Zeno's paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno's paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study (...) of certain principles of self-referential truth. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

In this sequel toSelf-reference in arithmetic Iwe continue our discussion of the question: What does it mean for a sentence of arithmetic to ascribe to itself a property? We investigate how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed point for the expressing formulae are obtained. In this second part we look at some further examples. In particular, we study sentences apparently expressing their Rosser-provability, their own${\rm{\Sigma (...) }}_n^0$-truth or their own${\rm{\Pi }}_n^0$-truth. Finally we offer an assessment of the results of both papers. (shrink)

This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...

Summary This paper is intended to discuss the problems occurring in the relation between the notion of truth and the question of self-reference. To do this, we shall review Tarski's (T) convention and its related terminology. We shall clarify the relation between truth and extension in order to lead into the question of semantic paradoxes appearing in the theoretical models concerned with truth. Subsequently, we shall review the logical system which develops in the reformulation of the modal proposal of the (...) (T) convention. In closing, we shall critically examine Kripke's interpretation from the proposals made by Tarski. (shrink)

We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.

In diesem Aufsatz wird ein neues Paradoxon vorgestellt, der Super-Lügner. Er ist stärker als alle bekannten Lügner-Sätze, nicht mehr eindeutig selbstreferentiell und läßt sich darüber hinaus in eindeutig in die Tarski-Hierarchie einordnen. Eine unendlich große Familie von Super-Lügnern auf Metaebenen ist konstruierbar. Schließlich widersetzt sich der Super-Lügner der Auflösung durch die neue vielversprechende Reflexionslogik LR von U. Blau.

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (shrink)