If it is certain that impossibilities can be believed, then the impossibilists already have their trousers half-way down.
The impossibilists certainly do not have their pants half down in the sense of being slovenly dialecticians.
Impossibilists grant that people often act as if they believe impossibilities.
Impossibilists try to keep up appearances by distinguishing between what people really believe and what they believe they believe.
One of the early impossibilists, George Berkeley (1710, 273), paraphrases apparent belief in terms of what we imagine we believe.
Many impossibilists follow Saul Kripke (1972, 1980: 3) in thinking that the indiscernibility of identicals is as "self evident as the law of contradiction" and hence maintain that false identity statements are necessarily false.
But none of these weakenings harmonize with the arguments deployed by actual impossibilists.
Impossibilists are inconsistent about inconsistency.
Bolder still are the impossibilists who think that Hintikka's result is an understatement; instead of being merely indefensible, "Someone else believes an inconsistency" is a contradiction (Purtill 1970).
However, the impossibilist can accept skepticism about modality only by undermining his own thesis.
For example, if the impossibilist has a technical sense of "believe" in which it means "consistently believe," then his audience will protest that they assumed he was using "believe" in an ordinary sense.
In one respect, the impossibilist is a lonelier debater than the solipsist.