Can a moral system be created purely through "logic and reason"?

In response to claim that morality can be created purely through logic and reason, I came up with the following argument:

It is difficult if not impossible to come to any conclusion whatsoever purely through logic and reason. Rene Descartes attempted to prove the existence of God this way. With what basic premise do you start?

He started with his famous dictum: Cogito ergo sum ("I think, therefore I am"), but his attempt to prove that God existed failed.

If we start this way, how do we possibly continue on to a complete system of morality? Can we make the second step to this: "To continue to think, and therefore exist, is desirable"?

Albert Camus concluded this: "There is but one truly serious philosophical problem, and that is suicide. Judging whether life is or is not worth living amounts to answering the fundamental question of philosophy."

The point is that no system that governs behavior can be created purely through logic and reason. We must start with some kind of premise or presupposition. We cannot use pure reason and logic alone to come up with a system of morality.