I have encountered the following problem a couple of times. This problem is this: When formalizing something in predicate logic, the predicate uses propositions as variables.1 We may refer to this as the predicate acting upon the variable. The predicate is a function similar to functions in mathematics like “F(x) = x4”. Predicates were also written like this (with parentheses) to begin with. Variables are written in the english lower-case letters beginning from x and i.e. {x, y, z, etc.}. For variables that have to do with time 't' is often used. Propositions are written in upper-case english letters beginning with P i.e. {P, Q, R, S, etc.}. What ought one to write, then, when a predicate acts upon propositions? Ought one to switch to lower-case but keep the same letters i.e. {p, q, r, s, t}? We ought to use the way which is the least confusing and which is powerful enough to express whatever meaning clearly we might want to express. Here are some possible ways to formalize it:
Using propositions as variables
Using propositions as variables
Using propositions as variables
I have encountered the following problem a couple of times. This problem is this: When formalizing something in predicate logic, the predicate uses propositions as variables.1 We may refer to this as the predicate acting upon the variable. The predicate is a function similar to functions in mathematics like “F(x) = x4”. Predicates were also written like this (with parentheses) to begin with. Variables are written in the english lower-case letters beginning from x and i.e. {x, y, z, etc.}. For variables that have to do with time 't' is often used. Propositions are written in upper-case english letters beginning with P i.e. {P, Q, R, S, etc.}. What ought one to write, then, when a predicate acts upon propositions? Ought one to switch to lower-case but keep the same letters i.e. {p, q, r, s, t}? We ought to use the way which is the least confusing and which is powerful enough to express whatever meaning clearly we might want to express. Here are some possible ways to formalize it: