# Dr. Volker Halbach

Philosophie.Forschung.Abgeschlossene Projekte.Habilitationen.PD Dr. Volker Halbach**Overview**

**Table of Contents**

**Summary by Chapters**

**In this book a develop a deflationist approach to semantics where truth and
reference are treated as logico-mathematical notions.**

**
Overview
**In this essay I present and defend a deflationist theory of the semantical concepts
of reference, truth and satisfaction. The theory is deflationist because it treats
these semantical concepts as logico-mathematical notions. Certain ‘substantial’
semantical concepts—such as the notion of reference in the causal-historical
theory of reference—are defined in terms of deflationary semantical concepts. In
this sense the proposed theory is deflationary. However, the semantical notions
are shown to be indispensable in our reasoning, contrary to the claim of some
deflationists.

Table of Contents

(links to the Summaries)

**1 Introduction **

1.1 The project

1.2 Definitions and Axiomatizations

1.3 To what category do objects belong which can be true?

1.4 A Sketch of Modalized Disquotationalism

**2 The History of Disquotationalism and Deflationism**

2.1 Frege

2.2 Ramsey

2.3 Tarski

2.4 Strawson

2.5 Ayer

2.6 Quine

2.7 Williams

2.8 The Prosentential Theory

2.9 Horwich

2.10 Field

2.11 Summary

**3 Material Disquotationalism **

3.1 The Status of the Disquotation Sentences

3.2 Proving Infinite Conjunctions

3.3 Expressing Infinite Conjunctions

3.4 The Adequacy of Material Disquotationalism

3.5 The Failure of Material Disquotationalism

**4 Modalized Disquotationalism **

4.1 Truth Analyticity

4.2 Reference and Satisfaction

4.3 The Challenge by Substantial Theories

5 Refinements

5.1 Truth in Foreign Languages?

5.2 Shapiro’s Puzzle

5.3 Indexicals, Demonstratives and Time

5.4 Paradox

6 Lewys Argument

6.1 The History of Lewy’s Argument

6.2 Consequences of Lewy’s Argument

6.3 The Propositionalist Response

6.4 Modalized Disquotationalism and Propositionalism

7 Deflationism and Conservativeness

7.1 Conservativeness: Terminology and Basic Considerations

7.2 The Commitments of Deflationism

7.3 The Innocence of Deflationist Truth

8 Technical Appendix

8.1 Notation and Technical Preliminaries

8.2 The Disquotation Sentences

8.3 Satisfaction Classes

8.4 T-Analyticity

8.5 Typed Disquotation

8.6 Untyped Disquotation

8.7 Interpretation of AT+ in KF

8.8 Interpretation of KF in AT+

8.9 Some Corollaries

8.10 Open Questions: Conservativeness

##### Summary by Chapters

**1 Introduction**

The main objective of the essay is an analysis of philosophical
uses of the notions of reference, truth and satisfaction. It is argued that, given
these objectives, only axiomatizations of these notions are feasible, but not explicit
definitions. Truth is primarily attributed to types of sentences, satisfaction is a
relation holding between formulas and strings of objects, and reference is a relation between singular terms and objects. A sketch of my version of deflationism,
Modalized Disquotationalism, concludes the chapter.

2 The History of Disquotationalism and Deflationism

This chapter surveys the main positions that have contributed to the emergence of modern deflationism. In particular, views by Frege, Ramsey, Tarski, Strawson, Ayer, Quine, Williams, Grover, Horwich and Field are outlined and discussed.

3 Material Disquotationalism

Disquotationalism maintains that truth is only a
device of disquotation and that therefore the disquotation sentences are of central
importance in the theory of truth. In particular, Material Disquotationalism is the
doctrine that the disquotation sentences
“A” is true if and only if
A govern the use of the truth predicate. The only purpose of the truth predicate is
the expression of infinite conjunctions and disjunctions. It is shown in what sense
a truth predicate axiomatized by the disquotation sentences can express infinite
conjunctions and disjunctions. However, Material Disquotationalism is rejected
because it does not allow for proofs of generalizations that ought to be provable
in an adequate theory of truth.

