It has been somewhat humorously claimed that
No person who calls themselves a Situationist is!
If I think about this informally for a second, it would seem to reason that anyone who believes this claim must believe they are not a Situationist. If we take a little liberty putting this in a modal logic where this can be written as
$\square(\square p \rightarrow \neg p) \rightarrow \square\neg p$
Where $p$ stands in for the arbitrary claim $\text{I am a Situationist}$. And $\square$ is the Doxastic logic modal meaning $\text{I believe}$ Although at this point what $p$ represents is no longer relevant and we can move beyond the framing to just talk about the logic.
This surprisingly looks a lot like Löb's theorem:
$\square(\square p \rightarrow p) \rightarrow \square p$
Which a modest reasoner should believe.
Now since this theorem seems reasonable and has a passing resemblance to an important theorem I thought I would try to prove it, and see what sort of reasoning is required to believe this claim.
However I can't seem to arrive at this no matter even with some strong axioms, such as a Type G reasoner. I am starting to wonder if maybe my naïve reasoning is not so great, that this statement might not be provable for Type G reasoners or even inconsistent.
What is required to prove this? Is it a consistent statement with a Type G reasoner?