Regarding "Economics is the science of choice":
I think an important phrase has been left out - Economics is the science
of choice _under conditions of scarcity_. Scarcity is what gives rise to
the notions of opportunity cost, of economizing activity and the related
notion of economic value, and of gains from trade. Lionel Robbins defended
this in The Nature and Significance of Economic Science; and before him
Wicksteed. The Austrians had a similar view.
One may dispute whether this captures economics (it misses empirical
studies of all sorts, for example) but if one is going to defend it as a
definition, the additional phrase "in a world of scarcity" seems to me to
be a necessary component.
Bruce Caldwell