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.

Generalized Update Semantics

Mind ◽  
2019 ◽  
Vol 128 (511) ◽  
pp. 795-835
Author(s):  
Simon Goldstein
Keyword(s):  
Modal Logic ◽  
Dynamic Semantics ◽  
Epistemic Modals ◽  
Kripke Semantics ◽  
Dynamic Update ◽  
Update Semantics ◽  
Construction Procedure ◽  
Special Cases ◽  
Truth Conditional ◽  
The Relationship

Abstract This paper explores the relationship between dynamic and truth conditional semantics for epistemic modals. It provides a generalization of a standard dynamic update semantics for modals. This new semantics derives a Kripke semantics for modals and a standard dynamic semantics for modals as special cases. The semantics allows for new characterizations of a variety of principles in modal logic, including the inconsistency of ‘p and might not p’. Finally, the semantics provides a construction procedure for transforming any truth conditional semantics for modals into a dynamic semantics for modals with similar properties.

III.—THE PHILOSOPHICAL SIGNIFICANCE OF MODAL LOGIC

Mind ◽  
1960 ◽  
Vol LXIX (276) ◽  
pp. 466-485 ◽  
Author(s):  
GUSTAV BERGMANN
Keyword(s):  
Modal Logic ◽  
Philosophical Significance

scholarly journals On the compositional checking of validity

1990 ◽  
Vol 19 (324) ◽  
Author(s):  
Glynn Winskel
Keyword(s):  
Modal Logic ◽  
Level Structure ◽  
Parallel Process ◽  
The Other ◽  
Reachable State ◽  
Compositional Reasoning ◽  
Parallel Processes ◽  
Special Cases ◽  
Finite State ◽  
State Language

This paper is concerned with deciding whether or not assertions are valid of a parallel process using methods which are directed by the way in which the process has been composed. The assertions are drawn from a modal logic with recursion, capable of expressing a great many properties of interest. The processes are described by a language inspired by Milner's CCS and Hoare's CSP, though with some modifications. The choice of constructors allows us to handle a range of synchronisation disciplines and ensures that the processes denoted are finite state. The operations are prefixing, a non-deterministic sum, product, restriction, relabelling and a looping construct. Arbitrary parallel compositions are obtained by using a combination of product, restriction and relabelling. We are interested in deciding whether or not an assertion A is valid of a process t. If it is valid, in the sense that every reachable state of t satisfies A, we write |= A:t. This paper investigates the extent to which the composition of t can guide methods for deciding |= A:t. For instance if t were a sum t_0 + t_1 we can ask what assertions A_0 and A_1 should be valid of t_0 and t_1 respectively to ensure that A is valid of t_0 + t_1. The paper formulates new compositional methods for deciding validity, and exposes some fundamental difficulties. Algorithms are provided to reduce validity problems for prefixing, sum, relabelling, restriction and looping to validity problems for their immediate components --- all these reductions depend only on the top-level structure of terms. The existence of these reductions rests on being able to 'embed' the properties of a term in the properties, or products of properties, of its immediate subterms. Because there is not such a simple embedding for the product construction of terms, as might be expected, similar reductions become much more complicated for products; although there are general results, and the reductions can be simple in special cases, the general treatment for products meets with fundamental difficulties. Whereas reductions for products always exist for this finite state language, they demonstrably no longer just depend on the top-level (product structure) of the term; in particular, a simple assertion is exhibited for which the size of the reduction must be quadratic in the number of states of the process. An attempt is thus made to explain what makes product different from the other operations with respect to compositional reasoning, and to delimit the obstacles to automated compositional checking of validity on parallel processes.

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 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.

scholarly journals Philosophical Issues from Kripke’s ‘Semantical Considerations on Modal Logic’

2016 ◽  
Vol 20 (1) ◽  
pp. 01
Author(s):  
John Divers
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Ontological Commitment ◽  
Semantic Theory ◽  
Kripke Semantics ◽  
Crucial Importance ◽  
Possible Worlds Semantics ◽  
Philosophical Discussion ◽  
Modal Space ◽  
Clear Conception

http://dx.doi.org/10.5007/1808-1711.2016v20n1p1In ‘Semantical Considerations on Modal Logic’, Kripke articulates his project in the discourse of “possible worlds”. There has been much philosophical discussion of whether endorsement of the Kripke semantics brings ontological commitment to possible worlds. However, that discussion is less than satisfactory because it has been conducted without the necessary investigation of the surrounding philosophical issues that are raised by the Kripke semantics. My aim in this paper is to map out the surrounding territory and to commence that investigation. Among the surrounding issues, and my attitudes to them, are these: (1) the potential of the standard distinction between pure and impure versions of the semantic theory has been under-exploited; (2) there has been under-estimation of what is achieved by the pure semantic theory alone; (3) there is a methodological imperative to co-ordinate a clear conception of the purposes of the impure theory with an equally clear conception of the content the theory; (4) there is a need to support by argument claims about how such a semantic theory, even in an impure state, can fund explanations in the theory of meaning and metaphysics; (5) greater attention needs to be paid to the crucial advance that Kripke makes on the precursors of possible-worlds semantics proper (e.g. Carnap 1947) in clearly distinguishing variation across the worlds within a model of modal space from variation across such models and, finally, (6) the normative nature of the concept of applicability, of the pure semantic theory, is both of crucial importance and largely ignored.

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