On the Translation from Quantified Modal Logic into the Counterpart Theory

It is commonplace to formalize propositions involving essential properties of objects in a language containing modal operators and quantifiers. Assuming David Lewis’s counterpart theory as a semantic framework for quantified modal logic, I will show that certain statements discussed in the metaphysics of modality de re, such as the sufficiency condition for essential properties, cannot be faithfully formalized. A natural modification of Lewis’s translation scheme seems to be an obvious solution but is not acceptable for various reasons. Consequently, the only safe way to express some intuitions regarding essential properties is to use directly the language of counterpart theory without modal operators.

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Representing Counterparts

The Australasian Journal of Logic ◽

10.26686/ajl.v11i2.2143 ◽

2014 ◽

Vol 11 (2) ◽

Cited By ~ 2

Author(s):

Andrew Bacon

Keyword(s):

Modal Logic ◽

Kripke Semantics ◽

Counterpart Theory ◽

Quantified Modal Logic ◽

De Re ◽

Actuality Operator

This paper presents a counterpart theoretic semantics for quantified modal logic based on a fleshed out account of Lewis's notion of a 'possibility'. According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. Following Hazen, a semantics for quantified model logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, and is equivalent to the more familiar Kripke semantics for quantied modal logic with an actuality operator.

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Counterpart Theory and Quantified Modal Logic

The Journal of Philosophy ◽

10.2307/2024555 ◽

1968 ◽

Vol 65 (5) ◽

pp. 113-126 ◽

Cited By ~ 315

Author(s):

David K. Lewis ◽

Keyword(s):

Modal Logic ◽

Counterpart Theory ◽

Quantified Modal Logic

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Quantified Modal Logic With Rigid Terms

Mathematical Logic Quarterly ◽

10.1002/malq.19880340308 ◽

1988 ◽

Vol 34 (3) ◽

pp. 251-259 ◽

Cited By ~ 2

Author(s):

Giovanna Corsi

Keyword(s):

Modal Logic ◽

Quantified Modal Logic

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QUANTIFIED MODAL LOGIC ON THE RATIONAL LINE

The Review of Symbolic Logic ◽

10.1017/s1755020314000021 ◽

2014 ◽

Vol 7 (3) ◽

pp. 439-454 ◽

Cited By ~ 4

Author(s):

PHILIP KREMER

Keyword(s):

Modal Logic ◽

Real Line ◽

Topological Spaces ◽

Topological Semantics ◽

Cantor Space ◽

Quantified Modal Logic ◽

Propositional Modal Logic ◽

The Family ◽

Modal Logic S4 ◽

Rational Line

AbstractIn the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the current paper is that QS4 is complete, indeed strongly complete, for the rational line.

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