For the first sentence in part 1 Claudia gave mustard to Oliver, we do want to assume here that to Oliver is a Goal. That is to say, it is connected to the tree using Merge, in the same way that we saw in class basically. The other possibility for a PP like to Oliver is that it might have been an adjunct, a modifier, setting the scene. But adjuncts don’t get theta-roles, so if the PP is a Goal, it must have been attached with Merge and not with Adjoin.

Here are a couple of sentences that I think can constitute evidence of this. First, consider a couple of uncontroversial adjuncts like the PPs in the office and by lamplight. There is no problem switching the order of these, so long as they come after to Oliver. But if to Oliver isn’t first, then any order we choose sounds weird.

Claudia gave mustard to Oliver in the office by lamplight

Claudia gave mustard to Oliver by lamplight in the office

*Claudia gave mustard by lamplight to Oliver in the office

*Claudia gave mustard in the office to Oliver by lamplight

*Claudia gave mustard in the office by lamplight to Oliver

*Claudia gave mustard by lamplight in the office to Oliver

I’ll leave it up to you to see why this test shows that to Oliver must be low, inside the VP, and not a PP attached to the VP (or vP) by adjunction. But these facts do suggest that pretty strongly.