Catherine Collin, Robin Woodburn, Dept of Electrical Engineering, Kings Buildings, University of Edinburgh, Edinburgh EH9 3JL After laying to rest the ghost of artificial neural networks implemented in analogue VLSI, the paper considers the more promising approach of modelling neurobiological elements and systems realistically in silicon: Neuromorphic engineering. It examines the reasons that have been cited as motivations for adopting the neuromorphic approach and explains why these motivations may not be rigorous enough. It suggests that a formal proof is required to demonstrate equivalence between the neurobiological element or system being implemented and the potential neuromorphism. A framework for this is proposed, using the tools of formal logic, that incorporates aspects of Marr and Newell's notions of levels of description. The framework asserts the non-neuromorphic nature of artificial neural networks and highlights the motivations for neuromorphic engineering that may be considered valid and those that are invalid.