Friday, November 15, 2013

A Pointless Point about Data Points

I've been, and continue to be, busy with my real work, so I have to apologize if these posts dribble out slowly, a bit at a time, rather than in one long, well-thought-out post the way Prof. Feser does. But maybe it will actually be an advantage to try to clear up one point at a time.

Ross gives three main arguments to support his claim B: "No physical system is determinate." These are:
  1. Kripke's addition/quaddition argument.
  2. Goodman's grue argument.
  3. The problem of limited data.
Kripke is the central point of Ross's argument, and it is the most difficult to tackle. I'm going to start at the other end, with (3).

The problem of limited data (PLD) is pretty easy to state. Suppose I have some system from which I can take data, and I am trying to determine what function the system is following in order to produce the data. If I take a limited number (say a finite number) of input-output pairs, there will be an infinite number of functions which fit the given data points. For example, suppose I have only three data points. Then there is exactly one quadratic function that will exactly fit those three points. But I could also fit the data with a cubic function, or a quartic function, or a polynomial of any higher degree, or an exponential function times an appropriate polynomial, etc.

Now, how does this help Ross establish his (B)? Actually, it doesn't help at all. The mere fact that I have a limited amount of data doesn't tell me anything about the process that is producing that data. Since the PLD applies equally to determinate and indeterminate systems, it can't. This seems completely obvious to me, but since it seems to be a point of contention, I will spell it out.

Suppose I get some set of N input-output pairs from a determinate process. (For Ross, this means having a human compute them.) Let someone else give me N input-output pairs from an indeterminate process that is simulating (in Ross's sense) the first process. (For Ross, this could be a computer.) Now, since Ross allows that the indeterminate process can simulate the determinate process very closely, the two data sets will be identical. (This is easy to see if we say the process in question is addition: the computer and the human will give the same outputs for the same inputs. Unless, of course, the human makes a mistake.)

Since the N input-output pairs are identical whether I get them from a determinate or an indeterminate process, there is obviously no way I can tell from the data which sort of process produced that data.

Now let's introduce the PLD. Clearly, it applies to both processes. So if (as Ross claims) the PLD provides support for the claim that the purely physical process is indeterminate, then it also provides support for the claim that the human-generated process is indeterminate. So the PLD strengthens Ross's case for B to the exact extent that it weakens his case for A (that humans are capable of determinate processes). In other words, it doesn't help him at all.

This is what I meant when I wrote that Ross's arguments don't go beyond epistemology. The PLD says I can have only limited knowledge about the process that produced the data. But it says nothing at all about the metaphysical properties of that process.


  1. Hi Robert,

    I think you've been misled by Ross. Although he appeals to work on "underdetermination" in support of his premises, his own argument has nothing to do with underdetermination, at least not in the sense of the underdetermination of theory by evidence, so that appeal is misleading. He seems to be conflating underdetermination with indeterminacy. If you ignore Ross's misleading appeals to authority and concentrate on his own argument, I think you'll see that it has nothing to do with epistemology. (And don't assume that Ross's "indeterminacy" is the same as Kripke's or Goodman's.)

    Unfortunately, this is in my view part of a pattern in Ross's paper. I think he is careless with terminology, doesn't define his terms, and conflates different meanings of them. That makes his argument very hard to follow, and I believe that he commits significant fallacies of equivocation.

  2. I have a feeling Ross and Feser would rebut this with a two part response, which in my opinion would combine to an unsatisfactory answer. First of all, you are able to dissect and reverse engineer the physical process into predictable component parts. They will claim not to only be interested in the data alone but the entire system. Thus a finite physical system is only able to fix a finite number of points and therefore cannot determine any function. At this point I wonder what they would have to say about chaotic systems that are finite and rule based, yet utterly unpredictable. Second they would just claim that humans can determine "pure functions," and for the most part this claim rests on Ross's insistence that we could not make sense of formal reasoning if we can't do determinate thinking, therefore math is impossible, etc. I even consider this a dubious claim, since scientists and mathematicians routinely make progress with incomplete knowledge. Ross would probably counter by asking "are you seriously contending that we don't know what addition is?" True, addition is a particularly good example, since we all seem to think we absolutely understand what it means. If the operation were more complex, like integration or differentiation, I think the argument would grow considerable less clear.

    In a way it's ironic that this argument kind of rests on the alleged incapacity of machines (physical processes) to understand things at a symbolic level. In other words, they are relegated to dealing with everything in rote manner. This is exactly opposite to Searle's argument that machines can only manipulate symbols, and that's why they can't understand meaning. Much of our capacity to understand all the ramifications of addition are due to our ability to manipulate it symbolically as just another mathematical operation, though this is an ability that Mathematica, a physical process, is also significantly capable of.