Originally Posted by OneHitWonder View Post
No, one of either the 11 or the 12 is no longer possible.

The "peeker" saw either the 11 or the 12. To be honest, if the "peeker" saw the 11, then he can not say or the 12. To be honest, if the "peeker" saw the 12, then he can not say or the 11.

He may say that what he saw is an element of the set defined by at least the 11. But, he may not honestly say that the specific roll or element of the set defined by at least the the 11 which he saw is that set. Can't roll or get a set of rolls on one roll. Unless the definition of the set is specially worded to work for both the general and the specific.
I don't mean to be rude, but is English your native language? The definition of the set is, in fact, worded to work for both the general and the specific. The question "did you get at least 11?" (assuming 'get' is understood to mean 'generate by rolling the dice', and 'at least 11' is understood to mean 'a configuration of the dice with at least 11 total pips on the top faces') is a straightforward yes-or-no question... no tricks. The set defined by 'at least 11', intersected with the set of possible rolls, is { 11, 12 }. And saying "I got at least 11" is the same as saying "I got an element of the set defined by 'at least 11'," with the advantage that it's how people actually talk.