Sober says something very interesting with respect to the notion that simplicity is evidence for the truth of a theory. If we consider simplicity as the mechanism that gives us a line for some scientific theory then it doesn’t like simplicity is evidence for truth. I remember the line fitting problem (or curve fitting problem) being describe to me in this manner (from Dr. Symons’ Philosophy of Science course). If you can remember from any science course you took in high school then you probably did some simple experiments and recorded what happened in that experiment. Now the text probably had a law that made a claim about how the experiments should come out. After you record the data and map them out on a graph you will not have a straight line like the law says. You have something more jagged. The law itself is a straight line.
Such a situation makes for an interesting dilemma, as Sober points out, “…theory that goes beyond the evidence by systematizing what appear to be unrelated data is simpler, and less probable, than the evidence itself.” (Sober 1975 p. 166) Which goes against what Popper (1968) and Quine (1966) argue. They argued that the simpler theories are more likely to be true, but Sober notices that the reverse is actually true. Applying simplicity reduces what the data actually tells us, we are sacrificing truth in order to get the line to fit. At the same time, if we don’t apply simplicity then a theory has no predictive powers. This does put us in a rather awkward situation, if we are more interested in truth, we should reject such theories. If we are more interested in accepting those scientific theories that apply simplicity and have some predictative ability then we should accept such theories. At the moment, I can’t really see any justification for making the move from the data to the line.
I noticed that Sober has made an interesting change somewhat recently concerning his views of simplicity, “Just as the question ‘why be rational?’ may have no non-circular answer, the same may be true of the question ‘why should simplicity be considered in evaluating the plausibility of hypotheses?’ (Sober 2001 p.19) Baker asserts that Sober is trying to justify ‘simplicity’ in terms of something ‘intrinsically valuable’ to simplicity itself, but I am not sure what that means.
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November 16, 2007 at 7:43 pm
Enigman
Maybe the fact that simplicity sometimes implies high probability is a fact that comes from our experience of a relatively simple world, rather than a priori? We would naturally be adapted to this world, attuned to its ways, so that we’d find the underlying laws to be relatively simple (at least at the level of ordinary experience, if not high energy physics). (Simplicity doesn’t imply truth of course; e.g. the inverse square laws make sense because they fit 3-dimensional space, rather than because “2″ is simpler than a higher number; were space n-dimensional then an inverse n-1 law would make sense, even though n-1 might be more complicated than 2.)
November 16, 2007 at 8:50 pm
cliffshill
Hmmmm… but do we lose something (truth, perhaps) when we make the jump from the data to the line even though it has a high probability of telling us something about a future event? I am rather worried (perhaps like Cartwright (1999)) that we do lose something. (I hope that makes sense)
November 17, 2007 at 4:44 am
Enigman
It makes sense (and you’ve given me some interesting references there to look up, thanks), but I tend to see truth (the correspondance between our words and the world) as aiming at a practical end, at our getting about in the world. So obtaining the line, which is more useful, is correctly described as our getting at a deeper truth. That’s not very satisfying…
…but the incontestable data is personal sense-data, which lies beyond language (and truth). The described data has already taken us into the realm of the doubtable. And it does seem that when an experiment yields results off the normal line that is probably because of experimental error, because of that datum (but not the sense-datum) being false.