If noncontextuality is defined as the robustness of a system's response to a
measurement against other simultaneous measurements, then the Kochen-Specker
arguments do not provide an algebraic proof for quantum contextuality. Namely,
for the argument to be effective, (i) each operator must be uniquely associated
with a measurement and (ii) commuting operators must represent simultaneous
measurements. However, in all Kochen-Specker arguments discussed in the
literature either (i) or (ii) is not met. Arguments meeting (i) contain at
least one subset of mutually commuting operators which do not represent
simultaneous measurements and hence fail to physically justify the functional
composition principle. Arguments meeting (ii) associate some operators with
more than one measurement and hence need to invoke an extra assumption
different from noncontextuality.Comment: 27 pages, 1 figur
