Principles of Truth

The second edition is now available as a paperback edition. See Ontos Verlag.

The volume is published by Ontos Verlag in the series Epistemische Studien and it is edited by Volker Halbach and Leon Horsten. The series editors are Michael Esfeld, Stephan Hartmann and Mike Sandbothe. It has appeared in June 2002.

Reviews

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Content

Volker Halbach and Leon Horsten: Contemporary Methods for Investigating the Concept of Truth - An Introduction

The Discussion about Deflationism

John Burgess: Is there a Problem about Deflationary Theories of Truth?

Paul Horwich: A Defense of Deflationism

Volker Halbach: Modalized Disquotationlism

Stewart Shapiro: Deflation and Conservation

Semantic Approaches to Truth

Hannes Leitgeb: Metaworlds: A Possible Worlds Semantics of Truth

Vann McGee: Ramsey and the Correspondence Theory

Axiomatic Approaches to Truth and Intensionality

Michael Sheard: Provability, Truth, and Naive Criteria

Andrea Cantini: Partial Truth

Leon Horsten: An Axiomatic Investigation of Provability as a Primitive Predicate


Overview

The discussion about deflationism
Burgess in his contribution explores the question how the deflationist position should be best formulated. He discusses seven alternative formulations, and argues that one of them is preferable over the others. He ends his paper on a somewhat disquieting note, by concluding that deflationism must presuppose that an account of the notion of assertion can be given which does not use the notion of truth.

Horwich (Truth 1990) has in earlier influential work developed a detailed articulation of one particular deflationist position: the so-called minimalist view of truth. This sparked a renewed interest in deflationism about truth, and generated numerous reactions. In his contribution to the present volume, Horwich recapitulates central tenets of his minimalist view, and responds to nine objections against minimalism.

We have seen that one problem problem for deflationism and disquotationalism is the deductive weakness of the T-sentences. They do not allow for proofs of certain generalizations; for instance, they do not prove that a conjunction is true if both conjuncts are true. Halbach proposes a disquotationalist theory of truth that overcomes this defect. Central to his a approach his the formalization of the deflationist doctrine that the T-sentences are in some sense necessary. This theory is highly nonconservative over the underlying arithmetical theory: it turns out to be proof-theoretically as strong as the system KF.

Shapiro continues in his contribution he discussion he initiated in the Journal of Philosophy 1998. This discussion is about whether the deflationist’s axioms for truth ought to be conservative and whether a non-effective consequences relation involving second-order logic, the omega-rule and the like can help the deflationist to save the conservativeness of an adequate truth theory. Shapiro reviews the state of the discussion and responds to objections by Field (Journal of Philosophy 1999), Azzouni (Journal of Philosophy 1999), Tennant and Halbach (Synthese 2000) who have rejected Shapiro’s criticism of deflationism or his suggestions for amending the deflationist’s theory of truth.

Semantic approaches to truth
Leitgeb in his contribution formulates a new semantic approach to truth and the paradoxes. Borrowing ideas from modal logic, he develops a possible worlds semantics for the notion of truth. The general idea is, roughly, that the semantic value of a formula of the form T(A) is determined by the value of the formula A in the possible worlds to which it is related. Intriguingly, the frames of the models that result are frames that are familiar from temporal logic.

McGee is concerned with a question which originates in work of Field (Journal of Philosophy 1972): how do our linguistic practices fix the reference of names and the satisfaction relation for simple formulas? McGee’s answer is that names and nonlogical predicates are to be `analysed away’ in a Ramseyan fashion. He shows how this solution proposal can also be presented in terms of the original, but since then superseded, Tarskian consequence relation. This proposal naturally gives rise to a supervaluation-like stance with respect to the semantic paradoxes. McGee has thereby provided a motivation for the supervaluation approach, which hitherto always had an air of ad hoc-ness to it.

Axiomatic approaches to truth and intensionality
Sheard’s contribution actually concerns both axiomatic and semantic approaches to truth. From common usages of the notion of truth by the speech community, he abstracts six global features which he argues to be desirable for a theory of truth to have. He investigates to what extent the major axiomatic and semantic theories of truth to date possess these desiderata.

Cantini in his contribution gives an overview of what is known about the Kripke-Feferman system and variants of it, and adds some new results. In particular, he investigates the truth systems that result when the Kripke-Feferman truth axioms are added to weaker background theories (such as intuitionistic arithmetic, linear logic) than full classical Peano Arithmetic.

There are intriguing connections between truth and the notions that are investigated in intensional logic, such as necessity, past / future, knowability. Results by Kaplan and Montague show that if modal and modal-epistemological notions are treated as predicates in a straightforward and seemingly natural axiomatic manner, liar-like diagonal arguments yield contradictions. In sum, intensional notions appear to be paradoxical in ways that are eerily similar to the way in which truth is paradoxical. The paper by Horsten in this volume attempts to explore the underlying connection between the semantical paradoxes and the intensional paradoxes. Also, this paper aims to contribute to the task of developing consistent and somehow reasonable axiomatic systems concerning intensional notions (such as knowability).

Nevertheless, it must be admitted that at present the connections between truth and the intensional notions are ill-understood. This whole area is in an unsatisfactory state. First, the claim that truth is a logico-mathematical (and not a properly philosophical) notion seems somewhat endangered by the fact that the intensional notions, which are semantically somehow intimately related to truth, are indeed properly philosophical notions. Second, one wonders why it is that the structures familiar from temporal logic come to the fore in Leitgeb’s possible worlds semantics for truth. Third, the consistent axiomatic theories for the intentional notions at present cannot rival those for truth in naturalness and elegance. This appears to be mainly due to the fact that in contrast with the situation for truth, illuminating semantical approaches to intensional notions treated as a predicate have been lacking. We have been lacking semantical guidance in our attempts to construct interesting axiomatic systems concerning intensional notions.

Volker Halbach & Leon Horsten

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