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The issue of compositionality is applied to the modelling of the mental lexicon in terms of neural networks as described in Fortescue (2009). The approach is illustrated by applying it to the analysis of a semantically complex verb, conquer, illustrating the need to draw upon top-down (social, stylistic) as well as bottom-up (sensory) affordances in modelling such lexical items. Thereafter, a collocation that requires the mutual adjustment of the semantics of its individual components is analysed. Finally, adjectives of temperature crucially involving “limbic” affordances are treated. In all instances, the relevance of universal conceptual “primitives” to the processes of paraphrase and (co)composition will be seen to be highly restricted.