A measurement, in a general sense, can be thought of observation: I observe your height or weight; or the exact colour of the sky in an unclouded night and the number of stars.
Now, there is a key on a table which I pick up in my left hand, and hide it in my palm with my fingers clenched in a fist; I ask you to observe it; so you look at my hand, and then I open my fist - you observe the key - and then I close my hand briefly, and open it again - and again you see the key.
This much is expected; from moment to moment the key in my hand is at it is; but this is not inevitable or indeed neccessary.
Say, in my right hand I pick up some plasticine; it is formless - without shape; and when I open my fist, I quickly shape it into a sphere; and then when I close it, I turn it back into some shapeless and formless piece of plasticine; and again when Inopen my fist - so you can observe what is in my hand, I quickly shape it into a cube and so on.
This notion is called Value-Definiteness (VD) and is a key input into the Kochen-Specker Theorem; the first example above affirms it, and the second denies it.
Aristotle would say, that for the second example, some thing - some value comes to be and ceases to be - condenses and rarifies; and this appears to be his understanding of things in the small; for example, in Physics VII.5, he writes:
in fact, the fragment in the bushel does not move ... because within the bushel no fragment exists, except potentially.
He would also say, given his comments on the notion of change (and recall that Heisenberg theorised measurement as a change); that measurements require a something that acts as a measurer and something that can be measurable.
But he would deny that a measurer can measure itself: this ruler in my hand can measure my height or yours - but it cannot measure itself; or rather it is as a vacuous truth - a tautology - an inch is exactly an inch; and by this, nothing new is said.
There are three inputs into the theorem; one we have mentioned - value definiteness; the other is non-contexuality (NC): it ought not to matter how you measure something - the result ought to be the same.
The final input is one specific to the formal structure of QM: that measurements are self-adjoint projections.
The theorem then denies that all three can be consistent together - one has to give; in QI for example projections are replaced by positivity.