 One way to see why not is to consider an analogy that champions of contrastive underdetermination have sometimes used to support their case. If we consider any finite group of data points, an elementary proof reveals that there are an infinite number of distinct mathematical functions describing different curves that will pass through all of them. As we add further data to our initial set we will definitively eliminate functions describing curves which no longer capture all of the data points in the new, larger set, but no matter how much data we accumulate, the proof guarantees that there will always be an infinite number of functions remaining that define curves including all the data points in the new set and which would therefore seem to be equally well supported by the empirical evidence. No finite amount of data will ever be able to narrow the possibilities down to just a single function or indeed, any finite number of candidate functions, from which the distribution of data points we have might have been generated. Each new data point we gather eliminates an infinite number of curves that previously fit all the data (so the problem here is not the holist’s challenge that we do not know which beliefs to give up in response to failed predictions or disconfirming evidence), but also leaves an infinite number still in contention.