Warning

There is a big difference between function symbols and predicates, though they are often confused because they both take terms as arguments. A term is either a name or a name-like entity formed using a function.

The difference is:

• If you apply a predicate to the right number of terms, you get a sentence which makes a claim and has a truth status.
• If you apply a function to the right number of arguments, you get another term, which should refer to a unique object of some sort. This is why function symbols can be applied over and over again in a way that is impossible for predicates.