Here’s a brief summary of the lecture I gave yesterday to the incoming freshman. Slides can be found here.
We started by looking at question formation. We assumed there was some kind of operation that transformed every sentence into some kind of question. For example:
1 b) Can John sing?
2 b) Is Mary singing?3 a) They are sleeping.
3 b) Are they sleeping?
In all of these cases (and in fact, every case with auxiliaries), we move the auxiliary verb in front of the subject. But what happens when we have two auxiliaries? Well, then we can choose to move either the first auxiliary or the second auxiliary:
4 b) Is he saying that she should sleep?
*4 c) Should he is saying that she sleep?
5 b) Will I get the books that are about computers?
*5 c) Are I will get the books that about computers?
In these examples, and most examples in English, you move the first auxiliary to make a question. If you move the wrong auxiliary (marked with *), you get word salad: total nonsense. But what about these examples?