The study in the first section provides the technical fundamentals of Q technique and its methodology, covering topics such as concourse, representative design, Q-sample structuring, Q-sort technique, correlation, factor analysis, factor rotation, factor scores, factor interpretation, and their historical, conceptual, and philosophical accompaniments in the context of a Q-methodological examination of philosophies of education. A second study involves two single cases and a demonstration of Newton’s unpublished fifth rule of reasoning in science, utilizing the same set of statements about philosophy of education. The final section addresses the roots of the Q-R controversy in the mid twentieth century debate focused on Burt’s reciprocity principle and its applicability or inapplicability to Q methodology. Factor analysis and quantum mechanics are shown to share several features in common, such as complementarity, uncertainty, probabilism, complexity, and entanglement, and especially their common measurements founded on matrix mechanics, which was introduced into psychology 20 years prior to its incorporation into physics. The quantum character of Q methodology is shown to be at the base of many misunderstandings and criticisms it has received during the years since its introduction.