Saturday, October 19, 2013

What Does Ross Say?

Well, no, I'm not making the sort of trivial, "silly" argument that Feser likes to ascribe to me. But before I can clarify this, it is necessary to clarify just what it is that Ross is saying.

Feser writes:

Part of the problem here might be that Oerter is not carefully distinguishing the following two claims:

(1) There just is no fact of the matter, period, about what function a system is computing.

(2) The physical properties of a system by themselves don’t suffice to determine what function it is computing.

Oerter sometimes writes as if what Ross is claiming is (1), but that is not correct.  Ross is not denying, for example, that your pocket calculator is really adding rather than “quadding” (to allude to Kripke’s example).  He is saying that the physical facts about the machine by themselves do not suffice to determine this.  Something more is needed (in this case, the intentions of the designers and users of the calculator). 

What exactly does Ross claim? Here is Ross from his paper:

Adding is not a sequence of outputs; it is summing; whereas if the process were
quadding, all its outputs would be quadditions, whether or not they differed in quantity from additions (before a differentiating point shows up to make the outputs diverge from sums).

For any outputs to be sums, the machine has to add. But the indeterminacy among incompossible functions is to be found in each single case, and therefore in every case. Thus, the machine never adds.

Extending the outputs, even to infinity, is unavailing. If the machine is not really adding in the single case, no matter how many actual outputs seem "right," say, for all even  numbers taken pairwise (see the qualifying comments in notes 7 and 10 about incoherent totalities), had all relevant cases been included, there would have been nonsums. Kripke drew a skeptical conclusion from such facts, that it is indeterminate which function the machine satisfies, and thus "there is no fact of the matter" as to whether it adds or not. He ought to conclude, instead, that it is not adding; that if it is indeterminate (physically and logically, not just epistemically) which function is realized among incompossible functions, none of them is. That follows from the logical requirement, for each such function, that any realization of it must be of it and not of an incompossible one. [emphasis added]
Ross is quite clear: he is not saying (2) at all. Neither is he saying (1). He is saying something stronger than either (1) or (2): the machine does not add - period. It is not that the physical properties of the system alone don't determine what function it is computing, the system isn't actually computing any function at all. "... if it is indeterminate (physically and logically, not just epistemically) which function is realized among incompossible functions, none of them is."

I just don't see how Feser can write "Ross is not denying, for example, that your pocket calculator is really adding rather than “quadding”..." for that is exactly what Ross is denying. 

It is this denial I had in mind when I said Ross couldn't apply the same reasoning to Hilda without denying that Hilda adds, too. But rather than re-visit that argument I will wait for the professor to (I hope) clarify. 


  1. I hadn't read Ross, only what Feser claims about him. I still haven't gone through the whole paper but I read enough to see your point. Feser has whitewashed Ross. Ross is even more confused than I thought. Ross does claim adding machines don't add. He means more by that than indeterminacy of meaning. But it's not clear what he means. And it's not clear what he means by "pure addition" either. I think he's deified his thought processes. I remember learning addition in grade school. There was no "pure addition" to it. It was flash cards and memorization. Then it was learning how to execute the algorithm properly. It was pretty messy stuff. How that became "pure" in Ross's mind is a mystery.

  2. I've read Ross's paper now. In Part I (determinacy of logical processes) it adopts a traditional, instinctive, essentialist view, and then pretty much just insists that we must accept this view. For example:

    "The single case of thinking has to be of an abstract "form" (a "pure" function) that is not indeterminate among incompossible ones. For instance, if I square a number-not just happen in the course of adding to write down a sum that is the square, but if I actually square the number-I think in the form "N X N = N2." "

    What does this mean? I assume Ross is not claiming that he must utter to himself the words "N X N = N2". But, absent that, what constitutes thinking in that form? All we need are some processes which pretty reliably produce the right result. And we can acquire those by practice. Why do we need anything more than that? Ross doesn't tell us.

    "Yet the "function" does not consist in the array of inputs and outcomes."

    Really? When children learn times tables by rote, and use them as the basis for multiplying small numbers, are they not multiplying? And don't we all continue to multiply small numbers in an automatic, habitual way as we get older? Though some of our arithmetic involves recollection of and attention to rules, much of it remains habitual. Ross gives no reason why such processes are insufficient for our purposes. If he merely denies that we can call them "multiplying", I think he's denying us a sensible use of language, but who cares. What's in a name? A rose by any other name...

    In Part III Ross puts into a critic's mouth the words, "We do not really add, either; we just simulate addition." I agree with the critic that we don't need Ross's mysterious "pure" functions. But I object to the insinuation that the critic must call the alternative "simulated addition". There's no reason why we can't continue to call what we do "addition". In any case, Ross is again mistaking a linguistic point for a substantive one. If we agreed to call what humans and calculators do "simulated addition", then "simulated addition" would be all we need, and we could carry on just as before. Contrary to Ross's assertion that this would be "expensive", nothing would change but our language. In fact we'd soon get tired of inserting the word "simulated" into our language so often, and we'd drop it again. That said, it would have a cost to philosophy. Calling what we do "simulated addition" would encourage the kind of misunderstanding of language that Ross exemplifies here.

  3. Robert, I agree with your interpretation of Ross. It's further supported throughout the rest of that section. At no point that I can see does Ross suggest that he has an alternative explanation which makes calculators capable of addition after all.

    Furthermore, I think the argument Feser attributes to Ross does Ross no favours. It argues only that determination requires the existence of human intentions. But physicalists generally accept the existence of human intentions. So this argument would do Ross no good unless he had already refuted physicalism.

  4. Good points, Richard. On the last point, I was waiting to see what Feser replies, but I agree with you, I think he's sunk either way.

    On Ross's "pure functions", he defines them in the book (in a footnote) as follows:

    "A pure function is one satisfied for an infinite number of functors, and determinate for each n-tuple, like "+", and complete in each and every instance (that is, it does not consist in a relationship among its cases, but explains them)."

    I have no idea what that last clause is supposed to mean.

    Ross seems to be aware that a complete list of inputs and outputs is a perfectly valid way of specifying a function - at least, he avoids claiming that the function is indeterminate even when the complete list is known. Feser, OTOH, seems to think that even a complete list doesn't do it.

  5. In case you're interested, Robert, I've just added a comment to Feser's latest blog post.