 This sort of foundationalist, infallibilist theory of knowledge is now thought of as Cartesian, but  Descartes  is simply following the Aristotelian tradition for which Aquinas became the preeminent spokesman. For Aquinas himself, however, the account just described serves as an aspirational ideal rather than a description of something we have actually attained. In practice, even where we have demonstrative knowledge, we usually cannot trace the principles all the way back to ultimate first principles like the law of non-contradiction. Critical questions, like the non-eternity of the world (§3), are contingent on the free choice of God and so have to be taken on faith. Even in places where certainty is possible in principle, large gaps in our knowledge remain. In general, “our cognition is so weak that no philosopher could have ever completely investigated the nature of a single fly” (On the Apostles’ Creed [Collatio in symbolum Apostolorum], proem). Accordingly, Aquinas distinguishes among various non-ideal cases. A demonstration that grasps the cause of a thing is a demonstration propter quid, but often—as in proving God’s existence—the best we can have is a demonstration quia, which tells us only that a thing is so. Much of what we know holds true only for the most part, and so fails to be necessary, and often the premises of an argument cannot be traced back to self-evident principles, in which case our argument is dialectical rather than demonstrative, yielding a conclusion that is merely plausible (probabilis) rather than apodictic.