If connectionism is to be an adequate theory of mind, we must have a theory of representation for neural networks that allows for individual differences in weighting and architecture while preserving sameness, or at least similarity, of content. In this paper we propose a procedure for measuring sameness of content of neural representations. We argue that the correct way to compare neural representations is through analysis of the distances between neural activations, and we present a method for doing so. We then use the technique to demonstrate empirically that different artificial neural networks trained by backpropagation on the same categorization task, even with different representational encodings of the input patterns and different numbers of hidden units, reach states in which representations at the hidden units are similar. We discuss how this work provides a rebuttal to Fodor and Lepore's critique of Paul Churchland's state space semantics.