Malebranche considers the following (Descartes-influenced) type of argument (it has several slightly different but closely related versions).
1. It is at least possible that there are external bodies.
2. We have nothing that proves to us there are no such bodies.
3. We have a strong inclination to believe there are such bodies.
4. Therefore, we have more reason to believe there are such bodies than to believe there are not any, our natural judgment being that there are.
5. We should follow our natural judgment when we cannot positively correct it by reason.
Therefore, we should believe there are external bodies.
Malebranche's attitude toward this argument is ambivalent. He calls it "sound enough," but denies that it is demonstrative. That is, he thinks that while the argument is correct in all its claims, we are capable of suspending judgment on it. On Cartesian principles, when we can suspend judgment we should, at least for theoretical purposes. The conclusion only follows with probability, not certainty; and in the eyes of Cartesians like Malebranche who are concerned with defeating skepticism, probability is not good enough.
His attitude can be contrasted with another Cartesian, Arnauld, who accepts this sort of argument as demonstrative. The issue between them is (5), or rather, the argument for it. The basis for (5) is this. We are set up in such a way that we tend to believe certain things. We are also made by God. If God made us so that we could not help but believe something false (i.e., such that we could not correct our belief), He would be a deceiver. God is not a deceiver. Therefore if we are made so as to believe something by natural judgment, and cannot correct our belief, what is believed is true. Both Malebranche and Arnauld agree with all this; but Malebranche is not convinced that we can apply this with certainty in this case. For it to apply, God must in some sense reveal to us that bodies exist, either by designing us a certain way or by some sort of revelation. While we are designed to tend to believe that bodies exist, we know that this design is linked entirely to issues of preservation, avoiding pain, etc.; that is, our tendency is wholly a matter of practice. We cannot conclude from this that God's intention in the design was that we believe that bodies really exist, rather than simply making it easier to live in the world by giving us a useful fiction. Therefore, Malebranche thinks we can only apply this reasoning with certainty if we have some way of being certain about the intentions of our design, which can only be the case if 1) we have clear information about our design (Malebranche thinks Adam in Eden would have had such information, but we certainly do not, because of original sin); or 2) our designer actually tells us through some message (Malebranche opts for this).
Arnauld, on the other hand, is clear that he thinks that, given our natural tendency to believe in the existence of bodies external to our minds, God would be a deceiver if there were no such bodies.
My own view on this point is that Malebranche has the stronger argument. In a Cartesian framework, "God is not a deceiver" is a good reliability-ensuring principle at a very general level of the design. That is, if God is not a deceiver, the cognitive faculties he gave us must be able to come to the truth. But there is nothing in the principle to tell us how easy or difficult coming to the truth might be, nor does it seem to give us any certainty about particular beliefs. Any thoughts?