In this chapter we are going to embark on a speculative journey – so, caveat emptor! There are some fascinating developments taking place in the fields of cognitive science and neuroscience that may hold the key to a radically new understanding of a host of fundamental problems in a variety of disciplines and provide new leads in philosophical thinking as well. I am referring to the exciting field of neural network research, which appears to be on the verge of revolutionizing our understanding of “dualisms” or of “dualities,” such as the relationship between brain and mind. My intentions in this chapter are simply to explore some possibilities implicit in the neural network model for rethinking our conception of “structure” in general, and suggesting, more particularly, a new approach to the theory of social structure. The insights derived from the neural network literature are only orienting analogies at this stage of our research. I do not make the claim that they provide a coherent new theory, only that, if correct, they would add significant new lines of argumentation on behalf of the heterarchical model of structure as it was developed in the previous chapter (which stands on its own, without any need for reference to neural networks). There is a very serious assumption here – one that can be modified by analytical means as we shall see later – that in order for the model of neural networks to be useful, one must accept, at least temporarily as if by a phenomenological bracketing, that there is no significant discontinuity between natural and social phenomena and, thus, between “natural structures” and “social structures.”