St. Thomas’s proof that sacred doctrine is a science rests on the idea that some sciences start from things evident to everyone while others don’t, and theology is a science in the second way. In modern discourse, this second sort of science is one that starts with formulas (literally “the short forms”) i.e. a short instruction that tells one what to do in the face of certain facts, but the reason for which is more or less hidden. So we could learn Euclid II. 4, every part of which can be reduced down to his common notions evident in themselves, but we can also just give kids a formula that works to show the same thing, i.e.: “the FOIL method”.
What’s fascinating is the extent to which the first sort of science is has been occluded by the second. It’s all formulas now, and to try to chase down their basis often leads only to a haze of assumptions, simplifications, and the occasional a priori argument. St. Thomas was working from the idea that all formulas must be shorthand for the findings of a purely deductive system, but it’s not clear that this is so. While one can generally be confident of hitting an a priori argument for purely mathematical things, even here no one has yet been able to reconstitute a complete science that they all belong to. Everything seems to fade off into the haze of pure relations, something like St. Thomas’s Trinitarian persons. A fortiori, the possibility of a purely deductive physical system seems even more dim. Science has the occasional deductive argument (Newton’s Principia or Minkowski’s proofs for space time) but attempts at a full and complete system seem to shatter into more localized discourses that are held together by models, guesswork, thought experiments, things we know are false but which make the math easier, and (sure) the occasional a priori argument.
The upshot is that St. Thomas is defining theology in opposition to a kind of knowledge that we cannot have, at least not with anything like our cognitive powers as presently constituted. But this seems to re-orient the trajectory of science as a whole. The purely deductive system is still an ideal, and there must be some coherent basis of formulas, but this science does not seem to be achievable with knowledge as we have it now, since a deductive system along those lines collapses into Godel’s theorems and Quine’s critiques of deductive empiricism. Aristotle’s vision of the purely deductive system in Posterior Analytics seems to be pointing to a consciousness that we cannot now enjoy, but which we clearly see is possible – and which is even the necessary basis for what fragments of science we have.
What St. Thomas thought was peculiar to divine science, namely that it was based on formulas that could only be resolved in a higher consciousness (i.e. “the light of glory”) might perhaps be better applied to human knowledge as such. Our knowledge will advance and deepen over time, but not by finding the system of systems. All we’ll ever get from following out what we now have is a greater and greater plurality of dialectical systems, not some deductive universal axiomatic system. That’s what God and the saints enjoy, and we have only suggestions of it. And signposts.