  The notion of entropy penetrates much of science. A key feature of the
all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity
(additivity over independent subsystems). However, there is a need for other
quantities. In statistical physics a parameterized family of non-extensive
entropy measures, now mainly known under the name of Tsallis-entropies, have
received much attention but also been met with criticism due mainly to a lack
of convincing interpretations. Based on the hypothesis that interaction between
Truth, held by ``Nature'', and Belief, as expressed by man, may take place,
classical- as well as non-classical measures of entropy and other essential
quantities are derived. The approach aims at providing a genuine
interpretation, rather than relying either on analogies based on formal
mathematical manipulations or else - more fruitfully, but not satisfactory - on
axiomatic characterizations.
