The current paper offers a perspective on what we term conceptive intelligence - the capacity of an agent to continuously think of new object definitions (tasks, problems, physical systems, etc.) and to look for methods to realize them. The framework, called a Brouwer machine, is inspired by previous research in design theory and modeling, with its roots in the constructivist mathematics of intuitionism. The dual constructivist perspective we describe offers the possibility to create novelty both in terms of the types of objects and the methods for constructing objects. More generally, the theoretical work on which Brouwer machines are based is called imaginative constructivism. Based on the framework and the theory, we discuss many paradigms and techniques omnipresent in AI research and their merits and shortcomings for modeling aspects of design, as described by imaginative constructivism. To demonstrate and explain the type of creative process expressed by the notion of a Brouwer machine, we compare this concept with a system using genetic algorithms for scientific law discovery.