Cezary Cieśliński

• University of Warsaw

We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principle...

Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that the principle “every true disjunction has a true disjunct” is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On...

We formulate and explore two basic axiomatic systems of typefree subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles...

Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic. In this article, we show that the principle "every true disjunction has a true disjunct" is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On th...

We compare the conceptual strength of two axiomatic theories of truth: KF and WKF. The first one has been designed to capture Kripke's fixed-point construction based on Strong Kleene logic. The second one is based on the Weak Kleene evaluation schema. In the paper "Relative truth definability of axiomatic truth theories", Kentaro Fujimoto proved th...

Disquotational theories of truth are often criticised for being too weak to prove interesting generalisations about truth. In this paper we will propose a certain formal theory to serve as a framework for a solution of the generalisation problem. In contrast with Horwich’s original proposal, our framework will eschew psychological notions altogethe...

This book analyses and defends the deflationist claim that there is nothing deep about our notion of truth. According to this view, truth is a 'light' and innocent concept, devoid of any essence which could be revealed by scientific inquiry. Cezary Cieśliński considers this claim in light of recent formal results on axiomatic truth theories, which...

We show that a typed compositional theory of positive truth with internal induction for total formulae (denoted by PT tot ) is not semantically conservative over Peano arithmetic. In addition, we observe that the class of models of PA expandable to models of PT tot contains every recursively saturated model of arithmetic. Our results point to a gap...

According to Paul Horwich, all the facts about truth can be explained on the basis of the so-called "minimal theory" (MT), whose axioms are purely disquotational: all of them are substitutions of Tarski's schema "p" is true if and only if p". It has been observed that Horwich's MT is too weak to prove generalizations like "For every phi, the negati...

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...

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 defl...

This paper describes Tarski’s project of rehabilitating the notion of truth, previously considered dubious by many philosophers. The project was realized by providing a formal truth definition, which does not employ any problematic concept. How to Cite This Article Link to This Abstract Blog This Article Copy and paste this link Highlight all...

We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions...

We investigate the properties of Yablo sentences and formulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

Conservativeness has been proposed as an important requirement for deflationary truth theories. This in turn gave rise to the so-called ‘conservativeness argument’ against deflationism: a theory of truth which is conservative over its base theory S cannot be adequate, because it cannot prove that all theorems of S are true. In this paper we show th...

By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a defl...

Conservativeness has been proposed as an important requirement for deflationary truth theories. This in turn gave rise to the so-called 'conservativeness argument' against deflationism: a theory of truth which is conservative over its base theory S cannot be adequate, because it cannot prove that all theorems of S are true. In this paper we show th...

We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory – a theory which is conservative over its base, but can’t be enlarged any further without losing its conservative character. There are indeed such theories; we show how...

We present a semantic proof of Lb's theorem for theories T containing ZF. Without using the diagonalization lemma, we construct a sentence AUT T, which says intuitively that the predicate autological with respect to T (i.e. applying to itself in every model of T) is itself autological with respect to T. In effect, the sentence AUT T states I follow...

We present a semantic proof of Gödel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate “heterological” is itself heterological. We show that this sentence doesn't follow from T and is equivalent (provably in...

We present a semantic proof of Gödel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate "heterological" is itself heterological. We show that this sentence doesn't follow from T and is equivalent (provably in...

1. Dyskwotacyjna teoria prawdy. Celem artykułu jest omówienie podstawowej trudności, na jaką natrafia tzw. dyskwotacyjna teoria prawdy – koncepcja często omawiana we współczesnych filozoficznych debatach. W zwięzłym sformułowaniu, trudność polega na tym, że dyskwotacyjna teoria wydaje się za słaba, aby w jej ramach można było dowieść wielu ważnych...