This SpringerBrief provides an interdisciplinary synthesis based on psychology, logic, mathematics, cognitive science, and the history of science. It presents psychology as a science that suffers from a reduced understanding of the most fundamental logic in our practical-bodily encounters with the world, including with our fellow human beings. The Brief offers a new “dual” logic that is based on the duality between identification and description of objects, including persons. The Brief ties in modern mathematics as a tool that can be used to catch this duality in a precise manner.  Featured topics in this Brief include:  The emergence of Mechanism. The duality in animal and human subject-object relations. Psychology’s compatibility with natural sciences. Four cornerstones of modern mathematics. The Extensional Method.  A New Logical Foundation for Psychology will be of interest to psychologist, philosophers, and mathematicians concerned with basic theoretical and methodological problems. .