There are people who think that all claims are opinions. And no opinion is better than any other.
It's clear to me that the reasons supporting 2 + 2 = 4 are on "higher ground" than the reasons supporting 2 + 2 = 5.
Upon pointing this fact out to one of these people, I can imagine that they can just say: "that's your opinion".
So, what are the best arguments against relativism?
If the position taken by the relativist is that there are no objective truths, then the relativist must first claim an exception:
P1. There are no objective truths (except this one).
By dint of special pleading, it has a way of limiting the legitimacy of the claimant.
This question misconstrues the problem, I think. Relativism isn't really a philosophical position or worldview, and can't be reasoned with on those grounds. Relativism is a defensive posture: a way of preserving a belief structure in the face of confusing or difficult arguments. A person retreats to relativism whenever they feel their views or beliefs are under attack, and cannot figure out how to justify their worldview effectively.
There is no argument against relativism; there's only a therapy for it. We have to get people to see that a retreat into relativism is a retreat into solipsism: a denial of the consensus reality that people negotiate in social life. People retreat to this solipsism because they would rather be isolated and right than connected and wrong, and don't realize that they have a voice in the ongoing negotiation that determines consensus reality. We have to ease the emotional valence of that black/white, right/wrong problematic so that people will more willingly enter into the social consensus. When we do that, people lose their knee-jerk defensiveness, and the urge towards relativism disappears.
Note that this implies a different attitude on our part. we cannot walk into a discussion insisting that 2+2=4 and deriding anyone who offers any other perspective. 2+2=4 isn't better because it's right in this sense; it's better because it's functional, and so our first question to someone who offers a different idea should be: what do they find functional in that idea? That can lead us to a discussion of different functionalities that might bring us towards some kind of consensus on differential values.
As exposed by Wolf Larson, there are some problems in the claim.
The first point is that it is "self refuting" when you observe that the claim "there are no objective truths" is a objective truth for the relativist. Even if he insists and say that your reasoning to explain that the premise is not relative, is itself a absolute, we begin a infinite regress, accusing one another of assuming some absolute truth, and the discussion have no point.
Another point to note is the conflict about the discourse and the reality. One thing is to negate the absolute truths in the level of discourse, another is to negate in the level of reality. Aristotle points this out. You can compare the discourse of the relativist with his own reality and live, that he will not treat as a relativist thing.
