  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.
