Per Skulason the reason why I ask is that it seems that "Store Saga" is late, derivative, and so not a good source if it's contradicted by others. Adam of Bremen is much closer in time, and many others seem to derive their information from him. So if, in *this particular issue*, I have problems fitting Store Saga with the stories from other sources (including the other sagas that assign more generations between the time of Ragnar Lodbrok and Gorm than the 2 generations in Store Saga will cover), I tend to distrust the info that is only sourced from Store Saga, but will have more trust in something that is stated in Adam of Bremen.
That's why I find "synthesis" incredibly frustrating during our discussion - we have a source conflict here, and discussing source conflict without naming the sources can only lead to confusion.
I'm not talking generic philosophy here, I'm talking about the specific sources for the specific question of "who was Hardeknut's father".