Do machines compute functions?

Robert Oerter has now replied to my most recent post about his criticisms of James Ross’s argument for the immateriality of the intellect.  Let me begin my rejoinder with a parable.  Suppose you presented someone with the argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal.  He says he is unconvinced.  Puzzled, you ask him why.  He replies that he is surprised that you think Socrates is mortal, given that you believe in the immortality of the soul.  He adds that all you’ve done in any case is to make an epistemological point about what we know about Socrates, and not really given any reason to think that Socrates is mortal.  For though the conclusion does, he concedes, follow from the premises, and the premises are supported by the evidence, maybe for all we know there is still somehow more to men than what the premises tell us.

You point out in response that given what you mean by “mortal,” there is no conflict here with the idea of the immortality of the soul, which is in any event completely irrelevant to the subject at hand.  You also point out that the fact that we can raise eccentric epistemological questions about the premises doesn’t entail that the argument is at all doubtful, much less that it is making a merely epistemological point.  And of course, as you also point out in passing, it is at any rate very odd to read the “All men are mortal” argument as epistemological given the way it has always been understood.

He now responds that you have not addressed his objections, since what matters is not that the argument has always been intended in a non-epistemological way, but whether it really is non-epistemological.  He also suggests that you are employing a double standard insofar as if you were consistent you would say that Socrates’ wife Xanthippe is mortal too, and yet you don’t talk about women but only men. 

You patiently note in reply that you have addressed his objections and that the passing remark about how the argument has always been understood was not the main point.  And you also note that there is no inconsistency, since “men” is obviously being used in the inclusive sense, intended to apply to female human beings as well as to male ones. 

His rejoinder is to insist that what the argument says is that all men are mortal, and that it quite clearly makes no reference to women.  Hence you are (he insists) not representing the argument correctly. 

At this point, as the Twilight Zone theme starts to play in your mind, you might have thoughts like the following.  First, none of what your interlocutor has said casts any serious doubt on the validity of the “All men are mortal” argument or on the truth of its premises.  It mostly doesn’t even really address the argument at all but just dances around it.  Hence you might wonder what on earth your interlocutor is going on about, and why he thinks it matters.   For that reason you would be baffled by the fact that he thinks he has somehow “sunk” the argument (as he confidently says he has).  If you were in an uncharitable mood, you might at least be tempted to wonder whether he is, after all, less interested in trying to understand and evaluate the argument than in coming up with ways to resist a conclusion he doesn’t like.  More charitably, you might think he is just confused. 

I must say that thoughts like these are increasingly going through my mind as this exchange continues.  Ross’s basic argument, you’ll recall, is: (A) All formal thinking is determinate, but (B) No physical process is determinate, so (C) No formal thinking is a physical process.  This is greatly oversimplified since Ross says a lot in defense of each premise, but that’s the basic structure.  The argument is valid, so to undermine it a critic would have to show that at least one of the premises is false.   Ross’s main considerations in favor of (A) have to do with the incoherence of trying to deny it.  Oerter has so far offered no response at all to (A) or the arguments for it.  He has focused instead on (B), and his main contention has been that the indeterminacy in question is really epistemological rather than metaphysical.  I have shown that he has not established this at all, and he has failed to respond to my criticisms.  Instead he has turned to questions of Ross exegesis, taking issue with what I said in the following passage from my previous post:

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). 

Oerter insists that I am misunderstanding Ross here.  As we will see in a moment, I am not misunderstanding him at all, but it is important to emphasize that even if I were, that would be completely irrelevant to the question of whether the argument for the immateriality of the intellect that we are debating is sound.  For one thing, and quite obviously, whether or not I have gotten Ross right on some exegetical matter is irrelevant to whether premises (A) and (B) of the argument in question are true, and whether the conclusion (C) follows from them.  So Oerter is, whether he realizes it or not, just changing the subject.  For another thing, it is not just Ross’s views that are in question here, but mine.  And I can assure Oerter that what I am claiming is (2) rather than (1).  So, even if what he had to say in his latest post was relevant to the cogency of Ross’s version of the argument in question, it wouldn’t affect my own version of it.

But as I say, Oerter just gets Ross wrong anyway.  In criticism of my claim that Ross is asserting (2) rather than (1), Oerter cites the following passage from p. 142 of Ross’s article “Immaterial Aspects of Thought”:

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]

End quote.  On the basis of this, Oerter triumphantly concludes: “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.”

