At Dr. Feser's blog, in the post alerting his readers to my posting "Immaterial Aspects of Thought" at FCA, a reader, David Brightly (DB), objected and I replied.
DB: "Isn't Ross, in his section II, really making an epistemological point? … we can see that every output will be the perfectly determinate sum of the inputs, provided the device operates within its design range of ambient conditions. … He's saying that it's indeterminate what the device is doing. I'm afraid I flatly disagree."
As Dr. Feser replied, the epistemological point hinges on an ontological difference between a plus- and a quus-machine (pm and qm). To wit, that the latter is “informed” in a way formally incompatible with how the latter is informed. In fact, the argument about physical indeterminacy wouldn’t even require differentiating outputs, since the outputs for the pm could be triggered by auditory inputs of the form “five,” “fünf,” “cinco,” etc., whereas the identical outputs on the qm could be triggered by—and therefore represent—auditory inputs of the form “John,” “Mary,” etc. Let us then imagine that the outputs for the pm were recorded by a digital video camera and set off fireworks, whereas the outputs of the qm triggered a video camera to shut off an idling engine down the street. In this way, both pm and qm would be “doing different things,” even though their physical composition and input/output array were identical.
I imagine the objector will say pm and pm are, on my hypothesis, actually just parts of larger physical systems—call them S(pm) and S(qm)—which are determinate in their own ways. The problem is that this objection already grants the essential point, namely, that, in and of themselves in purely physical terms, pm and qm are formally indeterminate. For all we know—and literally, for all their doing physically—they could always be running different functions. Indeed, even if we established the “forms” of S(pm) and S(qm), we could just rig one of them to a new video camera system and trigger some different physical outcome, in which case, even the larger systems would be indeterminate with respect to their endless formal possibilities. It’s not just that we don’t know which function a physical/material system is “running”; the problem is that nothing about the systems themselves in purely physical/material terms restricts—determines—their being instances of a single formal operation. Pure functions, however, can never be indeterminate in this way, and therefore crucially differ from physical systems. A pure function—say, addition—can never even possibly be “running” a different incompossible operation than what it is, nor can it even possibly “mutate” to alter its formal parameters without ceasing to be the same formal operation. Add to this that pure functions exhaustively include every possible instance of themselves, whereas any single case of a function in purely physical terms is just that—a single case of some function—and therefore the single-physical case is intrinsically formally-incommensurate with the instance-exhaustion of any pure function.
Presumably, the objector would claim that all physical functions are determinate in the sense that they all “tie in” to the entire cosmos. In this way, all physical systems would be like massive Rube Goldberg devices (e.g., S(qm) triggers a video camera to shut off a car, which traps a chicken inside, which kills the chicken and release noxious fumes, which float into the atmosphere, which deflect photons back into space, which eventually get sucked into a black hole, etc.”). The problem is, no matter how Byzantine one made his Goldberg cosmos, it would still be intrinsically formally-indeterminate, since it could suddenly advert to running an incompossible somewhere down the spatiotemporal road (“amplified grueness”). For that matter, the cosmos could collapse and cease to be—would we then be justified in saying any formal functions also ceased to exist? Purely formal functions cannot ever advert to running a different function, nor can they be limited to a subset of their instances. Hence, even the cosmos as a purely physical system is intrinsically indeterminate in a way formal operations cannot be. If the human mind is a purely physical system, it follows that our minds are always just as intrinsically indeterminate with respect to cases of formal truth, which means we never actually and formally-determinately perform pure functions, which is absurd. That is Ross’s argument.