Giacomo Tesio wrote an interesting post after a question arose during the DDD Day in Bologna on October, 8th.
He proposes an appealing point of view about what programming is and what’s the Domain Expert’s role in respect to “the problem” and “the matter“.
I still have to think it through. I’ll write about this topic in the next days.
Thanks, Giacomo for giving me food for thought.
Arialdo Martini 
Turns out that your question was far deeper than what I initially thought!
While discussing with Alberto about getters’ smell, architectures and everything, I realized that the subtle distinction between the problem and its matter leads to a completely different approach while modeling. This in turn leads to very different domain models, each with pro and cons.