I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.

When God works miracles, he does not do it in order to supply the wants of nature, but those of grace. Whoever thinks otherwise, must needs have a very mean notion of the wisdom and power of God.

I hold that it is only when we can prove everything we assert that we understand perfectly the thing under consideration.

I agree with you that it is important to examine our presuppositions, throughly and once for all, in order to establish something solid. For I hold that it is only when we can prove all that we bring forward that we perfectly understand the thing under consideration. I know that the common herd takes little pleasure in these researches, but I know also that the common herd take little pains thoroughly to understand things.

Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.

All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate.

It is necessary to believe that the mixture of evil has produced the greatest possible good: otherwise the evil would not have been permitted.