I'm taking a class on set theory, and we're beginning with a review of first-order logic. I did first-order logic a long time ago. I can now no longer remember if there is an important difference between propositional constants and propositional variables. Having Googled around a bit, it seems that these terms get used interchangeably quite often, but maybe there is some distinction I need to be aware of.
Perhaps some context about why I'm asking would help. We're doing the syntax of FOL right now, and in our syntax we have:
- Variables = {x, y, z,}
- Connectives = {¬, ∧, ∨, →, ↔, ∀x, ∃x}
- Predicates = {P, Q, R, S, T, U, V, W, =}
- Function symbols = {fi : i ≤ n}
The prof asked where 'constants' and 'propositional variables' go. I take it that by 'constant' the prof means 'individual constant' (AKA 'names,' 'individuals'). And I think these are going to be 0-ary function symbols. Now, I'm trying to figure out what he means by 'propositional variables' and where these things might go. Does he just mean "Where do things like P and Q in propositions of the form 'P → Q' go?" I think that's probably what he means, but I'm used to calling P and Q 'propositional constants' rather than 'propositional variables.' I have never encountered the term 'propositional variable' before, and searching around to see if there is a distinction between propositional constants and propositional variables has been unilluminating. Some people seem to suggest so, although I cannot understand why, while others seem to use the phrases interchangeably. Given this, I'm having a hell of a time guessing what the prof means by asking us where propositional variables fit into our syntax.