Several approaches to implementing symbol‐like representations in neurally plausible models have been proposed. These approaches include binding through synchrony (Shastri & Ajjanagadde, ), “mesh” binding (van der Velde & de Kamps, ), and conjunctive binding (Smolensky, ). Recent theoretical work has suggested that most of these methods will not scale well, that is, that they cannot encode structured representations using any of the tens of thousands of terms in the adult lexicon without making implausible resource assumptions. Here, we empirically demonstrate that the biologically plausible structured representations employed in the Semantic Pointer Architecture (SPA) approach to modeling cognition (Eliasmith, ) do scale appropriately. Specifically, we construct a spiking neural network of about 2.5 million neurons that employs semantic pointers to successfully encode and decode the main lexical relations in WordNet, which has over 100,000 terms. In addition, we show that the same representations can be employed to construct recursively structured sentences consisting of arbitrary WordNet concepts, while preserving the original lexical structure. We argue that these results suggest that semantic pointers are uniquely well‐suited to providing a biologically plausible account of the structured representations that underwrite human cognition.