A question that's been disputed here in the past is the existence of things not open to direct empirical verification, in the modern sense of the positive empirical sciences. One disputed reality is the existence of substances, which are not directly sensible, and which we only know through their "accidents" or sensible characteristics.
The book by Richard J. Connell I've been reading explains how metaphysical principles, such as substances, are known through their sensible, physical effects. As he writes on p. 175, "Undoubtedly, some people will be surprised to learn that, according to the Aristotelians, there is nothing in the intellect which was not originally in the senses in some manner."
Even the modern, empirical sciences infer the existence of non-sensible realities from their sensible effects:
Next, let us consider some examples from the experimental sciences. Magnetic fields are not directly observable; their existence is known through the medium of observable movements. Certainly, the observable motions are distinct from the magnetic fields and cannot be identified with them. These movements, which cannot be reduced to other, known attributes or realities, are the first things to be apprehended. The fact that they are not (notice the negation) accountable for by what is already known leads to the affirmation of another, unobservable attribute to explain the motion. The magnetic field is then conceived so as best to account for the observed effects. Indeed, the whole process of constructing an hypothesis on magnetic theory is measured by the demands of teh observed phenomena through which the very existence of the unobservable attribute is known.
An electric current is another illustration of the same kind of noetic procedure. The deflections of meter needles, the shocks that come from "hot" wires, etc.—surely none of these, either singly or collectively is the electric current. These phenomena lead to a knowledge of something else which is the current, but the phenomena themselves are not that current. (183-4)
So unless we want to dispose of the essences discovered by science, which are in themselves not sensible, there is no principled, non-arbitrary way to rule out inferences to metaphysical principles, even immaterial ones, so long as they have a basis in sensible reality.
The doctrine that has been outlined here can, I think, be interpreted to support the empiricists in their insistence upon the necessity of verifying the meaning of terms in sense experience, without, however, denying the reality of non-sensible substances and accidents; for, if their verification principle is understood as demanding that names signify either (1) things that are directly sensible, or (2) things that are not directly sensible but which are knowable through the medium of something that is, then the principle is true. On the other hand, the present doctrine, although insisting upon sense experience as the origin of intellectual knowledge, does not exclude true and meaningful metaphysical propositions, however difficult and infrequently attained the latter may be. To repeat, it does not, as a matter of principle, rule out all metaphysical statements, but only those which pretend to be prior and independent of experience—in other words, all rationalistic "metaphysics." (185)
Richard J. Connell, Matter and Becoming (Chicago: The Priory Press, 1966).