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So what do you make of the go in my example He will go to the house? It's clearly in the same position as, e.g., the to do in He is going to do his homework, another perphrastic future, this time in go.



No, it is not in the same position. Will and shall are auxiliary verbs for the future tense, also known as modal verbs. There is absolutely nothing periphrastic about either one.

http://www.mauspfeil.net/Shall+and+will.html

As to the construction "I am going to do my homework" it is NOT going plus an infinitive "to do", rather it is a "future tense future": "going to" plus a verb. See in this respect:

http://www.mauspfeil.net/Going-to_future.html

BTW, this web site is chock full of interesting stuff. Tons and tons of it. Another itneresting article is at:

http://www.mauspfeil.net/prescription_and%20description.html

TEd