Divine production and the 'Creation Problem'

The Nicene Creed states that when the Father begets the Son, the Father does not create the Son out of nothing. For a Christian scholastic like Scotus or Ockham, this suggests that no divine person is created:

(T1) For any divine persons x and y, if x produces y, x does not create y from nothing.

Now, if the Son and Spirit cannot be produced from nothing, then it might be tempting to think that they must be produced from something. But what could that 'something' be? Surely it cannot be any pre-existing materials. After all, the Son and Spirit are spiritual beings, so how could they be 'made' from anything material? It seems very plausible to think that the Son and Spirit cannot be produced from materials at all. Thus:

(T2) For any divine persons x and y, if x produces y, x cannot produce y with any material M.

However, (T1) and (T2) lead to problems. Consider the following.

Aristotle maintains that nothing can be produced unless it is produced from pre-existing materials. According to (T2) though, a divine person (e.g., the Son) cannot be produced from pre-existing materials. Thus, a divine person (like the Son) cannot be produced at all:

(1) For any x and y, if x produces y, x cannot produce y without any material m.
[From Aristotle.]

(2) The Father cannot produce the Son with any material m.
[From T2.]

(3) Therefore, the Father cannot produce the Son.
[From (1) and (2).]

Of course, scholastics like Scotus and Ockham want to affirm that

(4) the Father produces the Son,

but that contradicts(3), so one cannot hold all these claims at the same time, on pain of contradiction.

In order to avoid this, one might be tempted to give up Aristotle’s claim in (1), just as Avicenna did. After all, Avicenna was a good Muslim, so he believed in creation: some things can be produced without pre-existing materials.

However, Avicenna also holds that if a product is produced without any pre-existing materials, then it must be created from nothing. And that would entail that if a divine person is produced without pre-existing materials (as T2 says), then that person would be created from nothing.

(1*) For any x and y, if x produces y without any material m, x creates y from nothing.
[From Avicenna.]

(2) The Father cannot produce the Son with any material m.
[From T2.]

(3*) Therefore, if the Father produces the Son, the Father creates the Son from nothing.
[From (1*) and (2).]

But according to the Nicene Creed, no divine person is created from nothing, so:

(4*) if the Father produces the Son, the Father does not create the Son from nothing.
[From T1.]

But that contradicts (3*), so again we get a contradiction.

On the face of it then, both Aristotle’s and Avicenna’s theories of production present scholastic authors like Scotus and Ockham with a problem. For Aristotle’s and Avicenna’s theories entail that either the Son and Spirit cannot be produced at all, or they must be created from nothing, and neither consequence is acceptable for the Christian schoolmen. Hence, what I call the Creation Problem: how can the Son and Spirit be produced, but not created?