Wiki - The paradox of tolerance states that if a society is tolerant without limit, its ability to be tolerant is eventually ceased or destroyed by the intolerant. Karl Popper described it as the seemingly self-contradictory idea that in order to maintain a tolerant society, the society must retain the right to be intolerant of intolerance.
I think I understood the original post correctly.
I would argue that they can and do frame their arguments in such a way as to qualify themselves as victims of gay/trans intolerance. The most obvious would be any criticism of “cancel culture”. An argument that gay/trans supporters are “canceling” people for minor, not-intolerant slights would justify their counter-intolerance under the paradox, and set up the conditions I outlined.
I would say that your argument is overly technical.
Adam and Bob are both homophobes. Adam argues gay people shouldn’t exist, and then argues that’s gay people want to cancel him. Bob argues that gay people want to cancel him, and then argues that gay people should not exist. With the technical interpretation you have presented, I would have to conclude that Adam has violated the social contract. He has indicated intolerance against gay people first, justifying the counter-intolerance against him. Bob, however, claims to be intolerated by gay people, which then justifies his counter-intolerance of gay people.
I consider Adam and Bob to be functionally identical. I think a valid philosophical model would evaluate them equally. I consider the technicality you describe to be an insignificant error in logic rather than the fundamental operating principle of the paradox.
What you are talking about is more consistent with the “Non-Aggression Principle” than Popper’s Paradox.
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I was talking about the part:
If Adam is cancelled for being a homophobe, it is within this contract. My question is: Why was Bob cancelled? Has he done or said something? Has he agreed with Adam? Or was there only gossip about his opinion? The reasons for cancelling someone are important. As is causality. Adam and Bob are not functionally identical. Why is Adam a homophobe? Why was Bob cancelled? Maybe the started at the same spot, but here that is not clear.
Another point:
He argues they want to cancel him. How does he know that? What are his arguments, was there a thrat? This reads like an unbacked claim, an accusation. If that’s the case, then Bob would be in the wrong for false accusation.