It's not, it is just a term in common usage taken to the extreme in an attempt to be clever, in contravention of all conversational norms. I don't think there is any definition of tolerance that is mathematically sound and absolute.

It would be like saying "a peaceful person would never punch someone in the nose". But what if you needed to punch someone in the nose because they were trying to kill you for no reason? That doesn't mean peaceful people don't exist, or that peaceful people need to let random people murder them. It just means that the determination of peacefulness is contextual.

Yes such overloading leads to paradoxes. My favorite https://en.wikipedia.org/wiki/Unexpected_hanging_paradox

Huh, does the unexpected hanging paradox come from such an overloading? It isn't obvious to me how it is. I don't mean that in a way to suggest that it seems unlikely to me. It seems quite plausible to me that it is. I just don't see in what way. Could you elaborate on how it comes from an overloading?

FYI, I think that you missed that this idea that "a tolerant society does not tolerate intolerance" is better known as "Karl Popper's paradox of tolerance" You can find it under that name, numerous articles, from Wikipedia on down (1). Since 1945. it's widely known and accepted. It's not an actual contradiction, most "paradoxes" only appear that way on a superficial inspection.

it would be like saying, as the sibling comment did "a peaceful person would never punch someone in the nose" ... except that a society that aims for peace, and is beset with violent people, is going to have to quell that violence. This might involve reserving the right to punch the punchers.

https://en.wikipedia.org/wiki/Paradox_of_tolerance

You are conflating protection from violence with protection of free speech. Paradox of tolerance is a hypocritical concept used by people to excuse their own intolerance.

Restrictions on free speech are much more dangerous than any hate speech. You won't get a new Hitler by blocking speech you don't like. It's the opposite: new Hitler will start with blocking free speech. That's what every authoritarian regime does first.

> You are conflating protection from violence with protection of free speech.

No, I am saying that they are "like" each other. It's a comparison not a conflation. Mr Popper is absolutely not conflating anything - his original formulation is very much about speech.

> blocking free speech. That's what every authoritarian regime does first.

You mean, after they become the regime, and get a lock on the power to block free speech; which in turn is after using the free speech ability to emit the divisive populist rhetoric that propels them to that power? There is no regime ever, that blocks free speech before it is voted into power. At that stage they're only to happy to use it. The shutting it down comes later.

So, not first at all then. That was Popper's point.

> There is no regime ever, that blocks free speech before it is voted into power.

But there is, we've seen it just recently! Take the US presidential elections in 2020: big media companies, bigtech all were favouring one political party and have successfully suppressed crucial damaging information against their side and baselessly labelled it as 'fake news', which helped the favoured party take power. It immediately proceeded by shutting down the media accounts of the defeated opponent.

The ongoing hate-campaign against musk that started after him buying twitter can absolutely be interpreted as a reaction to breaking the monopoly on the flow of information.