 Daniel Howard-Snyder (2003) offers numerous objections to Craig’s theory. First, it can’t avoid either polytheism or different levels of divinity, either of which would make it unorthodox. The Cerberus analogy is criticized on the grounds that it would not be one dog with three minds, but rather, three dogs with overlapping bodies. (This seems clear in the parallel case of human conjoined twins; everyone considers them to be siblings, two humans with overlapping bodies, not a human with two heads.) While Craig’s theory upholds (with the creeds) one divine substance, by his own criteria each of the three Persons must be a substance as well, and the account says that each Person is divine. Thus, the theory implies polytheism (393–5). Here God is not a personal being, in the sense of being numerically identical with a certain self, even though it (God) has parts which are selves. Craig wants to say, for example, that each of the three is all-knowing, and also that God is all-knowing, in that God has parts which are all-knowing. But Howard-Snyder objects that,