Complexity trade-offs do not prove the equal complexity hypothesis

Complexity trade-offs are often considered as evidence for the hypothesis that all languages are equally complex; simplicity in one component of grammar is balanced by complexity in another. According to Shosted (2006), this "negative correlation hypothesis", as he calls it, was never validated using quantitative methods. The present paper recalls, in a first step, our previously found significant negative cross-linguistic correlations between syllable complexity and number of syllables per clause and per word, as well as an almost significant negative correlation between syllable complexity and number of morphological cases. All these correlations indicate complexity trade-offs between subsystems of language, as do the positive correlations found between syllable complexity, number of syllable types, and number of monosyllabic words. In a second step we argue against the view of such complexity trade-offs as proof of the equal complexity hypothesis. This hypothesis is hardly testable for several reasons: As long as it is impossible to quantify the overall complexity of a single language, it is also impossible to compare different languages with respect to that quantity. Secondly, it could – because of its character as a null hypothesis – never be corroborated for principal reasons.