Abstract
In this chapter it is argued that standard type theory is inadequate since it imports syntactic notions into the semantics. The idea that the meaning determines the syntactic behaviour of an item is argued to be fundamentally flawed. Instead, using truth conditions as the starting point, an alternative to the standard relations is defined, namely concepts. Concepts are insensitive to order and multiplicity of their arguments. In order to combine two concepts, special functions are needed, so-called linking aspects. The chapter closes with discussions of ambiguity in language by discussing the well-known Paderewski puzzle, and then turns to profiling, a technique known especially from cognitive linguistics.
Meanings are the topic of this chapter. More precisely, it is abstract meanings that we want to characterize. Unlike what is ordinarily assumed we do not consider the structure of the space of meanings and the functions on them a matter of arbitrary convention. Like with exponents we must ask what meanings actually are and how they can be manipulated.
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The actual referent systems operated with a pair of such injections but we can safely ignore that complication.
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This is evidently a simplified scenario. The visible facts may not be the same across speakers, thus accounting for a different layer of confusion. But it is important to note that the distinction between what is abstract in a language and what is not is real. In a sense, the fact that Tully is Cicero is not part of the abstract language.
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Kracht, M. (2011). Meanings. In: Interpreted Languages and Compositionality. Studies in Linguistics and Philosophy, vol 89. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2108-1_4
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