Pretty damning, huh?  Well, no.  For what Oerter does not do is quote the very next paragraph from Ross’s paper, which completely undermines his interpretation.  Here it is:

There is no doubt, then, as to what the machine is doing. It adds, calculates, recalls, etc., by simulation. What it does gets the name of what we do, because it reliably gets the results we do (perhaps even more reliably than we do) when we add by a distinct process. The machine adds the way puppets walk. The names are analogous. The machine attains enough reliability, stability, and economy of output to achieve realism without reality. A flight simulator has enough realism for flight training; you are really trained, but you were not really flying. [emphasis added]

End quote.  So, Ross plainly does say that there is a sense in which the machine adds -- a sense that involves simulation, analogy, something that is “adding” in the way that what a puppet does is “walking.”  How can that be given what he says in the passage Oerter quotes?  The answer is obvious: The machine “adds” relative to the intentions of the designers and users, just as a puppet “walks” relative to the motions of the puppeteer. The puppet has no power to walk on its own and the machine has no power to do adding (as opposed to “quadding,” say) on its own.  But something from outside the system -- the puppeteer in the one case, the designers and users in the other -- are also part of the larger context, and taken together with the physical properties of the system result in “walking” or “adding” of a sort. 

In short, Ross says just what I said he says.

Evidently the reason Oerter thinks all this is worth spilling pixels over is that he thinks his “Hilda” example shows that Ross is being inconsistent, and he needs for me to have gotten Ross wrong in order to make his “Hilda” example work.  I have already explained, in my previous post, why Ross is not at all being inconsistent.  But even if he were, it wouldn’t matter.  The alleged inconsistency, you’ll recall, is that Ross treats Hilda as adding despite the fact that we can’t tell from her physical properties alone whether she is, whereas he does not treat the machine as adding despite the fact that we can’t tell from its physical properties alone whether it is.  Suppose he really were inconsistent in this way.  How does that show that premise (B) of his argument is false (much less that (A) is false, or that the conclusion doesn’t follow)? 

Answer: It doesn’t.  The most such an inconsistency would show is that Ross needs to clarify what is going on with Hilda that isn’t going on with the machine.  And there are several ways he can do this consistent with the argument.  First, he could say what I would say (and what, as I have shown, he does in fact say himself, despite what Oerter thinks) -- namely that the machine does add in a sense, but just not by virtue of its physical properties alone.  There is perfect consistency here -- both systems, Hilda and the machine, add (albeit in analogous senses), but neither does so in virtue of its physical properties alone.

Second, he could opt for a Cartesian view of human nature and say that Hilda’s physical properties are in no sense involved in her adding.  Both the machine and Hilda’s brain are, on this interpretation, utterly devoid, even in an analogous sense, of anything like addition.  The difference is that Hilda’s body is associated with a Cartesian res cogitans that is what is really doing the adding.  There is perfect consistency here too, since Ross would be treating both physical systems -- the machine and Hilda’s body -- exactly alike.  This option might open up the epistemological question of how we can know Hilda’s res cogitans exists, but as I have emphasized ad nauseam, such epistemological issues are irrelevant to the metaphysical issue.  But this is, in any event, not Ross’s view, since his dualism is not of the Cartesian sort but rather of the Scholastic sort.  He makes clear on the very first page of the paper that he holds only that “truth-carrying thoughts cannot be wholly physical (though they might have a physical medium)” [my emphasis] and he adds in footnote 5 that:

But in part [physical], yes, in the sense that my utterances are physical. Moreover, the thought may not even be possible apart from feeling or sense, just as a gesture is not possible without bodily movement. The target in this paper is theories that thoughts are "no more than" physical or functions determined physically; not that, for us, they are "at least physically realized."

Third, Ross could even decide to deny that Hilda, any more than the machine, is adding -- that is to say, he could opt to become an eliminative materialist.  That is, in effect, what writers like Churchland, Rosenberg, et al. do.  They essentially accept the argument from (A) and (B) to (C) and in order to hold on to physicalism just conclude that there is, in the strict sense, no formal thinking rather than that there is formal thinking and that it is immaterial. 

Of course, Ross would not want to take either the second or third option, but the point is that merely to accuse him of inconsistency vis-à-vis the “Hilda” example does nothing to undermine his argument, but at most raises questions about what lessons to draw from it.  And Ross not only has an “out” with the first option -- it is just what he always had in mind all along.