Consider this sentence:
- No true sentence (i.e., sentence that is true) satisfies F.
In general, as in the Io case, it seems that:
- When F does not have semantic vocabulary and no sentence satisfies F, then (1) is unproblematically true.
If we accept (2), we get an interesting result. Suppose that F is the predicate "is identical to (1) and not-p", where "p" is any non-semantic statement. Then, (1) says that no true sentence is identical to (1) and is such that not-p. This is equivalent to the claim that if (1) is true, then p. In other words, in this case, (1) is equivalent to a Curry sentence just like:
- If (3) is true, then p.
No Curry sentence can be false. For if it's false, then it's true, because any material conditional with false antecedent is true. But whenever a Curry sentence is true, its consequent is true as well, by modus ponens (the antecedent is true because the Curry sentence is true!). So a Curry sentence is true when its consequent is true (assuming the consequent lacks semantic vocabulary) and is nonsense when its consequent is false.
Or so this argument shows. My own intuition is that (3) is nonsense even when p is true. But then I need to get out of the above arguments...