 Among the reasons to suppose that our representations are structured, Fodor argues, are the productivity and systematicity of thought (Fodor 1987; Fodor and Pylyshyn 1988; Aizawa 2003). Thought and belief are “productive” in the sense that we can potentially think or believe an indefinitely large number of things: that elephants despise bowling, that 245 + 382 = 627, that river bottoms are usually not composed of blue beads. If representations are unstructured, each of these different potential beliefs must, once believed, be an entirely new state, not constructed from representational elements previously available. Similarly, thought and belief are “systematic” in the sense that an organism who thinks or believes that Mengzi repudiated Gaozi will normally also have the capacity (if not necessarily the inclination) to think or believe that Gaozi repudiated Mengzi; an organism who thinks or believes that dogs are insipid and cats are resplendent will normally also have the capacity to think or believe that dogs are resplendent and cats are insipid. If representations are structured, if they have elements that can be shuffled and recombined, the productivity and systematicity of thought and belief seem naturally to follow. Conversely, someone who holds that representations are unstructured has, at least, some explaining to do to account for these features of thought. (So also, apparently, does someone who denies that belief is underwritten or implemented by a representational system of any sort.)