Ambiguity and free will: the topology of decision in quantum and quantum-like sciences

This article considers the relationships between quantum theory (QT) and quantum-like theories (QLTs), theories using mathematical models based on the formalism of QT, from a reverse perspective, that of QLTs. The article argues that QT is no longer a theory of the behaviour, in particular motion, of physical objects, as was the case in classical physics and relativity. Instead, QT is a form of decision theory, involving a special ‘topology’ of decisions, using the term topology in part metaphorically, but only in part, because it applies in its proper mathematical sense to the formalism of QT. Part of this topology is the concept of free will, reconsidered through the concept of decision. This character of QT is grounded in a particular type of interpretations of QT, ‘reality without realism’ (RWR) interpretations. To address the affinities and differences between QT and QLTs, the article introduces two new principles: ‘the unambiguity principle’, equally applicable in QT and QLTs, or in mathematics and science in general, and ‘the free will principle’, only applicable in QLTs and not in QT. The article also reflects on the limits of quantum-like sciences (QLSs) and mathematical–experimental science in general in dealing with human thinking and decision making. This article is part of the theme issue ‘Quantum theory and topology in models of decision making (Part 1)’.