The Problem of Cross-world Predication

Kocurek, Alexander W.

doi:10.1007/s10992-015-9389-z

Cited by 8 publications

(9 citation statements)

References 39 publications

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“…Our appeal to modal comparisons in this informal introductory section is intended merely to isolate our target notion of actuality. Recent discussions of the difficulties in formalizing modal comparisons include Wehmeier (2012) and Kocurek (2016).…”

Section: Necessitism For All P If Actually P Then Necessarily Actually Pmentioning

confidence: 99%

The Logic of Contingent Actuality

Glazier,

Krämer

2024

Ergo an Open Access Journal of Philosophy

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Current orthodoxy in modal logic and metaphysics has it that actuality is non-contingent in the following sense: for all p, if actually, p, then necessarily, actually, p. Call this thesis (Actuality) Necessitism and its negation (Actuality) Contingentism. Thus, according to Contingentism, there is at least one proposition p which is actually true but which could have been actually false. In another paper, one of us (Glazier 2023) has recently defended Contingentism. The present paper explores the logic of actuality under Contingentism. After informally introducing Contingentism and outlining what we take to be the main motivations for accepting it, we consider how contingent actuality should be taken to be. We argue that the nature, or essence, of actuality imposes certain limits on the extent to which actuality could have been different, and these then inform our view of the logic of actuality. Turning to the formal study of the logic of contingent actuality, we specify a formal language and a possible world semantics for that language and distinguish a number of natural notions of validity and consequence to which it gives rise. We present axiomatizations of the different resulting logics and examine the variety of iterated modalities in our systems. We establish soundness and completeness results.

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Section: Necessitism For All P If Actually P Then Necessarily Actually Pmentioning

confidence: 99%

The Logic of Contingent Actuality

Glazier,

Krämer

2024

Ergo an Open Access Journal of Philosophy

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“…It is only known that it is the number of the set in the world the number exists in. The difficulty identified here is with cross-world predication, which occurs when we want to say something about an object in one world and how it relates to objects in another world (Kocurek, 2016).…”

Section: A Diversity Of Modal Logicismsmentioning

confidence: 99%

The Potential in Frege’s Theorem

Stafford¹

2020

The Review of Symbolic Logic

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Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. We re-explore this idea and discover that in the setting of the potential infinite one can interpret first-order Peano arithmetic, but not second-order Peano arithmetic. We conclude that in order for the logicist to weaken the metaphysically loaded claim of necessary actual infinities, they must also weaken the mathematics they recover.

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“…Clearly, 3 and 4 are just notational variants of each other. [Kocurek, 2016] uses 4; [Butterfield, Stirling, 1987] and [Wehmeier, 2012] use 3, and so do I. That is, I set the interpretation of an n-ary predicate letter P to be a function G n → P(D n ).…”

Section: Introductionmentioning

confidence: 99%

A nonhybrid logic for crossworld predication

Borisov

2023

Logical Investigations

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Some sentences of natural languages, such as John might have been taller than Mary is, ascribe relations to objects each of which is associated with a possible world. In this example, Mary is associated with the actual world whereas John is associated with a possible world that can be distinct from the actual one. This phenomenon — the phenomenon of crossworld predication — cannot be reflected by means of standard modal logic. Some nonstandard logics accommodating crossworld predication have been proposed; the most expressive among them is Kocurek’s hybrid logic. All of them make use of nonstandard operators such as the operators of hybrid logic. In this paper, I propose a nonhybrid first-order modal logic for crossworld predication, CWPL, that demonstrates significant expressive power (though is less expressive than Kocurek’s hybrid logic) and has that advantage over other proposals that it makes no use of any nonstandard operators. Semantically, CWPL is based on crossworld interpretation of predicates that assigns extensions to each n-ary predicate with respect to n-tuples of possible worlds rather than single possible worlds. To be able to employ crossworld interpretation of predicates when evaluating formulae, I suggest relativizing truth values to partial functions from variables to possible worlds. In the paper, I describe CWPL’s syntax and semantics, provide a translation of CWPL into a two-sorted first-order logic, and compare it with Kocurek’s hybrid logic in terms of expressive power.

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The Problem of Cross-world Predication

Cited by 8 publications

References 39 publications

The Logic of Contingent Actuality

The Logic of Contingent Actuality

The Potential in Frege’s Theorem

A nonhybrid logic for crossworld predication

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