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A commentator wrote:

"Intolerance of intolerance" == Liar's Paradox/Halting problem. Language is a map, not the territory. Don't tolerate racism. Period.

I'm struggling to make the jump from the Paradox of Tolerance to the Liars Paradox - can someone help me with this?

My question is: Is "Intolerance of intolerance" equivalent to the Liar's Paradox?

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If you take a really silly literal view of the sentence the statement is a performative contradiction but not equivalent to the liar's paradox.

Let's say being intolerant of something is along the lines of forbidding it. This is plausible. So saying

I am intolerant of intolerance

means

Forbidding things is forbidden!

If we agree that forbidding things is forbidden, we have to ask---how are we forbidden from forbidding things?

The problem stems from an unstated context. In all likelihood the sentence really means something like

Forbidding things on the basis of ethnicity, gender, sexuality, religion, etc, is forbidden!

But of course nobody would have to spell that out; we all know what you mean when you say "intolerance" and "intolerant of intolerance" is just a fun phrase.

Finally, the statement isn't equivalent to the liar's paradox. If we affirm the liar's paradox we deny it, and if we deny the liar's paradox we affirm it. But if we deny "I am intolerant of intolerance" all we have is

I am tolerant of intolerance

or

Forbidding things is not forbidden!

which is clearly not a contradiction. This is because the sentence is not self-referential, unlike the liar's paradox.


A small note on the rest of the tweet: I find it incomprehensible. The liar's paradox is not the halting problem, and neither of them have anything to do with the map-territory distinction. Perhaps the writer means the concepts got at by language are different than the surface-level grammar, which is exactly right. But the first part of the tweet is just babble.

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Relations between concepts are not governed by much basic theory.
But theres many concepts that function in a similar way to truth and falsehood.

Lets first look at intolerance.

1) What I now say is not tolerated.

2) What I now say is "What I now say is not tolerated."

3) What I now say is tolerated. IFF "What I now say is not tolerated." is tolerated.

(IF only true sentences are tolerated then we get a contradiction:)

4) What I now say is tolerated IFF What I now say is not tolerated.

(So tolerance is related to truth and intolerance to falsehood.)

And now we look at "not permitted".

1) What I now say is not permitted.

2) What I now say is "What I now say is not permitted."

3) What I now say is permitted IFF "What I now say is not permitted." is permitted.

As before we demand that no lies be permitted!

4) What I now say is permitted IFF What I now say is not permitted.

The same method works (with minor modifications).

And heres the Liar "Himself":

1) What I now say is not true.

2) What I now say is "What I now say is not true."

3) What I now say is true IFF "What I now say is not true." is true.

4) What I now say is true IFF What I now say is not true.

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