<i>A</i>‐worlds and the Dot‐Notation

Agustín Rayo

in The Construction of Logical Space

Published in print June 2013 | ISBN: 9780199662623
Published online September 2013 | e-ISBN: 9780191755392 | DOI:
A‐worlds and the Dot‐Notation

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This chapter develops a device for simulating quantification over merely possible objects. The proposal is frugal in two different respects. First, it is metaphysically frugal: it is designed to be acceptable to modal actualists, and presupposes very little by way of ontology. (It makes use of set-theory, but does not assume a specialized modal ontology, or an ontology of properties.) Second, the proposal is ideologically frugal: it does not presuppose potentially controversial expressive resources such as infinitary languages or non-standard modal operators. The point of developing machinery that presupposes so little is that philosophers of different persuasions can put it to work without having to take a stance on difficult philosophical issues.

Keywords: modal actualism; possible world; dot; David K. Lewis; Kripke semantics; modal logic

Chapter.  8398 words.  Illustrated.

Subjects: Metaphysics ; Philosophy of Mathematics and Logic

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