Truth without standard models: some conceptual problems reloaded

A theory of truth is usually demanded to be consistent, but w -consistency is less frequently requested. Recently, Yatabe has argued in favour of w-inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against w-inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known w-inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth based on ᴌukasiewicz infinitely valued logic: PAᴌT.Fil: Barrio, Eduardo Alejandro. Instituto de Investigaciones Filosóficas - Sadaf; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Da Ré, Bruno. Instituto de Investigaciones Filosóficas - Sadaf; Argentin

Modality and Axiomatic Theories of Truth I: Friedman-Sheard

In this investigation we explore a general strategy for constructing modal theories where the modal notion is conceived as a predicate. The idea of this strategy is to develop modal theories over axiomatic theories of truth. In this first paper of our two part investigation we develop the general strategy and then apply it to the axiomatic theory of truth Friedman-Sheard. We thereby obtain the theory Modal Friedman-Sheard. The theory Modal Friedman-Sheard is then discussed from three different perspectives. First, we show that Modal Friedman-Sheard preserves theoremhood modulo translation with respect to modal operator logic. Second, we turn to semantic aspects and develop a modal semantics for the newly developed theory. Third, we investigate whether the modal predicate of Modal Friedman-Sheard can be understood along the lines of a proposal of Kripke, namely as a truth predicate modified by a modal operator

THE MATHEMATICS OF DEFLATIONARY TRUTH

Analytic conceptions of truth can be broadly classified along two lines, depending on how they answer the following two questions: 1. Has truth a substantial nature? 2. How many properties of truth are there? Traditional views, like correspondence, coherence, pragmatist views all answer “yes” to both questions. The second half of the last century and the last decades in particular, however, has witnessed the rapid growth in popularity of conceptions of truth answering “no” to at least one. Pluralist views hold that there is more than one property of truth, whereas deflationary views hold that truth lacks a substantial nature. Pluralist and deflationary views are today the main rivals in the field. This book focuses on deflationary views of truth and contributes to the general contemporary debate on truth by addressing an issue emerging from an appealing way to clarify what the insubstantiality o f (deflationary) t ruth might amount to: conservativeness

Strong and Weak Truth Principles

Niniejsza praca stanowi przegląd niedawnych wyników, zarówno opublikowanych, jak i jeszcze czekających na publikację, dotyczących różnych pojęć słabości i siły pojęcia prawdy, a także próbę ich systematyzacji i ukazania na tle szerszego nurtu badań. Omawiamy pojęcie granicy Tarskiego oddzielającej słabe i silne teorie prawdy. Omawiamy znane twierdzenia dotyczące niekonserwatywnych rozszerzeń podstawowej kompozycyjnej teorii prawdy oraz opisujemy pewną naturalną silną teorię prawdy, którą można scharakteryzować wieloma pozornie ze sobą niezwiązanymi układami aksjomatów. Na koniec przytaczamy inne możliwe eksplikacje pojęcia „siły” aksjomatycznych teorii prawdy.This paper is an exposition of some recent results concerning various notions of strength and weakness of the concept of truth, both published and not. We try to systematically present these notions and their relationship to the current research on truth. We discuss the concept of Tarski’s 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 truth, which admits a number of apparently unrelated axiomatisations. Finally, we discuss other possible explications for the notion of ‘strength’ in axiomatic theories of truth