There are countably infinite lists in ZF. That doesn’t make the general fact that in some situations you can produce a paradox with a countably infinite list, a reason to think you can do that in ZF. You might as well argue, “We can produce paradoxes in natural language. So maybe we can do it in mathematics too.”
And maybe you could have made that argument, before people tried it. As others have pointed out, many people have looked for contradictions in ZF for a very long time, and none have been found. There is no reason to think there are any.
I told the others, that the countably infinite sets MIGHT be infected, since a finite list of Yablo sentences DOESN’T yield a paradox.
While a countably infinite list of Yablo sentences—DOES yield the mentioned paradox.
AFAIK, the infinities come out of ZF. Don’t they?
There are countably infinite lists in ZF. That doesn’t make the general fact that in some situations you can produce a paradox with a countably infinite list, a reason to think you can do that in ZF. You might as well argue, “We can produce paradoxes in natural language. So maybe we can do it in mathematics too.”
And maybe you could have made that argument, before people tried it. As others have pointed out, many people have looked for contradictions in ZF for a very long time, and none have been found. There is no reason to think there are any.