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I’d say no.I have read Ross’s paper, and find it incredibly interesting, even if I am not full behind it as of yet (due primarily to my lack of complete understanding of it all).
I think I have a general idea of what he is getting at though. Say that one employs modus ponens in an act of reasoning. Going with the assumption that such reasoning is an entirely physical process (whether the reasoning itself is reducible to or emergent from said process), this process or function is going to be executed by various neuronal firings in the brain. For example:
(1) If Socrates is a man, then Socrates is mortal.
(2) Socrates is a man.
(3) Therefore, Socrates is mortal.
Here, the neural firings (or whatever physical process) corresponding to premises 1, 2, and the conclusion 3 will be of such-and-such an organization. The problem, however, it that one can use an invalid form as well. One can use a logical function like “modus phonenz”: p -**> q; p, ∴ q = p → q; p, ∴ q when p has a major premise whose subject starts with the letter “S,” ∴ r otherwise. Now, “modus phonenz” is obviously an invalid argument form, despite the fact that the premises and conclusions are still true, as well as the fact that the physical process corresponding to the reasoning process will be exactly the same. This is because the physical process is simply connecting the two premises and the conclusion, both in the case of modus ponens and in the case of “modus phonenz.” And one can think of any invalid form to correspond to an argument, depending upon the criterion necessary for validity. Thus, physical processes are indeterminate between incompatible forms.
The problem then, and one materialists seem to often deny for some reason, is that we do in fact have determinately formal thought when reasoning. If not, any argument we would ever make would be invalid, including any materialist position.
Does this seem to get it right?
Google Scholar lists only 16 citations of Ross’s paper, which implies it never managed to break outside the small hylomorphic philosopher community. Part of the reason, as you say, is the level of difficulty imposed by his terminology.
But mainly, I think it’s clearly implausible. In his example of NN, there’s no evidence that we can set up such programs in our minds, and that when I ask myself what is 1010 or 1616, it somehow goes to a CPU in my head. Actually, for 1010 I probably already remember the answer, but if not I may think “put a zero to the right of the first ten”. For 16*16, I happen to know the same trick works in any number base, so 16 in hexadecimal is 10, put a zero to the right of it, = hex 100, which I remember is 256 base ten. We all use such tricks, and the tricks depend on our past learning, we never calculate the way a computer would.
Same goes for logic and your example. The reason we’re so slow and error prone compared to a computer is that we don’t have a CPU’s programmable logic unit and arithmetic unit. So imho his premise of determinately formal thought is, at the very least, implausible.