A simple associationist neural network learns to factor abstract rules (i.e., grammars) from sequences of arbitrary input symbols by inventing abstract representations that accommodate unseen symbol sets as well as unseen but similar grammars. The neural network is shown to have the ability to transfer grammatical knowledge to both new symbol vocabularies and new grammars. Analysis of the state-space shows that the network learns generalized abstract structures of the input and is not simply memorizing the input strings. These representations are context sensitive, hierarchical, and based on the state variable of the finite-state machines that the neural network has learned. Generalization to new symbol sets or grammars arises from the spatial nature of the internal representations used by the network, allowing new symbol sets to be encoded close to symbol sets that have already been learned in the hidden unit space of the network. The results are counter to the arguments that learning algorithms based on weight adaptation after each exemplar presentation (such as the long term potentiation found in the mammalian nervous system) cannot in principle extract symbolic knowledge from positive examples as prescribed by prevailing human linguistic theory and evolutionary psychology.