If the subject is an Agent is the object always a Theme?
Interesting question.
This kind of comes down to the answer to the question “Is the direct object always a Theme?”, which is one that we will, in a certain sense, answer in the affirmative in the coming weeks. However, a verb that has two arguments need not always have a Theme (although it almost always does).
Trying to think of an example, the best I can come up with is go, which might arguably have an Agent and a Goal (as in I went to the kitchen). I say “arguably” because I can immediately see several objections, but for the point where we are now I think you can take go to be a transitive verb with an Agent and a Goal. (And I know that the opportunity is just now arising for you to make this determination. But as I’ve said, you should read the blog for hints to the homework.)
Some of those objections I immediately saw include the following, which you can think about, although again I’d stick with the hypothesis for now that go does have (at least in one form) an Agent argument and a Goal argument. In French, go behaves like an unaccusative (the past tense is formed with être), suggesting that the subject (in an active clause) is a Theme. On the other hand, it is (at least sometimes) clearly agentive in meaning, suggesting that the subject (in an active clause) is an Agent. I can see a couple of ways to resolve that, none particularly better than the others. Second, although I go doesn’t sound all that great in English (suggesting that another argument is required), the additional argument does not really seem to have to be a Goal per se, as in I went along the river or I went through the puddle. It seems to me that go requires the specification of some aspect of the path of motion, but it need not be the endpoint.
Another case in which it is not clear what the answer is to “Is the direct object always a Theme?” are double-object verbs, which we will discuss in short order. These are verbs like give in Anne gave Étienne her report. What’s peculiar about these is that they have two “objects”, neither of which is introduced with a preposition. Traditionally, report would be called the “direct object”, and we might even intuitively say it is the Theme, although we’ll analyze this in a different way when we get there.
Bottom line for now: Apart possibly from the verb go, your success rate will be almost perfect if you consider the object to be a Theme in cases where there is another participant that serves as the subject in active clauses.
[Note: I have several times mentioned “active clauses” above — what I mean by that is “not a passive”. The subject of a passive clause is what would have been the object of an active clause, so that confuses things when I try to use a structural specification like “subject” to identify an argument’s theta role. Example: I ordered the pizza (active) vs. The pizza was ordered (by me) (passive). In both cases, the pizza is the Theme.]