I recently posted on Malebranche's infinity challenge. In essence this challenge is this: Find an account of our idea of infinity that does not require that we perceive it in infinite being (i.e., God), and that does not illegitimately smuggle in the idea of infinity. It turns out to be very difficult to do; and, indeed, I think it is likely to be impossible for a number of very popular views of the mind today.
Now, Malebranche's vision-in-God thesis, the idea that all our ideas are divine ideas seen in God, was rejected, under the name 'ontologism' by the Catholic Church. Or, to be more exact, it was determined by Rome that Malebranche's thesis came dangerously close to a thesis that had already been condemned at the Council of Vienne (1311-1312), and this led to more specific condemnations in 1862. (Rather interestingly, the Council of Vienne gave Cartesians a great deal of trouble on other grounds as well; e.g., it asserts that the rational soul is the form of the body, and this was difficult to accommodate under a Cartesian view -- although not for lack of trying.) I haven't been able to find a text of the 1862 condemnations on-line, but John Paul II briefly mentions them, in a clear and lucid way, in section 52 of Fides et Ratio (although the note to that section gives the date as 1861; this is the only place I've seen that lists 1861 rather than 1862 - is this a typo in the encyclical, or is it the right date?).
So this brings up the interesting question: is there a way a Catholic (or anyone who agrees with the Catholic rejection of ontologism) could meet Malebranche's infinity challenge without accepting Malebranche's own solution?
I think there might be. A key premise in the argument is that we are finite substances. Now, this seems undeniable; but it would be possible to argue, I think, and on a scholastic view there would be good sense in arguing, that human beings are not finite in the relevant way, i.e., in the way required by the argument. Here is my thought. Most of the strength of Malebranche's argument comes from the fact that we can recognize mathematical infinites. Now, if, as scholastics hold, the rational soul is in itself immaterial, although fitted for a body, then it would follow that the soul is not finite relative to extension, i.e., not quantitatively finite. If the soul, however, is infinite in one aspect (it is not bounded by quantitative limits in some way), then this would seem to get around a great deal of Malebranche's argument. It still leaves some things unanswered, e.g., how we know the infinity of God - but there are scholastic answers to this. So there may be a scholastic answer to Malebranche. I can't think of any other account of the mind that would be able to provide such an answer: given that we can recognize potentially infinite things as infinite, either the intellect must in some sense be infinite or it must perceive something actually infinite - otherwise we have no explanation available to us of our situation.