Mathematical structures of natural intelligence (Q1675046)

The book under review is published in the Springer series entitled Mathematics in Mind that aims at revealing connections between mathematical modeling and natural and artificial intelligence. It is the result of the author's curiosity to find general structures able to describe aspects of human mind functioning. The text has a significant philosophical and psychological flavor interestingly combined with mathematical concepts. The book is structured in three parts, each containing several short chapters ending with summaries. The first part contains an introductory chapter -- The highest faculty of the mind, and continues with What is structure? -- Piaget's tour de force, where Piaget's concepts on structure as well as reversibility and irreversibility are discussed. The third chapter, Category theory: toward a relational epistemology, presents aspects related to universal constructions and the concepts of co-product. The last two chapters of the first part discuss how to trick the demon of entropy as well as neural networks and groupoids. The second part of the book has six chapters in which topics like natural intelligence in the wild, natural intelligence and meaning, from identity to equivalence, discussion on negation, the structuralist way of modeling and relationship between structures and wholes. The third part of the book contains four chapters in which the author discusses the origin and significance of numbers, metaphors and analogies and aspects related to symmetries, the last chapter being devoted to discussions regarding the interpretation and perspective of the presentations in the previous chapters. The author presents his vision on describing philosophical aspects regarding natural intelligence in mathematical terms. His point of view can be of interest for readers wishing to enrich their knowledge and make new connections.