Tolerance and Counterpart Theory

2021 ◽  
pp. 246-261
Author(s):  
Cian Dorr ◽  
John Hawthorne ◽  
Juhani Yli-Vakkuri
Keyword(s):  
Modal Logic ◽  
Counterpart Theory ◽  
Logical Revisionism

Many philosophers have thought that Tolerance Puzzles can be easily dissolved by adopting some form of counterpart theory, which is roughly the view that being possibly a certain way is having a counterpart that is that way. This chapter shows how standard versions of counterpart theory involve radical departures from standard modal logic (going far beyond Iteration-denial) which we claim are unacceptable, and argues that once counterpart theory is developed in such a way as to avoid such logical revisionism, it has no special capacity to resolve the puzzles.

scholarly journals Counterpart theories for everyone

Synthese ◽  
2020 ◽  
Vol 197 (11) ◽  
pp. 4691-4715
Author(s):  
Achille C. Varzi
Keyword(s):  
Modal Logic ◽  
Semantic Theory ◽  
Counterpart Theory ◽  
Philosophical Significance ◽  
Special Cases ◽  
Identity Based

Abstract David Lewis’s counterpart theory (CT) is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic (ML), suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions (all worlds are equally real, individuals are world-bound) that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans-world identity. In fact, one may welcome a framework that is general enough to include both Lewis’s counterpart-based account and Kripke’s identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted.

Toward a Scotistic Modal Metaphysics

1998 ◽  
pp. 48-54
Author(s):  
Woosuk Park
Keyword(s):  
Modal Logic ◽  
Lessons Learned ◽  
Counterpart Theory ◽  
Original Formulation ◽  
Modal Metaphysics ◽  
Individual Essence

The problem I tackle in this article is: Do we have in Scotus a modal logic or a counterpart theory? We need to take a rather roundabout path to handle this problem. This is because, whether it be in Lewis's original formulation or in others' applications, the crucial concept of 'counterpart' has never been clearly explicated. In section two, I shall therefore examine the recent controversy concerning Leibniz's views on modalities which centers around the counterpart relation. By fully exploiting the lessons learned from such an examination, I shall then launch a trilemma against a Leibnizian in section three. Section four shall make the claim that unlike Leibniz's case, Scotus's position is not endangered by the trilemma. One important premise will be adopted from my thesis presented elsewhere regarding the different between Scotus's haecceitas and Leibniz's individual essence. Another will be secured from a brief report on Scotus's views on similarity, which might be utterly original to modern eyes jaundiced by contemporary set theories.

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.

Sortal modal logic and counterpart theory

1998 ◽  
Vol 76 (4) ◽  
pp. 553-565 ◽  
Author(s):  
Murali Ramachandran
Keyword(s):  
Modal Logic ◽  
Counterpart Theory

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 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
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