What goes for thought, goes for talk, the chain of impossibilities precludes (even insincere) assertion of impossibilities.
Therefore, we should infer that it is possible to believe impossibilities and should reject Hume's principle that conceivability implies possibility.
Just as one cannot prove to the eliminativist that there are beliefs by appealing to the infallibiilty of belief in "There are beliefs," one cannot prove to the eliminativist that some impossibilities can be believed by appealing to the infallibility of belief in "Some impossibilities can be believed.
This sense is lenient enough to permit belief in impossibilities.
My belief that impossibilities can be believed enjoys a Cartesian aloofness from the extrinsic factors cited by Brown.
Brown could reply that I only indirectly believe that impossibilities can be believed.
All I need to prove my thesis is the possible existence of a single conceptually well-adapted believer in believable impossibilities.
However, even those who believe that impossibilities can be believed may object that I am begging the question against the impossibilist.
The impossibilist will admit that if I believe that I can believe an impossibility, others can believe that they can believe impossibilities.