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In recent years and recent decades the logic and semantics of demonstrative expressions (sometimes called instead indexicals) has been the subject of intensive and extensive interest. The treatment of indexicals was the main step Richard Montague took in going beyond the plain vanilla version of possible-worlds semantics. He distinguished different occasions of language use from the possible worlds in which the use takes place. David Kaplan developed a treatment of demonstratives by associating to linguistic expressions a second meaning entity, called character, over and above its sense (in the Fregean sense). Being able to deal with demonstrative reference was one of the main motivations of the entire much-touted situation semantics of Perry and Barwise. It is the purpose of this paper to show that all these treatments are inadequate and to sketch a better one. In doing so, we will find that the basic notions of all formal semantics, such as possible world, situation, reference,etc. are in a serious need of clarification. The clarification attempted here turns on the way an interpreted language is supposed to be applied to the world. This application problem is what has prompted the reference to 'small worlds' in my title.

DOI: 10.1007/978-94-017-2531-6_9

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