Consider the two sentences
John taught himself calculus.
John taught himself.
In the first sentence 'himself' is the indirect object and 'calculus' is the direct object. In the second sentence, does 'himself' become the direct object?
An interesting observation:
If we drop the direct object from
John gave himself a massage.
We get 'John gave himself' which is not a grammatical sentence. Yet, we can drop 'calculus' in the above sentence, and still get a grammatical one. Furthermore, to both trimmed expressions, a listener can respond 'Taught himself what?" and "Gave himself what?" respectively. This is why I'm not sure whether 'himself' in the second sentence is a direct or indirect object.
Best Answer
With the verb 'teach', 'calculus' will always be a direct object and 'himself' will always be an indirect object. What did he teach? Calculus. (Direct object). Whom did he teach? Himself. (Indirect object).
Other examples: "Sam hit me" or "Sam hit the table". Whom/What did she hit? Me, the table. 'whom' and 'what' have the same answer (Direct object). "Valerie told me the truth." What did she tell me? The truth (DO). Whom did she tell? Me (Indirect object). 'whom' and 'what' have a different answer. "Tom acted crazy and started talking to the TV". To whom did he start talking? To the TV (IO). "He washed his clothes" or "He washed himself". What/Whom did he wash? His clothes, himself (Direct object).
Hope this helps.