Saving the symmetry principle, I: two fallacies

Vanessa Heggie has posted a clear, visible summary of what she rightly calls a “core principle” for historians of science, namely the “symmetry principle.” So this is a great opportunity for me to explain why I disagree with much that my fellow historians of science have written on this topic. Behind the symmetry principle there is an insight that is true, important and worth keeping. But we need to save this insight from the ideas that are often associated with it, many of which I think we should reject.

The basic insight is that there is a certain inference, which I will call The Fallacy, that is a tempting yet unreliable way of way of explaining the beliefs of past scientists. The point of this post, the first in a series, is to separate The Fallacy from another fallacy that is so unappealing that no-one had even thought of it before historians of science started finding it everywhere.


The Fallacy

Consider Galileo's theory that the uneven shading of the moon is due to the shadows cast by hills and mountains on the moon's surface. Most of us prefer this theory to one of its seventeenth-century rivals, according to which the moon is a perfectly smooth sphere whose visible blotches are due to the uneven density of the crystalline matter of which it is made.

The fallacy is to say that since the theory is true, Galileo must have believed it because of the evidence in its favour, while those who rejected it must have done so out of superstition, prejudice or self-interest. In general:

Theory X is true, therefore everyone who held it did so for good reasons, while everyone who denied it did so for bad reasons.

This is what I will call The Fallacy. As I have stated it, this fallacy applies to two people with conflicting beliefs, but this limitation is one of convenience rather than necessity. The same kind of fallacy could be applied to two beliefs that have opposite truth-values but that do not contradict each-other. Or it could be applied to two beliefs held by the same individual. Or it could be of these cases in one.

For an example of the latter, consider Galileo's theory that comets are exhalations that mount in a straight line from the surface of the earth. The fallacy would be to infer from the truth of Galileo's moon theory that he held it from a combination of accurate observation and sound inference, and from the falsity of his comet theory that he held it out of dogmatism, amour propre, etc.


The Other Fallacy

It may look like I have simply repeated Vanessa's account with a different example (she uses Leibniz v Newton rather than Galileo). But there's a crucial difference. The teaser at the top of Vanessa's post says that “No one believes something simply because it is true”, and the fifth paragraph urges historians to “forego the assumption that [Newton] believed in his law of gravity because it was true.” This suggests that the fallacy that Vanessa has in mind is something like this:

Theory X is true, therefore everyone who held it did so because it was true, while everyone who denied it did so for bad reasons.

Call this the The Other Fallacy. It is the same as The Fallacy except that it replaces “good reasons” with “truth” as an explanation of the true beliefs of past scientists.

Although The Other Fallacy is indeed a fallacy, I think it is a very rare one, even among the most Whiggish of old-fashioned historians. Imagine asking George Sarton (to pick one such historian) why Copernicus believed that the earth goes round the sun. Would Sarton have said “because the earth does indeed go around the sun”, or perhaps “because Copernicus thought 'the earth goes around the sun' was a true statement”?

I doubt it. Instead he would have said something like: “because Copernicus looked at a whole lot of data, did a bunch of calculations, and found that a number of key phenomena—such as the retrograde motions of the planets and the fact that he never observed Mercury and Venus on the opposite side of the earth to the sun—could be explained in very neat manner by supposing that the earth is just another planet.”

To put one of the first two replies in Sarton's mouth is to commit what I have called the constructivist straw man. Another way to commit the same error is to say that Sarton and his ilk denied that “human agency” or “human activity” played any role in the beliefs of scientists.

Both forms of the straw man can be found in this transcript, which Vanessa links to in her post. First comes the suggestion that, some time in the seventies or eighties, historians started to see scientific knowledge has “a human product, something that had to be made and maintained.” In other words, earlier historians had thought that “true knowledge was immaculate, untouched by human hands.” (This is true only on the perverse assumption that calculating, experimenting, and reasoning—the sorts of things that interested Sarton et. al.—do not count as human activities).

Next in the transcript comes the misattribution that lies behind The Other Fallacy. How did these earlier historians explain the beliefs of scientists, if not as the result of human action? Answer: by appeal to the truth of those beliefs. For example, they would “say that Isaac Newton thought that there was an inverse square law of gravity acting instantly at a distance through empty space between the centers of distant bodies because there is [such a law].”

(Disclaimer: the historian featured in this transcript is my thesis advisor. Clarification: yes, I am disagreeing with my thesis advisor on this point, although I agree with him on much else.)

The problem with The Other Fallacy is that it sets the bar too low. A campaign against it is like an anti-smoking campaign that urges smokers to stop committing murders. Since most smokers are not murderers, the campaign is unlikely to have any effect except perhaps to convince non-smokers that many smokers are, in fact, murderers.

Likewise, urging people to avoid The Other Fallacy is unlikely to solve the real problem, which is The Fallacy. Those who commit the latter are likely to continue doing so, happy in the knowledge that they have not committed The Other Fallacy. And those who avoid The Other Fallacy may end up convincing themselves that everyone else is more wrong-headed than they really are.


