Ross gives three main arguments to support his claim B: "No physical system is determinate." These are:
- Kripke's addition/quaddition argument.
- Goodman's grue argument.
- The problem of limited data.
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.