There are things you might have written, but didn’t, and never will. so “People can write in the Philosophy Forum anything, except what they never will write” looks in this sense false. One might have written what one didn’t write. We need here to be clear as to whether we are using a existential quantification, as you are, or a modal quantification, as I am. I think the instability here comes from modality, not truth.
The Liar is not dependent on indexicality, as “I am a Cretan”; nor modality, as in that we might have written something other than we do write; nor self-reference. All good points, since each of these can be used with without contradiction or paradox.
There are versions of the Liar that do not rely on self-reference. The obvious one is
- (A) Sentence B is false
- (B) Sentence A is true
Yalbo’s paradox is even more fun, since no sentence ever ultimately refers to itself, nor is it clear that there is some overall circularity.
It’s worth here again drawing parallels to my discussion of Aesthetics. There I proffered the argument that whatever definition of art one might offer, some artist will produce an item of art that undermines that definition. It may be that whatever general solution or analysis of paradoxes is offered, some logician will produce a paradox that bypasses that analysis.
At the least, no simple diagnosis of paradoxes is apparent.