Expressive completeness in modal language

Hazen, Allen

doi:10.1007/bf00263656

Cited by 56 publications

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“…Many linguists and philosophers now argue that English has at least the full expressive power of a language with explicit quantification over worlds and times. 17 Let's suppose this is correct for a moment. Even so, it's not clear that English speakers are therefore committed to modal realism.…”

Section: Ontological Commitmentmentioning

confidence: 99%

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The Problem of Cross-world Predication

Kocurek

2016

J Philos Logic

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While standard first-order modal logic is quite powerful, it cannot express even very simple sentences like "I could have been taller than I actually am" or "Everyone could have been smarter than they actually are". These are examples of cross-world predication, whereby objects in one world are related to (sometimes the same) objects in another world. Extending first-order modal logic to allow for crossworld predication in a motivated way has proven to be notoriously difficult. In this paper, I argue that the standard accounts of cross-world predication all leave something to be desired. I then propose an account of cross-world predication based on quantified hybrid logic and show how it overcomes the limitations of these previous accounts. I will conclude by discussing various philosophical consequences and applications of such an account.

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Section: Ontological Commitmentmentioning

confidence: 99%

“…For instance, Priest[33, p. 123] and Fitting[13, p. 4] argue this 17. See Partee[31], Cresswell[10], Stone[39], Kratzer[23],King [21], Schlenker[36], and Schaffer[35] for a discussion.…”

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confidence: 99%

The Problem of Cross-world Predication

Kocurek

2016

J Philos Logic

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“…The main reason for this is that we cannot 'quantify back' into the previous world after we used a ♦ operator. For a summary of expressivity problems of first-order modal logic, see [17], [19]. Now the dynamical statement like "Only b's worldline changes" is also such a statement.…”

Section: Axiom 9 (Axiom Of Direct Measurements)mentioning

confidence: 99%

Axiomatizing relativistic dynamics using formal thought experiments

Molnár

Székely

2014

Synthese

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Thought experiments are widely used in informal explanations of Relativity Theories; however, they are not present explicitly in formalized versions of Relativity Theory. In this paper, we present an axiom system of Special Relativity which is able to express thought experiments formally and explicitly. Moreover, using these thought experiments, we can provide an explicit definition of relativistic mass based merely on kinematical concepts and thought experiments on collisions. Using this definition, we can geometrically prove the Mass Increase Formula m0 = m · √ 1 − v 2 in a natural way, without postulates of conservation of mass and momentum.

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“…Let's follow Hazen (1976) in presenting Lewis' counterpart theory as a two-sorted theory: one sort of variables v, w, . In this case, we render our quantified modal claims using a counterpart relation.…”

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confidence: 99%

“…More precisely: For any world w, there is a world w at which all the rich of w exist and are poor. 10 Again, the relevant results follow from those in Hazen (1976) and Hodes (1984b). 11 With , it is rendered as follows: 9 Harold Hodes considers the operator and gives the following useful gloss: "[' '] is to '@' as on a typewriter "back-space" is to "carriage-return"."…”

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confidence: 99%

Indispensability Arguments and Instrumental Nominalism

Pettigrew

2012

The Review of Symbolic Logic

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In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that mathematical objects exist on the grounds that we make indispensable reference to such objects in our best scientific theories (Quine, 1981a;Putnam, 1979a) and in our everyday reasoning (Ketland, 2005). I wish to defend a particular objection to such arguments called instrumental nominalism. Existing formulations of this objection are either insufficiently precise or themselves make reference to mathematical objects or possible worlds. I show how to formulate the position precisely without making any such reference. To do so, it is necessary to supplement the standard modal operators with two new operators that allow us to shift the locus of evaluation for a subformula. I motivate this move and give a semantics for the new operators.

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Expressive completeness in modal language

Cited by 56 publications

References 0 publications

The Problem of Cross-world Predication

The Problem of Cross-world Predication

Axiomatizing relativistic dynamics using formal thought experiments

Indispensability Arguments and Instrumental Nominalism

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