TITLE: What is the difference between a predicate symbol and a function symbol in predicate logic?
QUESTION [5 upvotes]: There are a lot of questions and answers on what the difference a predicate and a function in predicate logic is on this website, but there is no question/answer on what the difference between a predicate symbol and a function symbol is.

REPLY [5 votes]: Once we interpret the symbols:
A function applied to one or more objects gives you another object, while a predicate applied to one or more objects gives you a claim
For example, under the standard interpretation for the language of arithmetic:
$1+2$ gives you the object $3$ (and  $1+2$ is not a claim)
$1<2$ gives you the claim that $1$ is smaller than $2$ (and $1<2$ is not an object from the domain)