Validity in intensional languages: a new approach.

Hanson, William H.; Hawthorne, James

doi:10.1305/ndjfl/1093870758

Cited by 5 publications

(7 citation statements)

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“…What this shows, therefore, is that a model theory for a modal language seems to have, at least on the face of it, the resources needed to see a full model as assigning a meaning proper to the non-logical terms, since each model is standardly seen as containing a set of possible worlds. Hanson & Hawthorne [1985] have proposed a model theory for modal language which is based on this intuition. As they argue, if each model is based on the frame which contains all possible worlds, we can see each interpretation (that is, model built on this frame) as assigning a meaning proper to the non-logical terms.…”

Section: Part IVmentioning

confidence: 99%

“…But such an endeavor, unfortunately, falls without the scope of the present thesis and will consequently have to wait for another occasion. Cocchiarella [1975Cocchiarella [ , 2002 and Hintikka [1980Hintikka [ , 1982, but also Hanson & Hawthorne [1985] criticize Kripke Semantics, though their concerns are not limited to readings of as logical necessity. Our concern in the coming sections is to show that this criticism is mistaken if it is meant to apply to our current view of a valid argument of our language as one that is truth preserving in all possibilities under all interpretations.…”

Section: The Criticism Of Kripke Semanticsmentioning

confidence: 99%

“…A Kripke Frame, F , is a tuple W, @ , where W is a set and @ ∈ W . 144 What this really amounts to is demanding that validities be 143 We will later look at a claim to this effect made by Hanson & Hawthorne [1985], a claim that validity for a modal language should be decided on just one frame: the intended frame which reflects the structure of the modal space under investigation. However, this discussion is best taken in relation to quantified languages since those are Hanson & Hawthorne's primary object of investigation.…”

Section: There Is a Fixed Class Of Logical Possibilitiesmentioning

confidence: 99%

“…We can understand a world as simply a member of W , in which case the criticism becomes that W should have a certain size in each model, a size that reflects how many logically possible worlds there really are, and similarly, constraints should be put on the function ψ in order to adequately capture the number of objects existing in those worlds. 146 We will look at a claim from Hanson & Hawthorne [1985] to this effect in a later section.…”

Section: Quantified Languagesmentioning

confidence: 99%

“…Hawthorne [1985] point to a puzzle in standard Kripke Semantics for modal logics.The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and one model structure defined on this class that does correctly the things that model structures are supposed to do.…”

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confidence: 97%

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Model-Theoretic Accounts of Logical Consequence - Themes from Etchemendy

Christensen¹

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<p>This thesis is a discussion and continuation of a project started by John Etchemendy with his criticism of Tarski's account of logical consequence. To this end the two central concepts of the thesis are those of an interpretational and representational model-theoretic account of logical consequence, respectively. The first chapter introduces Etchemendy's criticism of Tarski's account of logical consequence, a criticism which turns essentially on an interpretation of Tarski according to which his proposed account gives rise to a purely interpretational model-theoretic account of logical consequence. Consequently there must be a representational aspect to our model-theoretic definition of logical consequence. The second chapter introduces Etchemendy's notion of logical consequence: that of being truth preserving in virtue of the semantics of the involved terms. While this notion is representational, we argue that Etchemendy's notion of a categorematic treatment of terms reintroduces an interpretational aspect back into the model theory. The chapter investigates the resulting notion, compares it to other notions in the literature, and presents certain results that can be proved, under certain conditions, about this notion in relation to the notion of being truth preserving in virtue of the semantics of all terms. Chapter three of the thesis is concerned with the question of how a standard model, seen as a domain and an interpretation function, manages to capture the different notions of model-theoretic consequence. As we explain, this question is most pressing when we want our models to both represent and interpret, and we will present a theory which allows us to see the models as both representing non-actual possibilities as well as provide interpretations for the terms. The fourth chapter applies the lessons of the preceeding chapters to argue that Kripke Semantics can be seen as capturing the notion of being truth preserving in all possibilities under all interpretations of the non-logical terminology in the case where our language is augmented with an operator, ⃞, to represent logical necessity. We will argue this point by contrasting it with, though not necessarily disagreeing with, claims made by various authors to the effect that Kripke Semantics is not the appropriate semantics when our language contains an operator for logical necessity.</p>

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Section: Part IVmentioning

confidence: 99%