scholarly journals Representing Counterparts

2014 ◽  
Vol 11 (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.

scholarly journals Counterparts, Essences and Quantified Modal Logic

2022 ◽  
pp. 1-14
Author(s):  
Tomasz Bigaj
Keyword(s):  
Modal Logic ◽  
Counterpart Theory ◽  
Quantified Modal Logic ◽  
Semantic Framework ◽  
De Re ◽  
Modal Operators ◽  
Sufficiency Condition ◽  
Essential Properties ◽  
Natural Modification ◽  
Translation Scheme

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.

Categories and Modalities

2018 ◽  
Author(s):  
Kohei Kishida
Keyword(s):  
Modal Logic ◽  
Category Theory ◽  
Kripke Semantics ◽  
Counterpart Theory ◽  
Stone Duality ◽  
Topological Semantics ◽  
First Order ◽  
Propositional Modal Logic ◽  
First Order Modal Logic

Category theory provides various guiding principles for modal logic and its semantic modeling. In particular, Stone duality, or “syntax-semantics duality”, has been a prominent theme in semantics of modal logic since the early days of modern modal logic. This chapter focuses on duality and a few other categorical principles, and brings to light how they underlie a variety of concepts, constructions, and facts in philosophical applications as well as the model theory of modal logic. In the first half of the chapter, I review the syntax-semantics duality and illustrate some of its functions in Kripke semantics and topological semantics for propositional modal logic. In the second half, taking Kripke’s semantics for quantified modal logic and David Lewis’s counterpart theory as examples, I demonstrate how we can dissect and analyze assumptions behind different semantics for first-order modal logic from a structural and unifying perspective of category theory. (As an example, I give an analysis of the import of the converse Barcan formula that goes farther than just “increasing domains”.) It will be made clear that categorical principles play essential roles behind the interaction between logic, semantics, and ontology, and that category theory provides powerful methods that help us both mathematically and philosophically in the investigation of modal logic.

scholarly journals On the Translation from Quantified Modal Logic into the Counterpart Theory

2012 ◽  
Vol 23 (9) ◽  
pp. 2323-2335
Author(s):  
Yu-Ming SHEN ◽  
Ju WANG ◽  
Su-Qin TANG ◽  
Yun-Cheng JIANG
Keyword(s):  
Modal Logic ◽  
Counterpart Theory ◽  
Quantified Modal Logic

Rigid Designation, Direct Reference, and Indexicality

2010 ◽  
Author(s):  
Scott Soames
Keyword(s):  
Modal Logic ◽  
Analytic Philosophy ◽  
Basic Structure ◽  
Direct Reference ◽  
Saul Kripke ◽  
Quantified Modal Logic ◽  
De Re ◽  
Rigid Designation ◽  
David Kaplan ◽  
Naming And Necessity

This chapter discusses the contributions of Saul Kripke and David Kaplan, which are leading elements of a body of work that changed the course of analytic philosophy. It first deals with the views of Kripke. The necessity featured in Naming and Necessity is the nonlinguistic notion needed for quantified modal logic and the modal de re. Kripke's articulation of this notion is linked to his discussion of rigid designation, and metaphysical essentialism. The remainder of the chapter deals with Kaplan, focusing on the tension between logic and semantics; the basic structure of the logic of demonstratives; direct reference and rigid designation; and English demonstratives vs. “dthat”-rigidified descriptions.

Counterpart Theory and Quantified Modal Logic

1968 ◽  
Vol 65 (5) ◽  
pp. 113-126 ◽  
Author(s):  
David K. Lewis ◽  
Keyword(s):  
Modal Logic ◽  
Counterpart Theory ◽  
Quantified Modal Logic

scholarly journals The New Aristotelian Essentialists

Metaphysica ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 87-93 ◽  
Author(s):  
Harold W. Noonan
Keyword(s):  
Modal Logic ◽  
Kit Fine ◽  
Quantified Modal Logic ◽  
De Re ◽  
Seminal Work

AbstractIn recent years largely due to the seminal work of Kit Fine and that of Jonathan Lowe there has been a resurgence of interest in the concept of essence and the project of explaining de re necessity in terms of it. Of course, Quine rejected what he called Aristotelian essentialism in his battle against quantified modal logic. But what he and Kripke debated was a notion of essence defined in terms of de re necessity. The new Aristotelian essentialists regard essence as entailing but prior in the order of explanation to de re necessity. In what follows I argue that the concept of essence so understood has not been adequately explained and that any attempt to explain it, at least along the lines most familiar from the literature, must be flagrantly circular or make use of de re modal notions.

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