Nothing is necessitated whose opposite is possible.

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 a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.

Reality cannot be found except in One single source, because of the interconnection of all things with one another. I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general.

Let there be two possible things, A and B, one of which is such that it is necessary that it exists, and let us assume that there is more perfection in A than in B. Then, at least, we can explain why A should exist rather than B and can foresee which of them will exist; indeed, this can be demonstrated, that is, rendered certain from the nature of the thing.

In whatever manner God created the world, it would always have been regular and in a certain general order. God, however, has chosen the most perfect, that is to say, the one which is at the same time the simplest in hypothesis and the richest in phenomena.

Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.