Lakatos and machine creativity

We argue that Lakatos’ work on the history and philosophy of mathematics is of key relevance to machine creativity as it suggests ways in which to explore and transform concept spaces, rerepresent knowledge and change evaluation criteria. We describe approaches to implementing methods which Lakatos identifies, including our own approach, which extends Colton’s HR and has enabled us to automatically generate mathematical conjectures, concepts and examples which were previously impossible in HR - including Goldbach’s conjecture. The methods are of general importance as they can be applied to many domains - we describe their theoretical application to game plans, two-dimensional geometry, moral philosophy, philosophy of mind, political argument and meta-level reasoning.