Feser summarizes Ross's argument like this:
All formal thinking is determinate.
No physical process is determinate.
Thus, no formal thinking is a physical process.
Specifically, Ross refers to "pure functions" that humans can define but that cannot be implemented by any purely physical system. He gives examples like adding, squaring a number, and the modus ponens of logic.
Now, what makes Ross think that a physical system cannot add? Of course he knows that mechanical devices and computers are capable of performing sums, but he says they are only simulating addition, not truly adding. He writes:
Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process "satisfies." That condition holds for any finite actual
"outputs," no matter how many. That is a feature of physical process itself, of change. There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms ("functions"), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y + 1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.
Now, I can go along with Ross as far as the epistemological aspect of his conclusion: no matter how many input-output pairs we examine, we can never know what function is being computed. But Ross claims much more: he says physical systems are not just epistemologically indeterminate but "physically and logically" indeterminate, too. That is, it's not just that we can't know what function the machine is computing, but there really is no fact of the matter about what the output will be until it actually happens.
The problem is, the argument Ross gives is not up to the task of proving that claim.
First of all, what does Ross mean by "empirically adequate"? He is not using this in the sense of van Fraasen, for whom empirical adequacy means agreement, not just with all past observations, but with all possible observations. For Ross explicitly mentions a "differentiation point", possibly at some remote future time, at which the outcomes disagree. Nor does he mean "agreement with all future observations", for the same reason. So he must mean merely "agreement with all past observations."
But having two hypotheses that agree with all past observations is not enough to tell us that the physical system is actually (physically) indeterminate. It only says that our information is insufficient to distinguish between the two.
Another example Ross gives is the problem of determining a function, knowing only a finite number of data points. He (correctly) points out that there is an infinity of curves that will agree on those finite data. But this just says we don't know what the function is that produced the data. It doesn't follow that there is no such function at all. But that's what Ross needs for his conclusion that physical systems are not just epistemically indeterminate, but physically indeterminate.
Ross's other arguments draw on Goodman's and Quine's work. These, too, also only reach as far as epistemology. Goodman's grue problem suggests that we can never know for sure whether we are inducting on the right categories. But it is a long way from that epistemological claim to the claim that there are no correct categories for induction to work on. Duhem's claim about undertermination says only that we can't know what part of whole complex of assumptions, theories, and practices is at fault when an experiment disagrees with theory. Again, this is only an epistemological claim. True, Quine tried to extend this uncertainty to the whole realm of human knowledge - but this extension hardly helps Ross's claim that humans can add, employ modus ponens, etc. Thus,none of Ross's arguments, either in the article or in his book, Thought and World, take us beyond epistemological indeterminacy.
I have to say it is exceedingly odd to see Feser defending physical indeterminism here. In our discussions of quantum mechanics and causation he argued strenuously that there is no such thing as physical indeterminism - not even in the case of quantum mechanics (where nearly all physicists accept fundamental indeterminism). So I'm wondering how Feser can square real, physical and logical indeterminism with the principle of causality.