This article criticizes recent attempts to explain creative thought as an off-shoot of syntactic mechanisms, such as recursion in language, and proposes an alternative. It agrees with the syntax-centric hypothesis on two fronts. First, it is claimed that a supramodal notion of creative thought, or what paleoarcheologists call human innovativeness, emerged in the human evolution in a sudden quantum transformation that occurred between 200,000–50,000 years ago. Second, it is argued that human innovativeness is linked with certain formal linguistic computations. Where it perceives weakness is in the claim that formal recursion by itself could transform a finite mind into an infinite one. A new hypothesis is proposed, according to which recursive symbol manipulation provides a controlled, volitional access to a more primitive, pre-existing creative non-discursive thought potential by means of non-veridical "wild" triggering.