The text discusses the logical foundations of quantum mechanics and their relationship to classical logic. It begins by quoting Bridgman, who highlights the challenge of thinking about the very small, as quantum theory suggests that classical forms of thought may fail. The text then explores how states of knowledge can change during cognition, with transitions either being transitive or symmetric. Intuitionistic logic is suitable for transitive transitions, while quantum logic is needed for symmetric ones. Intuitionistic and quantum logics are considered key non-classical logics, with analogies between them being important for scientific methodology. In physics, quantum logic is associated with the lattice of results of quantum observations. The text argues that the standard quantization of classical theories is a simple substitution of quantum logic for classical logic, resulting in a corresponding quantum theory. This substitution transforms classical physical quantities into quantum observables. The text also proposes that intuitionistic logic is a natural basis for thermodynamics, as it can handle the uncertainty and transitions in knowledge about physical quantities in thermodynamic systems. The text further notes that intuitionistic logic has been successful in classical mathematics, with Cohen's forcing being equivalent to intuitionistic set theory. It concludes by suggesting that quantum logic could also be used in classical mathematics after an appropriate embedding.The text discusses the logical foundations of quantum mechanics and their relationship to classical logic. It begins by quoting Bridgman, who highlights the challenge of thinking about the very small, as quantum theory suggests that classical forms of thought may fail. The text then explores how states of knowledge can change during cognition, with transitions either being transitive or symmetric. Intuitionistic logic is suitable for transitive transitions, while quantum logic is needed for symmetric ones. Intuitionistic and quantum logics are considered key non-classical logics, with analogies between them being important for scientific methodology. In physics, quantum logic is associated with the lattice of results of quantum observations. The text argues that the standard quantization of classical theories is a simple substitution of quantum logic for classical logic, resulting in a corresponding quantum theory. This substitution transforms classical physical quantities into quantum observables. The text also proposes that intuitionistic logic is a natural basis for thermodynamics, as it can handle the uncertainty and transitions in knowledge about physical quantities in thermodynamic systems. The text further notes that intuitionistic logic has been successful in classical mathematics, with Cohen's forcing being equivalent to intuitionistic set theory. It concludes by suggesting that quantum logic could also be used in classical mathematics after an appropriate embedding.