As for Ibn Rushd’s objection to Abū Hāmid when he says, “‘Composite’ is not analogous to ‘existent,’ but rather to ‘setting in motion,’” this can be answered in several ways.
First, the discussion concerns rational meanings, not verbal analogies. The point here is that the eternal, necessarily existent essence, which possesses attributes, need not have a separate assembler who has brought the essence and its attributes together. Just as something that truly exists does not require another existent thing, but may exist in its own right without requiring an agent, so too its possession of attributes does not require an agent.
Second, suppose we grant that this is verbally analogous to setting something in motion. Regarding your statement, “It is an attribute involving being acted upon, additional to the essence of the things that have undergone composition”: if you mean that it is additional to the essence, the attribute, and the attribute’s subsistence in the essence, this is false. If, however, you mean that it is the attribute’s subsistence in the essence, or the attribute itself that subsists in the essence, nothing in this entails that it involves being acted upon by an agent distinct from the bearer of the attribute.
Third, if “setting in motion” means one thing setting another in motion, this is not analogous to the matter under dispute. No one has conceded that the eternal essence, which possesses its inseparable attributes, contains anything assembled by someone. If, however, it means motion in general, then the meaning becomes