 As in the shift from  Similarity 2  to  Similarity 3,  this seems like a successful move, with many (although not all) of the aforementioned concerns being met. But, again, the role of isomorphism has shifted. The crucial ingredient is the agent’s intention and isomorphism has in fact become either a representational style or normative criterion for accurate representation. Let us now assess how well isomorphism fares as a response to these problems, and the others outlined above.