Russell and Modality

Nowadays modal logic is one of the important areas of logic, but at the beginning of the emergence of modern logic, there was not much attention to this branch of logic, and even the founders of modern logic, including Russell, had an anti-modal position. One of the factors that led Russell to adopt such a position was the belief that logic is truth functional and extensional, and this is something that the introduction of modality destroys.Of course During the long period of his philosophical work, Russell has taken many and varied positions about modal notions. From the beginning, he did not have an anti-modal position. At first, he considered necessity as a description of an implication, and after some time, he introduced it as a primitive, basic and indefinable concept. Then, in some of his works, following Moore, he considered necessity as a kind of logical priority of propositions, but in the end he took an anti-modal position and tried to completely discard the modal notions. He said that these concepts are properties of propositional functions, not properties of propositions. But Russell has used second-order logic for explaining the modal concepts and explaining the difference between possibility and existence (which declares both of them to be properties of propositional functions), but even with this, he is not able to completely remove the modal notions from language and logic.