To see yourself as others do.
That could easily happen
In an impossible world.
So if you rented out another brain,
That brain would need to vacate.
And your own would take over.
But then you wouldn't be “seeing yourself as others do”.
You'd just be fusing two selves into one.
There's no first-person purity or truth.
Acts of introspection
Exist in a gauze of theory.
There's even a veil of perception
Between your self
And your own private items.
So, perhaps, as classical introspecters,
We don't see the wood for the trees.
All this points in the direction of third persons.
Third persons may know you better
Than you know yourself.
No Cartesian indubitability here, then.