Book contents
- Frontmatter
- Contents
- Preface to the First Edition
- Preface to the Second Edition
- Mathematical Prolegomenon
- Part I Propositional Logic
- Part II Quantification and Identity
- 12 Classical First-order Logic
- 13 Free Logics
- 14 Constant Domain Modal Logics
- 15 Variable Domain Modal Logics
- 16 Necessary Identity in Modal Logic
- 17 Contingent Identity in Modal Logic
- 18 Non-normal Modal Logics
- 19 Conditional Logics
- 20 Intuitionist Logic
- 21 Many-valued Logics
- 22 First Degree Entailment
- 23 Logics with Gaps, Gluts and Worlds
- 24 Relevant Logics
- 25 Fuzzy Logics
- Postscript: A Methodological Coda
- References
- Index of Names
- Index of Subjects
17 - Contingent Identity in Modal Logic
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the First Edition
- Preface to the Second Edition
- Mathematical Prolegomenon
- Part I Propositional Logic
- Part II Quantification and Identity
- 12 Classical First-order Logic
- 13 Free Logics
- 14 Constant Domain Modal Logics
- 15 Variable Domain Modal Logics
- 16 Necessary Identity in Modal Logic
- 17 Contingent Identity in Modal Logic
- 18 Non-normal Modal Logics
- 19 Conditional Logics
- 20 Intuitionist Logic
- 21 Many-valued Logics
- 22 First Degree Entailment
- 23 Logics with Gaps, Gluts and Worlds
- 24 Relevant Logics
- 25 Fuzzy Logics
- Postscript: A Methodological Coda
- References
- Index of Names
- Index of Subjects
Summary
Introduction
17.1.1 In this chapter we will look at the behaviour of contingent identity in modal logic. We assume that the logic to which identity is being added is any quantified normal modal logic, constant or variable domain, without the Negativity Constraint. Recall that if L is any logic L(CI) is L augmented by contingent identity.
17.1.2 First, we will take all constants to be rigid designators. We then look at the addition of descriptors.
17.1.3 Finally, we will take up briefly two important philosophical issues concerning identity, tense and modality.
Contingent Identity
17.2.1 In 16.4.1 we looked at a problem concerning SI. Later in 16.4 we saw how the distinction between rigid and non-rigid designators solves the problem. But there would appear to be a more virulent form of it. The Morning Star is the planet Venus, as is the Evening Star, m = v = e. But arguably, these noun phrases are rigid. So it follows by NI that □m = e; and this would seem not to be true. It would seem to be a contingent matter that the heavenly object that appears in the sky around dawn, and christened by the Ancients ‘the Morning Star’, turned out to be identical with the heavenly body that appears in the sky around dusk, and christened by the Ancients ‘the Evening Star’. The latter, for example, could have turned out to be Mercury.
- Type
- Chapter
- Information
- An Introduction to Non-Classical LogicFrom If to Is, pp. 367 - 383Publisher: Cambridge University PressPrint publication year: 2008