I began posting on the symmetry principle in March 2013, in response to a post by Vanessa Heggie on the H Word. After eight posts and nearly eighteen months, it is time to bring this desultory marathon to an end. In the interests of brevity and coherence, here is a six-step guide to saving the symmetry principle. Each step corresponds to one or two posts in the series.
1. Get the fallacy right. What kind of inference does the symmetry principle forbid? Here is one kind of false inference: the earth really does move, so the motion of the earth is a sufficient explanation of Copernicus' belief that it moves. Very few historians have ever made this inference, so there is little point in fulminating against it. The real worry is inferences like this: the earth really does move, so the evidence for the earth's motion is a sufficient explanation of why Copernicus believed it to move. The difference is between explaining a belief by its truth and explaining a belief by the believer's arguments and evidence.
2. Take distinctions seriously. To get the fallacy right we need to distinguish between the truth of a belief and the evidence in favour of a belief. This may seem like an esoteric distinction, but we have no choice but to make the distinction if we want to understand the symmetry principle. The distinction is especially important if we want to communicate the symmetry principle to non-historians. If we do not make the distinction ourselves, we cannot expect non-historians to do so, and if they do not do so then we should not be surprised if they reject the symmetry principle. Another reason to make the distinction is that evidence gets a bad name if it is constantly confused with truth, since evidence usually explains more than truth.
3. Make room for truth. Truth nevertheless does explain something. The motion of the earth may not be a sufficient explanation of Copernicus' belief, but it is surely part of the explanation. There are other ways in which truth can legitimately enter into writing about past science. For example, it is philosophically respectable to say that theories are true insofar as they correspond to reality. And it is undeniable that factual evidence has played a role in the beliefs of past scientists. A blanket ban on truth does more harm than good in the history of science.
4. Be a minimalist about symmetry. Every historian of science knows that she should treat true beliefs in the same way as false ones. But what does this mean in practice? Does it mean that both sides of all past debates in science were equally reasonable? Or that historians should aim for completeness, always reporting the good reasons on the losing side and the bad reasons on the winning side? Or does it mean that we should ignore good reasons altogether and focus on social factors rather than cognitive ones? Or that, as a matter of fact, the social factors dominate in most cases? Properly understood, the symmetry principle does not imply any of these things. It simply forbids us from inferring the goodness of a believer's reasons from the truth-value of their belief.
5. Face up to the skeptical challenge. The reason this inference is forbidden is that people can be right for the wrong reasons and wrong for the right reasons. But what if we apply that principle to today's science? Maybe our best theories are wrong, despite the good reasons in their favour. Historians tend to welcome this thought as an antidote to dogmatism. In fact it is a serious threat to the symmetry principle, because few people will accept a principle that implies that today's theories are no better than Aristotle's. We need to work harder to reconcile symmetry and scientific realism. For example, we can observe that the argument from realism to asymmetry only works for consensual beliefs and not for those under dispute.
6. Aim for understanding not self-delusion. Suppose that symmetry is indeed consistent with realism. Shouldn't we nevertheless suspend our realism when we do history, just to make sure that it does not distort our results? Shouldn't we forget that the earth moves when we study Ptolemaic astronomy? No, we should not. If our knowledge of our former skews our view of the latter, then we have failed to grasp some fundamental points about past science. We should try to grasp these points rather than playing evasive mind games.
If we take these steps then we have a good chance of rescuing the symmetry principle from the false or irrelevant principles that are sometimes associated with it. These steps focus on what the symmetry principle is not, rather than what it is. But we need both to grasp the symmetry principle. So here is one more rendition of the minimalist, truth-friendly, and realist-friendly, version of the principle that I have defended in this series: the truth of a belief does not imply that the believer had good reasons for holding that belief, and the falsity of a belief does not imply that the believer had bad reasons for holding that belief. In short, historians should not reason from truth-value to goodness-of-reason.
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