I might be missing something, but it seems as if you’re needlessly complicating the situation.
First of all, I’m not convinced that sentences ought to be able to self reference. The example you give, “All complete sentences written in English contain at least one vowel” isn’t necessarily self-referencing. It’s stating a rule whic is inevitably true, and which it happens to conform to. I could equally well say “All good sentences must at least one verb.” This is not a good sentence, but it does communicate a grammatical rule.
But none of this has a priori truth—they just happen to conform to accepted standards—and I don’t think they demonstrate the usefulness of self-referencing. English grammar allows you to self-reference, but defining “Cat (n): a cat” is a tautology. English also allows you to ask the question “What happened before time began?” and while that is a perfectly valid sentence, it’s a meaningless question.
As a corollary, mathematical notation allows me to write “2+2=5” (note—the person who writes this down isn’t claiming that 2+2=5, she is far better versed than Aurini in the reasons it equals 4, she is just demonstrating that she can write down nonsense). This doesn’t require a defense of arithmetic; it’s simple enough to point out that the equation is nonsense.
“This sentence is false.” “What happened before time?” “My pet elephant that I named George doesn’t exist.” I don’t see that a rebuttal is necessary, meaningful, or even possible in these situations. It’s enough to say “That’s stupid,” and move on to something interesting.
The sentence “All good sentences must at least one verb.” has at least one verb. (It’s an auxiliary verb, but it’s still a verb. Obviously this doesn’t make it good; but it does detract from the point somewhat.)
I might be missing something, but it seems as if you’re needlessly complicating the situation.
First of all, I’m not convinced that sentences ought to be able to self reference. The example you give, “All complete sentences written in English contain at least one vowel” isn’t necessarily self-referencing. It’s stating a rule whic is inevitably true, and which it happens to conform to. I could equally well say “All good sentences must at least one verb.” This is not a good sentence, but it does communicate a grammatical rule.
But none of this has a priori truth—they just happen to conform to accepted standards—and I don’t think they demonstrate the usefulness of self-referencing. English grammar allows you to self-reference, but defining “Cat (n): a cat” is a tautology. English also allows you to ask the question “What happened before time began?” and while that is a perfectly valid sentence, it’s a meaningless question.
As a corollary, mathematical notation allows me to write “2+2=5” (note—the person who writes this down isn’t claiming that 2+2=5, she is far better versed than Aurini in the reasons it equals 4, she is just demonstrating that she can write down nonsense). This doesn’t require a defense of arithmetic; it’s simple enough to point out that the equation is nonsense.
“This sentence is false.” “What happened before time?” “My pet elephant that I named George doesn’t exist.” I don’t see that a rebuttal is necessary, meaningful, or even possible in these situations. It’s enough to say “That’s stupid,” and move on to something interesting.
Warning, nitpicks follow:
The sentence “All good sentences must at least one verb.” has at least one verb. (It’s an auxiliary verb, but it’s still a verb. Obviously this doesn’t make it good; but it does detract from the point somewhat.)
“2+2=5” is false, but it’s not nonsense.