  In 1862, George Boole derived an inequality for variables, now known as
Boolean variables, that in his opinion represents a demarcation line between
possible and impossible experience. This inequality forms an important
milestone in the epistemology of probability theory and probability measures.
  In 1985 Leggett and Garg derived a physics related inequality, mathematically
identical to Boole's, that according to them represents a demarcation between
macroscopic realism and quantum mechanics. Their formalism, constructed for the
magnetic flux of SQUIDS, includes general features and applies also to many
other quantum experiments.
  We show that a wide gulf, a wide divide, separates the "sense impressions"
and corresponding data, as well as the postulates of macroscopic realism, from
the mathematical abstractions that are used to derive the inequality of
Leggett-Garg. If the gulf can be bridged, one may indeed derive the said
inequality, which is then clearly a demarcation between possible and impossible
experience: it cannot be violated and is not violated by quantum theory. We
deduce from this fact that a violation of the Leggett-Garg inequality does not
mean that the SQUID-flux is not there when nobody looks, as Leggett-Garg
suggest, but instead that the probability measures may not be what Leggett-Garg
have assumed them to be, when no data can be secured that directly relate to
them. We show that similar considerations apply to other well known quantum
interpretation-puzzles including that of the two-slit experiment.
