A theory of truth / Yannis Stephanou.

Format:

Book

Author/Creator:

Stephanou, Yannis, author.

Series:

Lecture notes in logic ; 55.

Lecture notes in logic ; 55

Language:

English

Subjects (All):

Logic.

Truth.

Physical Description:

1 online resource (xi, 345 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2024.

Summary:

How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical logic significantly, and endorses principles like 'No sentence is both true and false' and 'No sentence is neither true nor false'. The book starts with an introduction to the paradoxes, suitable for newcomers to the subject, before presenting its approach. Four versions of the theory are covered, extending the theory to a determinacy operator and to a full first-order language with quantifiers. Each includes all Tarskian biconditionals that can be formulated in its language. The author uses original methods to prove the consistency of each version and compares the theory to alternative non-classical theories, including Field's paracomplete approach, Ripley's nontransitive system and Zardini's contraction-free calculus.

Contents:

Cover

Half-title

Series information

Title page

Imprints page

Contents

Preface

Chapter 1 Aspects of paradox

1.1. The liar and its variants

1.2. Propositions and truth-values

1.2.1. No proposition expressed

1.2.2. Lack of truth-value

1.3. The problem in a formal setting

1.4. Tarski and Kripke

1.5. The project

Chapter 2 Against classical logic

2.1. Different treatments of the paradoxes

2.2. The first argument against classical logic

2.3. The second argument against classical logic

2.4. Variants of the arguments

2.4.1. No set of truths

2.4.2. Another paradox?

2.4.3. Propositions again

2.4.4. Quantifying into quotation

Chapter 3 Ambiguity and indexicality

3.1. Ambiguity

3.1.1. The Tarskian hierarchy again

3.1.2. Shifts of meaning

3.2. How well motivated is the contextual approach to the liar?

3.2.1. The three-stage reasoning about sentence-types

3.2.2. The three-stage reasoning about sentence-tokens

Chapter 4 A propositional theory of truth

4.1. What kind of logic?

4.1.1. Avoiding contradiction

4.1.2. Espousing and abandoning principles

4.1.3. Avoiding substructuralism

4.2. A propositional logic

4.3. The theory of truth

4.4. Strengthening the logic

Chapter 5 Proving central theorem 1

5.1. Preliminaries

5.1.1. Appropriate classes

5.1.2. C-insertable classes

5.1.3. The rule (Con)

5.1.4. Extending a class

5.2. Two theorems

5.3. Proof of Central Theorem 1

5.4. Concluding remarks

Chapter 6 Truth and determinacy

6.1. The concept of determinacy

6.2. A logic of determinacy

6.3. A theory of truth with the determinacy operator

6.4. Proving Central Theorems 2 and 3

6.4.1. Central Theorem 2

6.4.2. Central Theorem 3.

6.5. Trying to explain the failure of classical logic.

Chapter 7 A first-order logic and theory of truth

7.1. The logic

7.1.1. What kind of first-order logic?

7.1.2. Adorned wffs, frames and codesignation

7.1.3. Models[sub(∗)] and models

7.1.4. Validities and invalidities

7.2. A first-order theory of truth

Chapter 8 Proving central theorem 4

8.1. A problem

8.2. Preliminaries

8.2.1. C-implying and C-equivalence

8.2.2. Acceptable adorned conditionals

8.2.3. The rules (Con) and (Uni)

8.2.4. Extensions

8.3. Two theorems again

8.4. Parallel formulae

8.5. Constructing a sequence of models

8.6. Reaching Central Theorem 4

Chapter 9 Another first-order theory of truth

9.1. Syntax and arithmetic

9.2. A new language

9.3. Syntactic definitions

9.4. The new theory of truth

9.5. Proving Central Theorem 5

Chapter 10 Truth in different non-classical logics

10.1. Field saving truth

10.1.1. Revising Kripke

10.1.2. Substitution of equivalents and the law of non-contradiction

10.1.3. Other differences from Field

10.2. Tennant's core logic

10.3. Zardini's substructuralism

10.4. And Ripley's substructuralism

Afterword

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 09 Oct 2023).

Other Format:

Print version:

ISBN:

9781009437141 (ebook)

Access Restriction:

Restricted for use by site license.