Relativism is the idea that there is no universal, objective truth, and instead depends on the context and perspective. There is one concerning point however, which is the following relativistic statement:
"There are no absolute truths."
One can argue that this is an absolute truth, and therefore this statement is self contradictory. This is considered a criticism of relativism. However, I argue that this statement is imprecise to begin with, because it's essentially Russell's paradox. Russel's paradox is a contradiction that arises when we have a self referential property. More precisely, let A be the set of all sets that are not members of themselves. If A is not an element of A, then by definition A is in A, and vice versa.
We can reformulate the above statement "There are no absolute truths" into Russell's paradox. (EDIT: the following argument is incorrect/flawed because it is ambiguous what kind of set theoretic object the collection of all absolute truths is.)
Let B be the set of absolute truths. If B is empty, then the statement "B is empty" is an absolute truth, so B is not empty. And if B is not empty, then the set B is an element of B because a set of absolute truths is also an absolute truth.
Another way to look at this issue to consider the following: Let's consider the determination of absolute truth to be a function f that assigns a value of 1 to a statement x if it is absolutely true, and 0 if it is not. Now, the claim "there are no absolute truths" is the claim that for all possible statements x, f(x)=0. The problem is f(x)=0 is a statement itself (let's call it y), and we can evaluate f on this statement y. This is the crux of the self referential issue and is the same one as russell's paradox.
So what is the solution to this? In mathematics, it seems like there are a couple of different solutions. One solution is to restrict the definition of "set," in line with the ZFC axioms. Another is to go into type theory, where a set is of type 1, an object that contains itself (like in russell's paradox) is type 2, an object that contains itself (or rather is self referential) "twice" is type 3, etc.
What is are the possible solutions in terms of philosophy?