Brian Bosse raised this question over the phone the other day. This re-post from February 2010 answers it.
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According to the Athanasian Creed, the Persons of the Trinity, though each of them uncreated and eternal and necessary, are related as follows. The Father is unbegotten. The Son is begotten by the Father, but not made by the Father. The Holy Spirit proceeds from the Father and the Son. Let us focus on the relation of the Father to the Son. When I tried to explain this to Peter the atheist, he balked at the idea of one necessary being begetting another, claiming that the idea makes no sense. One of his arguments was as follows. If x begets y, then x causes y to begin to exist. But no necessary being begins to exist. So, no necessary being is begotten. A second argument went like this. Begetting is a causal notion. But causes are temporally precedent to their effects. No two necessary beings are related as before to after. Therefore, no necessary being begets another.
I first pointed out in response to Peter that the begetting in question is not the begetting of one animal by another, but a begetting in a different sense, and that whatever else this idea involves, it involves the idea of one necessary being depending for its existence on another. Peter balked at this idea as well. "How can a necessary being depend for its existence on a necessary being?" To soften him up, I looked for a non-Trinitarian case in which a necessary being stands in the asymmetrical relation of existential dependency to a necessary being. Note that I did not dismiss his problem the way a dogmatist might; I admitted that it is a genuine difficulty, one that needs to be solved.
So I said to Peter: Look, you accept the existence of Fregean propositions, items which Frege viewed as the senses of sentences in the indicative mood from which indexical elements (including the tenses of verbs) have been removed and have been replaced with non-indexical elements. You also accept that at least some of these Fregean propositions, if not all, are necessary beings. For example, you accept that the proposition expressed by '7 + 5 = 12' is necessarily true, and you see that this requires that the proposition be necessarily existent. Peter agreed to that.
You also, I said to him, have no objection to the idea of the God of classical theism who exists necessarily if he is so much as possible. He admitted that despite his being an atheist, he has no problem with the idea of a necessarily existent God.
So I said to Peter: Think of the necessarily existent Fregean propositions as divine thoughts. (I note en passant that Frege referred to his propositions as Gedanken, thoughts.) More precisely, think of them as the accusatives or objects of divine acts of thinking, as the noemata of divine noeses. That is, think of the propositions as existing precisely as the accusatives of divine thinking. Thus, their esse is their concipi by God. They don't exist a se the way God does; they exist in a mind-dependent manner without prejudice to their existing in all possible worlds. To cop a phrase from the doctor angelicus, they have their necessity from another, unlike God, who has his necessity from himself.
So I said to Peter: Well, is it not now clear that we have a non-Trinitarian example in which a necessary being, the proposition expressed by '7 + 5 = 12,' depends for its existence on a necessary being, namely God, and not vice versa? Is this not an example of a relation that is neither merely logical (like entailment) nor empirically-causal? Does this not get you at least part of the way towards an understand of how the Father can be said to beget the Son?
To these three questions, Peter gave a resounding 'No!' looked at his watch and announced that he had to leave right away in order to be able to teach his 5:40 class at the other end of the Valle del Sol.
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