Mark Blaug’s normative methodology of economics is an attempt to articulate certain intuitions about how economic science could be improved by making it more “realistic”. I discuss two such articulations, one in terms of falsificationist principles, the other in terms of an alleged trade-off between relevance and mathematical rigour. My conclusion is that Blaug’s methodology is itself unrealistic, both descriptively and normatively. His (well intended) methodological prescriptions for the improvement of economics are not based on a systematic, consistent, descriptively adequate, and normatively viable account. I suggest that Blaug’s intuitions can be developed into a more realistic account by incorporating the analysis of two further topics...