One commenter on my blog requested an explanation of the difference between Apollinarianism and orthodoxy.
Apollinarianism is the view that Jesus had a true body and human soul, but not a rational human spirit/mind - instead he had (according to Apollinaris the younger) only a divine spirit/mind. In some ways this is similar to the monophysite position that alleged that Jesus had only one will, namely the divine will. By this, Apollinaris created a union that blended the human and divine natures. Thus, Apollinaris could speak of the crucifixion of the Logos and the worship of the flesh of Jesus, since there was only one nature of Jesus - a blended human/divine nature.
The Orthodox position is that Jesus was fully God and fully man. Thus, Jesus was one person who had both a true human nature and a divine nature. The proof of this doctrine, against the Apollinarian doctrine, can get somewhat nuanced. However, the basic argument might be summarized in this way: if the divine nature is changed in any way it is no longer the divine nature: similarly if the human nature is incomplete (such as by lacking a rational spirit/mind), then Jesus was not made in every way like us, yet without sin.