X-bar Theory and the Cantor Set - Theoretical Issues in Self-similarity
Gertjan Postma
January 2020

This squib is a theoretical legitimation of the empirical study in self-similarity and quantificational variability (Postma 2020a). We do so by describing and interpreting some parallels between classical X-bar Theory and the Cantor set: they share a fractal geometry and have the same Hausdorff dimension. The splitting of the segment [0;1] of the real numbers ℝ into the Cantor set part 𝒞 (with Lebesgue measure 0) and its complement set 𝒯 (with Lebesgue measure 1), provides an overall model of the components of language. It is argued that, if we further split the Cantor set 𝒞 into a set of end points ℰ and a complement set of "internal" points ℐ, an isomorphism can be designed between the triple (ℰ, ℐ, 𝒯) and natural language in compositionality, formal semantics (quantification), and lexical semantics. We argue that the structure of the internal part of the Cantor set ℐ, which is self-similar, can serve as a syntactic model in which self-similarity restricts quantificational variability.
Format: [ pdf ]
Reference: lingbuzz/004984
(please use that when you cite this article)
Published in: pre-publication
keywords: x-bar theory, cantor set, self-similarity, wh-items, quantificational variability, semantics, syntax
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