  A property of a system is called actual, if the observation of the test that
pertains to that property, yields an affirmation with certainty. We formalize
the act of observation by assuming that the outcome correlates with the state
of the observed system and is codified as an actual property of the state of
the observer at the end of the measurement interaction. For an actual property,
the observed outcome has to affirm that property with certainty, hence in this
case the correlation needs to be perfect. A property is called classical if
either the property or its negation is actual. It is shown by a diagonal
argument that there exist classical properties of an observer that he cannot
observe perfectly. Because states are identified with the collection of
properties that are actual for that state, it follows that no observer can
perfectly observe his own state. Implications for the quantum measurement
problem are briefly discussed.
