"know that p" clarifies the sense of "know", i.e., to know a proposition. The symbols "q" and "p" here stand in for propositions and "that p" is common parlanc

"know that p" clarifies the sense of "know", i.e., to know a proposition. The symbols "q" and "p" here stand in for propositions and "that p" is common parlance. Its not about introducing variables.