Illustrations may be helpful for the mind, but they can also mislead,
because not every side of the illustration can be applid to the
situation. I realize that my illustration regarding privative
systems can be misunderstood.
As I see it, the imperfective aspect has another meaning than the
perfective one, so we cannot subsume the imperfective aspect under
the perfective one vice versa, as can be done with "lionness" and
"lion".
I define aspect on the basis of three parameters, a) the distance of
focus,b) the angle of focus, and c) the breadth of focus. Point a) is
always different between the two aspects, but b) and c) can be
(almost) similar in a few situations, as in (1) and (2)
(1) 1 Kings 6:1 in the fourth year of Solomon's reign over Isreal, in
the month of Ziv, the second month, he began to build (WAYYIQTOL) the
house to YHWH
(2) 2 kings 14:1 In the second year of Jehoash son of Jehoahaz king
of Israel, Amaziah son of Joah king of Judah became king (QATAL)
The two examples seems to be very similar, but they are different.
The imperfective WAYYIQTOL focuses, not on just a point, but on the
first part of the building work; so the focus includes the beginning
and a part of the action. The focus of the perfective QATAL of (2)
is narrover, just on the entrance into the state (entrance into a
state is a definition given in the text-books of a QATAL realized as
a static verb). Usually the area of focus of a QATAL is broader than
in the case of a YIQTOL, as in (3).
(3) 2 kings 14:2 and he reigned (QATAL) in twenty-nine years.
In situations where the focus is not important, both aspects can be
used, as in Psalm 2:1,2 and in many states. In other situations where
the focus is important is the correct aspect chosen.