The chapter discusses the application of non-classical logics, particularly quantum logic and intuitionistic logic, in the context of scientific methodology and physics. It highlights the limitations of classical logic in the realm of quantum mechanics, where transitions between states of knowledge are either transitive or symmetric. Quantum logic is introduced as a theory of the lattice of results of quantum observations, and its equivalence with the canonical formalism of quantum mechanics is a subject of ongoing research. The author proposes two theses: 1. The quantization of a classical theory involves substituting quantum logic for classical logic, leading to a corresponding quantum theory. 2. Intuitionistic logic serves as a natural basis for thermodynamics, addressing the challenges posed by thermal fluctuations and irreversibility in mechanical processes. The chapter also touches on the use of non-classical logics in classical mathematics, noting that intuitionistic logic is more successful in this context due to its ability to handle certain paradoxes and limitations of classical logic.The chapter discusses the application of non-classical logics, particularly quantum logic and intuitionistic logic, in the context of scientific methodology and physics. It highlights the limitations of classical logic in the realm of quantum mechanics, where transitions between states of knowledge are either transitive or symmetric. Quantum logic is introduced as a theory of the lattice of results of quantum observations, and its equivalence with the canonical formalism of quantum mechanics is a subject of ongoing research. The author proposes two theses: 1. The quantization of a classical theory involves substituting quantum logic for classical logic, leading to a corresponding quantum theory. 2. Intuitionistic logic serves as a natural basis for thermodynamics, addressing the challenges posed by thermal fluctuations and irreversibility in mechanical processes. The chapter also touches on the use of non-classical logics in classical mathematics, noting that intuitionistic logic is more successful in this context due to its ability to handle certain paradoxes and limitations of classical logic.