It is relatively easy to recognize that geometry and arithmetic are different kinds of science than biology and physics. There are plenty of people who think that a complete physics would explain everything in chemistry and biology and psychology; there are far fewer (none?) who think it will explain all the difficulties in mathematics. The one body of knowledge cannot be reduced to the other. For Aristotle and St. Thomas, there is a third body of knowledge that is just as irreducible as mathematics and physical science: metaphysics. “Irreducible” does not mean “unrelated”- just as there have always been important, unavoidable, and essential points of intersection between mathematics and physical science, there has always been intersections between metaphysics and other doctrines. But the irreducible and autonomous character of each of these sciences limits what we could assume could be given by a complete science.
The distinctive note of metaphysics is that it deals with what is not limited to material or mobile existence, where “motion” is understood as any imperfect state between two contraries (irrespective of whether there is rest at one of the contraries) and “material” is understood in relation to the activity of sensation (that whose existence and activity is proportionate to a corporeal organ). We do not know the things of metaphysics simultaneously or before we know the physical world, but we do know them in such a simultaneous fashion hypothetically. By “hypothetically” I mean by an “if..then” consequence. We know, simultaneous with our experience of the mobile and material world, that if a metaphysical entity exists, then it could be described positively by certain notions we gather from experience. Chief among these notions is the notion of “being”. It is not that we look at being and see its division into the physical and the trans-physical, rather we look at being and see that it is intrinsically incapable of being limited either to any kind of existence, even if the only kind of existence we happen to know is corporeal. Our notion of being is not such that it allows us to rule out the possibility of the trans physical. Such a judgment would require that being be a genus, which it is not.
Even after we set forth a proof that divides being into the corporeal and the incorporeal (and the reason why we call these two different “beings” is not made immediately clear at the moment) it is not the case that we can say “X percentage of the group ‘being’ is corporeal, 100-x percentage is incorporeal”. Being is not a collective whole like this. Collective wholes require homogeneity, and one of the first things that we can know about being is that it is not the name of a genus. “Being” not a logical whole like “animal” which contains vertebrates or invertebrates, or like “number” that contains both the even and the odd. There is no existent animal or number that is not some species of animal or number; but every existent being is not some species of being, since there are no species of being. Being could only have species if it was itself a genus, but it is not.
This character of being as non-generic requires as much expertise to understand as any other science. Who would expect a mathematician or physical scientist to have cultivated the sort of experience that helps him deal with being? How many people recognize that being is not a genus? After getting this, do they see its significance? What is there in physical or mathematical science that illuminates you to speak properly of the transcendence of being? Can anyone actually believe that a complete physics will solve the problem of the transcendence of being? Can anyone even believe that a complete physics would even raise the question? After you figure out these basic problems in metaphysics, you can move on to some really hard ones.