Book contents
- Frontmatter
- Contents
- Introduction
- 1 Russell's Version of the Theory of Definite Descriptions
- 2 Existential Import, ‘E!’ and ‘The’
- 3 The Reduction of Two Paradoxes and the Significance Thereof
- 4 The Hilbert-Bernays Theory of Definite Descriptions
- 5 Foundations of the Hierarchy of Positive Free Definite Description Theories
- 6 Predication and Extensionality
- 7 Nonextensionality
- 8 The Philosophical Foundations of Free Logic
- 9 Logical Truth and Microphysics
7 - Nonextensionality
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Introduction
- 1 Russell's Version of the Theory of Definite Descriptions
- 2 Existential Import, ‘E!’ and ‘The’
- 3 The Reduction of Two Paradoxes and the Significance Thereof
- 4 The Hilbert-Bernays Theory of Definite Descriptions
- 5 Foundations of the Hierarchy of Positive Free Definite Description Theories
- 6 Predication and Extensionality
- 7 Nonextensionality
- 8 The Philosophical Foundations of Free Logic
- 9 Logical Truth and Microphysics
Summary
INTRODUCTION
Consider the statement
(1) Necessarily 9 = 9.
(1) is believed by most philosophical logicians to be non-extensional according to each of two prominent conceptions of extensionality. First, it fails the salva veritate substitution test when ‘9’ is replace by the co-referential singular term ‘the number of planets’. Second, in possible world semantics, its truth is regarded as dependent on the reference-in-all-possible-worlds of ‘9’, or, alterntively, on the intension of ‘9’ conceived as a function from possible worlds to individuals.
More generally, a statement is SV-Extensional according to the salva veritate substitution conception just in case singular terms co-referential with a statement's constituent singular terms, predicates co extensive with the statement's constituent predicates, and statements co-valent with a statement's constituent statement(s), substitute in that statement salva veritate. A statement is not SV- Extensional if there is at least one failure of salva veritate substitution. (This is close to the characterization in Quine's Word and Object.)
A statement is TD-Extensional according to the truth-value dependence conception just in case its truth value depends only on the extensions simpliciter, if any at all, of its constituent singular terms, predicates and statements. A statement is not TD-Extensional if entities other than extensional entities areinvolved in the computation of its truth value.
- Type
- Chapter
- Information
- Free LogicSelected Essays, pp. 107 - 121Publisher: Cambridge University PressPrint publication year: 2002