In Meditation V of the Meditations on First Philosophy, Descartes considers a second argument for the existence of God. Descartes posits that the certainty of the existence of God should have “at least the same level of certainty” as the truths of mathematics.
This phrase could possibly be interpreted to mean either “certainly as certain as” or “more certain than.” A common view seems to be that since Descartes is reasoning from the Principle of Contradiction (PoC) that he is arguing for the certainty of God to be equal to that of mathematics. That is, since it is both impossible that a triangle should have other than three sides, likewise it is equally impossible that existence not appertain to God, hence they are of equal logical certainty per the PoC.
Working with this recently, I came to understand that Descartes concluded that the existence of God is more certain than that of mathematics, on ontological rather than logical grounds, thus that the phrase should be understood as “more certain than.” As I worked with the second argument I also found that it collapses on ontological grounds, as Descartes begs the question of the existence of God in the proof of the existence of God. What follows is an excerpt from a paper on the subject.
I find the resolution to the question of what he meant by “at least the same level of certainty” by examining not the argument from the PoC per se, but in its terms, in what was proven by the argument. What we see is that Descartes considered that he proved the existence of God. It is here that we find that Descartes considered that he had established that the existence of God was more certain than mathematics.
“…apart from God, there is nothing else of which I am capable of thinking such that existence belongs to its essence.” (Meditation V, emphasis mine)
In the above statement of Meditation V we find that for Descartes the existence of God is more certain than that of mathematics, as existence belongs to God’s essence alone. That is, in Meditation V Descartes argued on the basis of the logical certainty of the PoC to the ontological certainty of God. As eternally true as mathematics and geometry may be, existence is not of their essence; God alone is ontologically certain. Thus the truths of mathematics are ontologically contingent on the existence of God, and the existence of God must necessarily be more certain than that of mathematics and geometry for the latter to be certain. We find that this is consistent with the conclusion of the first argument in Meditation III; in that argument, Descartes concluded that the objective reality of God was greater than anything else, hence more certain than any other thing.
Descartes’ summary statement in the closing paragraph of Meditation V corroborates this view.
“Thus I see plainly that the certainty and truth of all knowledge depends uniquely on my awareness of the true God, to such an extent that I was incapable of perfect knowledge about anything else until I became aware of him. And now it is possible for me to achieve full and certain knowledge of countless matters, both concerning God himself and other things whose nature is intellectual, and also concerning the whole of that corporeal nature which is the subject-matter of pure mathematics.” (Meditation V, emphasis mine)
The emphasis in the above is mine, to point out that for Descartes the truths of mathematics and geometry, as certain as they are, follow on the certainty of God. On my view, this then is how we are to understand Descartes’ phrase “at least the same level of certainty.” Descartes intends this greater certainty not as logical certainty, but as ontological certainty, and in his consideration that was exactly what he had established in Meditation V by proving existence as necessarily, and solely, belonging to God’s essence. Thus the existence of God is a fortiori more certain than the truths of mathematics.
On this basis I propose that his argument of Meditation V is fallacious, in that he begs the question of the existence of God in the proof of God’s existence.
We have seen that in the second argument for the existence of God in Meditation V that Descartes considered that he had established the existence of God via the logical certainty of God with respect to mathematical and geometric verities. Arguing from the PoC, the certainty of the existence of God was established to be as certain, and as incontrovertible, as mathematical truth. That is, the ontological certainty of God is as logically certain as the verities of mathematics. However, as we have seen, Descartes also argued forcefully in Meditation V that existence belonged to God alone as part of his essence: God alone is ontologically certain.
It is here that we find that Descartes begs the question of the existence of God in proving the existence of God. In Descartes’ argument God alone is ontologically certain, hence the verities of mathematics are contingent on the existence of God. As he argued in the closing paragraph of Meditation V, without God there is no certain knowledge of mathematical and geometrical truths. Thus we find Descartes to be arguing for the existence of God to be at least as certain as mathematical truth, yet in the same argument concluding that God alone is ontologically certain, thus the knowledge of mathematical truth is contingent on the certain existence of God. That is, the certain existence of God is presumed, and necessary, for the truths of mathematics, from which truths then the certain existence of God is established.
On ontological grounds it is impossible that the argument of Meditation V should ever succeed, precisely because what Descartes wishes to establish is the existence of God. Since a key premiss of Descartes’ argument is that existence appertains solely to God’s essence, and thus that all else is contingent on the existence of God, there is therefore no possible reference for his argument that does not depend on, and thus beg the question of, God’s existence for its certainty.
I conclude that in the argument of Meditation V that Descartes begs the question of the existence of God, and the argument of Meditation V collapses.