequate theory of truth for S must be nonconservative and that, for this reason, truth cannot be deflationary :493–521, (...) 

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with wellestablished positions (...) 



In the paper we investigate typed axiomatizations of the truth predicate in which the axioms of truth come with a builtin, minimal and selfsufficient machinery to talk about syntactic aspects of an arbitrary base theory. Expanding previous works of the author and building on recent works of Albert Visser and Richard Heck, we give a precise characterization of these systems by investigating the strict relationships occurring between them, arithmetized model constructions in weak arithmetical systems and suitable set existence axioms. The (...) 

In recent decades deflationary theories of truth have been challenged with a technical argument based on the notion of conservativeness. In this paper, I shall stress that conservative extensions of theories and expandability of their models are not equivalent notions. Then, I shall argue that the deflationary thesis of the unsubstantiality of truth is better understood as leveraging on the stronger notion of expandability of models. Once expandability is involved in the argument, some notable consequences follow: the strategy proposed by (...) 

The existence of a close connection between results on axiomatic truth and the analysis of truththeoretic deflationism is nowadays widely recognized. The first attempt to make such link precise can be traced back to the socalled conservativeness argument due to Leon Horsten, Stewart Shapiro and Jeffrey Ketland: by employing standard Gödelian phenomena, they concluded that deflationism is untenable as any adequate theory of truth leads to consequences that were not achievable by the base theory alone. In the paper I highlight, (...) 

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pretheoretical or to a semiformal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of intertheoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated (...) 

Definitional and axiomatic theories of truth  Objects of truth  Tarski  Truth and set theory  Technical preliminaries  Comparing axiomatic theories of truth  Disquotation  Classical compositional truth  Hierarchies  Typed and typefree theories of truth  Reasons against typing  Axioms and rules  Axioms for typefree truth  Classical symmetric truth  KripkeFeferman  Axiomatizing Kripke's theory in partial logic  Grounded truth  Alternative evaluation schemata  Disquotation  Classical logic  Deflationism (...) 