Descartes discussed his position on the eternal truths in April of 1630 with Mersenne; the topic comes up because of Descartes's insistence that mathematical truths depend on God just like everything else:
It will be said that if God had established these truths he could change them as a king changes his laws. To this the answer is: Yes he can, if his will cna change. 'But I understand them to be eternal and unchangeable.'--I make the same jdugment about God. 'But his will is free.' Yes, but his power is beyond our grasp. In general we can assert that God can do everything that is within our grasp but not that he cannot do what is beyond our grasp. It would be rash to think that our imagination reaches as far as his power. (AT I, 146; CSMK 23)
Mersenne pressed for clarification so in a letter of early May, Descartes explains, linking the position to the strongly voluntarist Cartesian account of simplicity, in which divine knowing is a form of willing:
As for the eternal truths, I say once more that they are true or possible only because God knows them as true or possible. They are not known as true by God in any way which would imply that they are true independently of him. If men really understood the sense oftheir words they could never say without blasphemy that the truth of anything is prior to the knowledge which God has of it. In God willing and knowing are a single thing in such a way that by the very fact of willing something he knows it and it is only for this reason that such a thing is true. So we must not say that if God did not exist nevertheless these truths would be true; for the existence of God is the first and the most eternal of all possible truths and the one from which alone all others proceed. (AT I, 149-150; CSMK 24)
Mersenne was not satisfied and pressed the point again, so in late May we find Descartes explaining himself again:
You ask me by what kind of causality God established the eternal truths. I reply: by the same kind of causality as he created all things, that is to say, as their efficient and total cause....You ask also what necessitated God to create these truths; and I reply that he was free to make it not true that all the radii of the circle are equal--just as free as he was not to create the world. And it is certain that these truths are no more necessarily attached to his essence than are other created things. You ask what God did in order to produce them. I reply created things. You ask what God did in order to produce them. I reply that from all eternity he willed and understood them to be, and by that very fact he created them. Or, if you reserve the word created for the existence of things, then he established them and made them. In God, willing, understanding and creating are all the same thing without one being prior to the other even conceptually. (AT I, 151-153; CSMK 25-26)
Other things intervene, and thus this is all of the discussion at that time, but Descartes does briefly mention his thesis again in correspondence with Mersenne from 1638:
You ask whether there would be real space, as there is now, if God had created nothing. At first this question seems to be beyond the capacity of the human mind, like infinity, so that it would be unreasonable to discuss it; but in fact I think that it is merely beyond the capacity of our imagination, like the questions of the existence of God and of the human soul, I believe that our intellect can reach the truth of the matter, which is, in my opinion, that not only would there not be any space, but even those truths which are called eternal -- as that 'the whole is greater than its part' -- would not be truths if God had not so established, as I think I wrote you once before.... (AT II, 138; CSMK 102-103)
There is another passage in the correspondence, this time in a letter to Mesland from 1644, in which Descartes summarizes his position on eternal truths:
I turn to the difficulty of conceiving how God would have been acting freely and indifferently if he had made it false that the three angles of a trianglewere equal to two right angles, or in general that contradictories could not be true together. It is easy to dispel this difficulty by considering that the power of God cannot have any limits, and that our mind is finite and so created as to be able to conceive as possible the things which God has wished to be in fact possible, but not be able to conceive as possible things which God could have made possible, but which he has nevertheless wished to make impossible. The first consideration shows us that God cannot have been determined to make it true that contradictories cannot be true together, and therefore that he could have done the opposite. The second consideration assures us that even if this be true, we should not try to comprehend it, since our nature is incapable of doing so. And even if God has willed that some truths should be necessary, this does not mean that he willed them necessarily; for it is one thing to will that they be necessary, and quite another to will this necessarily, or to be necessitated to will it. (AT IV, 118, CSMK 235)
And he goes on to base this again on his conception of divine simplicity. There are a few other places that have a bearing, but these suffice for the basic picture.
Thus Descartes's position is easy enough to lay out:
(1) All truths whatsoever depend on the divine will, even mathematical and logical principles.
(2) Truths are necessary, possible, or impossible because God wills that they be.
(3) God's freedom and power is so extensive that he could even make contradictions true.
(4) God has eternally willed some things to be true (perhaps even necessarily true) so that they may be called eternal truths.
The controversies are over how to put this together. Some have argued that Descartes holds that no truths are strictly necessary (as opposed to always true); others have held (more plausibly, I think) that he holds that God makes some truths necessary, but that their necessity itself is contingent on the divine existence. One can interpret Descartes's claim as simply a stricture on us: we know that God is infinitely powerful, we know that God's infinite attributes exceed our finite abilities to comprehend them, so while we know some of the things God can do, we should never say that we know something He cannot do, because it could be that our reason for thinking so is just an effect of the finitude of our human minds rather than an actual limitation on divine power. But Descartes sometimes seems to suggest a stronger position, in which we actually know that God could have made necessary truths false or non-necessary.
(I started thinking about Descartes on eternal truths due to this post at "The Prosblogion".)
