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2014 | OriginalPaper | Buchkapitel

On the Essential Flatness of Possible Worlds

verfasst von : Neil Kennedy

Erschienen in: Recent Trends in Philosophical Logic

Verlag: Springer International Publishing

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Abstract

The objective of this paper is to introduce and motivate a new semantic framework for modalities. The first part of the paper will be devoted to defending the claim that conventional possible worlds are ill-suited for the semantics of certain types of modal statements. We will see that the source of this expressive limitation comes from what will be dubbed “worldly flatness”, the fact that possible worlds don’t determine modal facts. It will be argued that some modalities are best understood as quantifiers over modal facts and that possible worlds semantics cannot achieve this. In the second part of the paper, I will present a new semantic framework that allows for such an understanding of modalities.

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Vorheriges Kapitel Tableau Metatheorem for Modal Logics

Nächstes Kapitel Collective Alternatives

The term “flat” is sometimes used to mean that the modal facts supervene on the basic facts, as Humean supervenience would have it (cf. [8], p. 14). It seems that in this usage of the term, “flat” applies to the universe, whereas my flatness applies to single worlds.

\(\fancyscript{T}\) is a tree iff \(<\) is an anti-reflexive, transitive and connected relation \(<\) on \(T\) such that, for all \(t\in T\), its restriction to \(\{s\in T : s\le t\}\) is linear. In a tree, there is only one path from right to left but possibly many from left to right.

Note that “being a square” and “being a circle” are not properties of this universe.

The reader can assume that the agents are immaterial and only have epistemic properties.

These product frames are just a special case of what Gabbay and Shehtman [3] call “fibered semantics”, the general technique of mending two or more structures together to yield a further structure. Not all such combined structures have the property that the modalities have no interactions amongst themselves, thus some combined structures may actually turn out to have non-flat worlds. In fact, there is even reason to suspect that possibility spaces can be described as a special case of fibered semantics. However, since fibered semantics of this kind haven’t been explored to my knowledge, thinking in those terms will not be especially useful.

Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic, Cambridge tracts in theoretical computer science (Vol. 53). Cambridge: Cambridge University Press.

Davies, M., & Humberstone, L. (1980). Two notions of necessity. Philosophical Studies, 38, 1–30.CrossRef

Gabbay, D., & Shehtman, V. B. (1998). Products of modal logics: part 1. Logic Journal of IGPL, 6(1), 73.

Gabbay, D., & Shehtman, V. B. (2000). Products of modal logics: part 2. Logic Journal of IGPL, 8(2), 165–210

Gabbay, D., & Shehtman, V. B. (2002). Products of modal logics: part 3. Studia logica, 72(2), 157–183

García-Carpintero, M., Macià, J. (Eds.). (2006). Two-dimensional semantics. Oxford: Oxford University Press.

Lewis, D. K. (1973). Counterfactuals. Oxford: Blackwell.

Lewis, D. K. (1986). On the plurality of worlds. Oxford: Blackwell.

Prior, A. (1967). Past, present and future. Oxford: Oxford University Press.

10.

Segerberg, K. (1973). Two-dimensional modal logic. Journal of Philosophical Logic, 2(1), 77–96.

Titel: On the Essential Flatness of Possible Worlds
verfasst von: Neil Kennedy
Verlag: Springer International Publishing
Buch: Recent Trends in Philosophical Logic
Print ISBN: 978-3-319-06079-8

Electronic ISBN: 978-3-319-06080-4

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-06080-4_9

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