The geometry vs. the algebra of meaning

In thispaper Gärdenfors’s geometric approach to meaning in natural language iscompared to Jackendoff's algebraic one, and this is done against the backdropof formal semantics. Ultimately, the paper tries to show that Jackendoff'sframework is to be preferred to all others. The paper proceeds as follows. InSection 2, the common theoretical commitments of Gärdenfors and Jackendoffare outlined, and it is attempted to argue briefly that they are on the righttrack. In Section 3, the basics of the two frameworks to be compared are laidout, and it is assessed how they deal with some central issues in semantictheory, namely reference and truth, lexical decomposition, and compositionality.In Section 4, we get into the nitty-gritty of how Gärdenfors and Jackendoffactually proceed in semantic analysis, using an example of a noun and a verb(embedded in a sentence). In Section 5, the merits of Gärdenfors's empiricismwhen it comes to word learning and concept acquisition are assessed andcompared to the moderate nativism of Jackendoff, and it is argued thatJackendoff's nativism is to be preferred. In the sixth section, the semanticinternalism common to both frameworks is commented on.