•  572
    How Tarski Defined the Undefinable
    European Review 23 (01). 2015.
    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.
  •  493
    We investigate the properties of Yablo sentences and for- mulas 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.
  •  463
    T-equivalences for positive sentences
    Review of Symbolic Logic 4 (2): 319-325. 2011.
    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.
  •  427
    Truth, Conservativeness, and Provability
    Mind 119 (474): 409-422. 2010.
    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 that the problems confronting the deflationist are in fact more basic: even the observation that logic is true is beyond his reach. This seems to confli…Read more
  •  399
    The Innocence of Truth
    Dialectica 69 (1): 61-85. 2015.
    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.
  •  371
    Deflationary Truth and Pathologies
    Journal of Philosophical Logic 39 (3): 325-337. 2010.
    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 deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt…Read more
  •  294
    Typed and Untyped Disquotational Truth
    In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth, Imprint: Springer. 2015.
    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.
  •  121
    Interpreting the compositional truth predicate in models of arithmetic
    Archive for Mathematical Logic 60 (6): 749-770. 2021.
    We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.
  •  107
    Gödelizing the Yablo Sequence
    Journal of Philosophical Logic 42 (5): 679-695. 2013.
    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, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivale…Read more
  •  104
    Deflationism, conservativeness and maximality
    Journal of Philosophical Logic 36 (6). 2007.
    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 however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that th…Read more
  •  64
    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 are crucial for understanding and evaluating the philosophical thesis of the innocence of truth. Providing an up-to-date discussion and original persp…Read more
  •  59
    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 altogether, replacing them with the epistemic notion of believability. The aim will be to explain why someone who accepts a given disquotational truth theory T…Read more
  •  45
    The paper contains a discussion of a basic difficulty encountered by adherents of the disquotational conception of truth. The problem is that the disquotational theory seems to weak to prove many important truth-theoretical generalizations, like e.g. "All substitutions of the law of excluded middle are true". Various ways of saving the disquotationalist from this objection are analyzed and deemed unsatisfactory
  •  38
    Heterologicality and Incompleteness
    Mathematical Logic Quarterly 48 (1): 105-110. 2002.
    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 to the consistency of T. Finally we show how to construct a similar incompleteness proof for Peano Arithmetic.
  •  31
    Löb's theorem in a set theoretical setting
    Studia Logica 75 (3). 2003.
    We present a semantic proof of Löb'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 semantically from T. Then we show that this sentence indeed follows from T and therefore is true.
  •  28
    Models of PT- with Internal Induction for Total Formulae
    with Bartosz Wcisło and Mateusz Łełyk
    Review of Symbolic Logic 10 (1): 187-202. 2017.
    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 in the philosophical project of describing the use of the truth predicate in model-theoretic contexts.
  •  26
    Axioms for Type-Free Subjective Probability
    with Leon Horsten and Hannes Leitgeb
    Review of Symbolic Logic 1-16. forthcoming.
    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 principles about type-free subjective probability.
  •  17
    The two halves of disjunctive correctness
    with Mateusz Łełyk and Bartosz Wcisło
    Journal of Mathematical Logic 23 (2). 2023.
    Ali Enayat had asked whether two halves of Disjunctive Correctness ([Formula: see text]) 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 the other hand, the converse implication “any disjunction with a true disjunct is true” can be conservatively added to [Formula: see…Read more
  •  7
    Paradoxes of Barbara Stanosz
    Studia Semiotyczne—English Supplement 29 48-61. 2017.
    Professor Barbara Stanosz was a years-long lecturer at the Institute of Philosophy, University of Warsaw. In her work she mainly – but not exclusively – focused on the theory of language, particularly semantics and the issues of logical description of phrases in language. She was an author of renowned textbooks, including the famous Ćwiczenia z logiki [Exercises in logic], a vastly popular exercise book helping students to acquire the material on propositional logic, predicate logic and set theo…Read more
  •  4
    Paradoksy Barbary Stanosz
    Studia Semiotyczne 28 (1): 51-62. 2015.
    Prof. Barbara Stanosz była wieloletnią wykładowczynią Instytutu Filozofii Uniwersytetu Warszawskiego. W swej pracy naukowej zajmowała się głównie – choć nie wyłącznie – teorią języka, w szczególności semantyką oraz problemami logicznego opisu wyrażeń językowych. Jest autorką cenionych podręczników: to właśnie jej zawdzięczamy słynne Ćwiczenia z logiki – cieszący się ogromną popularnością zbiór zadań, ułatwiających przyswojenie materiału z zakresu rachunku zdań, logiki predykatów i teorii zbiorów…Read more
  • Dlaczego prawda jest (nie)definiowalna
    Filozofia Nauki 1. 2005.
    The aim of this paper is to consider the question about the reasons of the indefinability of truth. We note at the start that a formula with one free variable can function as a truth predicate for a given set of sentences in two different (although related) senses: relative to a model and relative to a theory. By methods due to Alfred Tarski it can be shown that some sets of sentences are too large to admit a truth predicate (in any of the above senses); the limit case being the set of all sente…Read more
  • Arytmetyka i intensjonalność
    Filozofia Nauki 4. 2001.
    The paper consists of two pats. The first part contains a critical review of "Gödel theorems, possible worlds and intensionality" by W. Krysztofiak. Krysztofiak argues that Gödel's incompleteness theorem and, in particular, the technique of aritmetization of syntax, gives rise to intensionality and intentionality in arithmetic. The author tries to show that these claims are mistaken and based on a simple misunderstanding of the incompleteness theorem and its proof. In the second part the author …Read more