In this paper we present new propositions about the ontology of design and a clarification of its position in the general context of rationality and knowledge. We derive such ontology from a comparison between formal design theories developed in two different scientific fields: Engineering and Set theory. We first build on the evolution of design theories in engineering, where the quest for domain-independence and " generativity " has led to formal approaches, likewise C-K theory, that are independent of what has to be designed. Then we interpret Forcing, a technique in Set theory developed for the controlled invention of new sets, as a general design theory. Studying similarities and differences between C-K theory and Forcing, we find a series of common notions like " d-ontologies " , " generic expansion " , " object revision " , " preservation of meaning " and " K-reordering ". They form altogether an " ontology of design " which is consistent with unique aspects of design.