I fully agree with and understand Rosen. I think you’re failing to see that
The fact that this proposition “has a truth value” doesn’t change that.
I agree with you, but it seems we can also use contingent truths to produce constant propositional functions as well. I’ve used “I am hungry” as an example. That’s where we run into the problem of trying to make sense out of the statements “‘I am hungry’ is true for all x in the domain” and “‘I am hungry’ is true for some x in the domain.” Problems such as this seem to suggest that maybe we can’t just make a constant propositional function out of any domain and any proposition p. That’s one of my, if not my main, concern. Rosen doesn’t seem to address this issue. Nor does any other textbook on logic or math. And I can’t find anything on the Internet.
A function is a recipe for getting a result. The assembled ingredients are not the result … you have to process them.
This is a function:
Take 1 cup of x
Mix with 1 cup of chopped tomatoes
Bake at 350 degrees for 1 hour
When you get a specific x like potatoes, you still only have potatoes, tomatoes and a required operation.
The actual result of the function is the baked product.
A propositional function adds another level.
It proposes something like:
‘This recipe produces an edible result.’
Take 1 cup of x
Mix with 1 cup of chopped tomatoes
Bake at 350 degrees for 1 hour
Again, the ingredients are not the result and now the baked product is also not the result. The result is the answer to the proposition which is true/false or yes/no.
One problem with ‘I am hungry’ is that unless you are always hungry or never hungry, then for a given x then it will evaluate both to true and false so it doesn’t produce a function. For example if x=Tuesday, then you might be hungry in the morning and not in the afternoon - two values for the same x.
That’s not surprising because it’s not an actual problem.
This seems a very, very strange way to write things. Ordinarily, “F(x)” might mean “x is hungry”. But I guess it’s possible. We might say that “F(x)” that means “2 + 2 = 4” or even “Frank is Frank” is always true.
Well, I got my answer, no thanks to any of you. If F(x) = proposition p, there’s no predicate for F(x). Since a predicate for F(x) is a required component of a propositional function, constant propositional functions of the type I mentioned cannot exist.