4 Modalized Disquotationalism

In contrast to Material Disquotationalism, the
modalized version pays attention to the modal status of the disquotation sentences.
According Modalized Disquotationalism, the disquotation sentences are
analytic in the truth predicate. Thus the disquotation sentences constitute the
meaning postulates for truth. Analogous points can be made for reference and
satisfaction. The problems of analyticity are discussed and it is shown that analyticity in the truth (reference, satisfaction) predicate is not subjected to the same difficulties as the general notion of analyticity. Modalized Disquotationalism overcomes the problems of Material Disquotationalism because the generalizations that are not provable in the theory of Material Disquotationalism are provable in the theory of Modalized Disquotationalism. This increase of deductive power is obtained via the analysis of analyticity.

5 Refinements

Disquotation applies only to expressions one understands. Thus
the notions of reference, truth and satisfaction apply only to expressions of one’s
own language. However, Modalized Disquotationalism can deal with expressions
of foreign languages by invoking translations (in one’s own language). For instance, a singular term of a foreign language refers to an object a if and only if its translation refers to a in the sense of disquotationalism. The required notion of translation is not irreducibly semantical but can be explained in naturalistic terms along the lines proposed by Quine. Thus no new genuinely semantical notions are introduced beyond the logico-mathematical notions of reference, truth and satisfaction. According to an argument by Shapiro, some sentences do not have translations. Thus Modalized Disquotationalism cannot ascribe truth to them. Shapiro concludes that the disquotational theory of truth does not suffice and a substantial non-disquotational truth predicate is indispensable. I show why this argument fails. Using translations further well-known problems of disquotationalism can be solved. In particular, the problems arising from indexicals, demonstratives and similar context-sensitive devices can be dealt with in this way.

**
6 Lewy’s Argument
**Modalized Disquotationalism is based on the claim that the disquotation sentences and analogous principles for satisfaction and reference are in some sense analytic. Arguments put forward by Lewy and many other philosophers purport to show that these principles fail to be analytic (and a priori and necessary) in any sense. According to their view, truth, satisfaction and reference obtain always contingently on our linguistic conventions. The general validity of Lewy’s argument would violate some basic intuitions. For instance, no sentences would be analytically (or necessarily) true. It has been proposed to avoid these problems by ascribing truth and satisfaction to propositions and relations rather than sentences and formulas. I show that this proposal has certain drawbacks. I propose my own solution of Lewy’s puzzle by invoking translations again.

7 Deflationism and Conservativeness

7 Deflationism and Conservativeness

It is investigated in what sense Modalized Disquotationalism may be called a deflationary theory of reference, truth and satisfaction. I show that no theory of truth (even Material Disquotationalism) is not neutral with respect to non-semantical questions. Thus if deflationism implies that semantics has to be neutral with respect to ‘substantial’ (i.e., non-semantical) questions, then deflationism fails. However, Modalized Disquotationalism is deflationary in the sense that it reduces semantics to logico-mathematical notions (reference, satisfaction and truth) and unproblematic naturalistic terms.

8 Technical Appendix

8 Technical Appendix

Some logical features of Modalized Disquotationalism is studied in a formally precise setting.

Some chapters and sections are based on papers that have been published previously. However, all papers have been modified.

Some chapters and sections are based on papers that have been published previously. However, all papers have been modified.

- Chapter 3 is based on ”‘Disquotationalism and Infinite Conjunctions”’, Mind 108, 1999, 1–22.
- Section 4.1 is based on ”‘Disquotationalism Fortified”’, in Circularity, Definitions, and Truth, Anil Gupta and Andr´e Chapuis (eds.), Indian Council of Philosophical Research, New Dehli, 2000, 155–176.
- Chapter 7 is based on ”‘How Innocent is Deflationism?”’, Synthese 126, 2001, 167–194.
- Chapter 8 is based on ”‘Disquotational Truth and Analyticity”’, to appear in The Journal of Symbolic Logic.