Charles Matthews A problematic concept. Not that just this sort of thought doesn't occur in real games: it does.
Here are two ways of thinking about it.
If I recall correctly, minerals are graded on a scale of 1 to 10 for hardness, so perhaps diamond = 10, and talc = 1. This is the Moh scale.
The dogmatic concept of thickness says it is at the top of the scale - only groups with GoMoh score of 10 need apply. There are such groups, for example those that stay connected with two eyes even if your opponent plays a ko threat against them which you ignore.
There are, however, groups with useful outside influence at all levels of the scale. Perhaps an unsupported stone at a 10-4 point might rank at GoMoh level 1.
You should chase your opponent towards your thick positions; you should not chase your opponent into frameworks that your are trying to build up, since that only works well if you succeed in killing. These are the fundamentals of direction of play based on influence.
In a given situation, which way do you chase? Perhaps we can use this as a criterion to set GoMoh level 5.
Say that this is the cross-over point: a framework is given level 4 or below if you definitely prefer to make territory while attacking with it, because it is full of empty space or contains shape weaknesses or you have problems with your own eye space if you force the opponent's weak group into it.
On the other hand a thicker position is given level 6 or above, if using it to make territory is an inadequate strategy, which fails to give 'value for money' for the stones you have 'invested'. The reasoning is similar to a card game, in which you must play the good hands well in order to benefit over the whole evening.
A framework that is invaded once may be 'hardened' by the process (say from level 3 to level 8); which is why there is often a serious change in the game in the second half of the middlegame.
See framework theory.
See discussion of phases of the game at classification of positions.