The geometry vs. the algebra of meaning: Gärdenfors vs. Jackendoff

Abstract: In this paper Gärdenfors’s geometric approach to meaning in natural language is compared to Jackendoff's algebraic one, and this is done against the backdrop of formal semantics. Ultimately, the paper tries to show that Jackendoff's framework is to be preferred to all others. The paper proceeds as follows. In Section 2, the common theoretical commitments of Gärdenfors and Jackendoff are outlined, and it is attempted to argue briefly that they are on the right track. In Section 3, the basics of the two frameworks to be compared are laid out, and it is assessed how they deal with some central issues in semantic theory, namely reference and truth, lexical decomposition, and compositionality. In Section 4, we get into the nitty-gritty of how Gärdenfors and Jackendoff actually 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 empiricism when it comes to word learning and concept acquisition are assessed and compared to the moderate nativism of Jackendoff, and it is argued that Jackendoff's nativism is to be preferred. In the sixth section, the semantic internalism common to both frameworks is commented on.