That's right, the machine can not answer the sentence: "This sentence is false" or "I always lie" etc.
About the sentences: "What is my shoe size?", The machine is not supposed to ANSWER your QUESTIONS, but say if they are true or false, therefor you can't ask her questions.
The realy fun part begins when you try to think about HOW true is the sentence.
Let's take the sentence: "This sentence is false". mark it's
validity as x. we'll set x between 0 and 1, when 0 is completely false and 1 is completely true. then if x is it's validity, 1-x will be it's falseness. if you analize the sentence, you will get that by it's context
x=1-x. the only solution for this equasion is 0.5.
therefor, the sentence is half true.
p.s. sorry about the rutten spelling, I was in a hurry.