Truth and evidence are not the same thing, and it matters

Perhaps historians attack The Other Fallacy, rather than The Fallacy, because the two are hard to tell apart. After all, as noted above, the only difference between them is that between explaining a person's belief by its truth, and explaining that belief by the arguments or evidence that the person found in its favour. And aren't these pretty much the same thing?

No! In the context of a debate, whether in the present or in the past, they are completely different beasts.

This is easy to see from the three quotes I put in the mouth of George Sarton. Imagine if we tried putting those quotes into the mouth of Copernicus rather than Sarton. Does the De Revolutionibus contain statements like: “'the earth moves around the sun' is a true statement, therefore the earth moves around the sun”? Or statements like: “the earth moves around the sun, therefore you should believe that the earth moves round the sun”?

Probably not. Or if it does, they were not the sorts of statement that convinced people that the earth went around the sun. And nor are they the sorts of statement that are used today to convince people that vaccinations work, or that climate change is real, or that God does or does not exist. And this is not something that “modern historians” discovered some time in the seventies and eighties. No sane person has ever denied it.

This should be uncontroversial. Granted, there are controversial issues nearby. There are the questions of the extent to which standards of evidence have varied over time and place, whether there is some super-standard that allows us to assess this alleged multiplicity of standards, whether evidence can reliably inform us about unobservable entities like quarks and quasars, and whether evidence can be decisive in resolving scientific disputes. But we do not need to agree on any of these issues in order to agree that giving evidence for a proposition is different from asserting that the proposition is true.

This large, uncontroversial difference does not stop historians of science running the two together as if they were the same thing, usually when passing judgement on dead historians of science. I've already given one example from a prominent historian. Here's another, from Stephen Shapin's 2010 book Never Pure:

Once upon a time, so the story goes, students of science too believed that truth was its own recommendation, or, if not that, something very like it. If one wanted to know, and one rarely did, why it was that true propositions were credible, one was referred back to their truth, to the evidence for them, or to those methodical procedures the unambiguous following of which testified to the truth of the product.

In this passage Shapin at least recognises that the truth of a claim and the evidence for it are different things. But only just: he also says that they are “very like” each-other. He implies, absurdly, that students of science used to be uninterested in how scientists justified their beliefs. And on the preceeding page he attributes to an unnamed group of “modernist methodologists”—presumably people like Hans Reichenbach, Rudolph Carnap, and Karl Popper—the view that “truth shines by its own light.”

The conflation of truth and justification does an injustice not only to old-fashioned historians like Sarton but also to present-day internalists. The latter may be defined as historians of science whose main interest is the mixture of luck, skill and insight by which past scientists—as individuals or as groups, over months or over centuries—developed arguments for their claims the natural world.

Internalists can be as symmetric as anyone, giving as much attention to the errors of “winners” as they do the insights of the “losers.” They do not give complete accounts of their subject (show me a historian who does!). But they do far more than simply put tautologies in the mouths of past scientists.

To sum up, by conflating truth and evidence we make the latter look as unimportant as the former in the resolution of debates, whether in the present or the past. This is an error as bad as The Fallacy. It is silly to appeal to the presumed truth of a claim in order to persuade people that the claim is true. By contrast, it is silly not to appeal to the presumed evidence for the claim in order to persuade people that the claim is true.

Having identified what I think is the good idea behind the symmetry principle, in my next post I hope to explain why it is a good idea. This can be done, but it is harder to do than my colleagues usually make out.



Postscript 1. If the error that I am attributing to my fellow historians is such a bad one, why had no-one spotted it until now? Actually, at least one person had. Ian Hacking wrote the following in a footnote to his 1999 book The Social Construction of What?:

Evidence, or reasonableness, is quite another matter from truth. [The sociologists of science Barry Barnes and David Bloor] are often taken to hold a symmetry thesis about evidence: you cannot invoke the evidence available to a community for a belief p, in order to explain why people in the community believed p... I find this claim (about evidence, not truth) unsatisfactory (232).

Why did Hacking put this point in a footnote rather than in the main text? Because he only mentioned the symmetry principle on his way to talking about something else, and that thing (the distinction between “nominalism” and “inherent-structurism”) was relevant to truth and not to evidence.

I'm still trying to work out why other commentators on the symmetry principle have not made the point that Hacking made in his footnote, and that I made in the above post. I'ld be delighted to know of any examples of people who have made the point in print.


Postscript 2. Maybe I'm being too harsh. Maybe Shapin et. al. want to draw the following contrast. One can say that a scientist believed P because they were convinced, on the basis of the evidence, that it was true. Or one can say that the person believed P because they were convinced, independently of their views of the truth-value of P, that it was in their interests to believe it.

On this reading, “No-one believes things just because they are true” is shorthand for “No-one believes things just because they are convinced, on the basis of the available evidence, that they are true.”

But if this is what is meant, why not just say “No-one believes things just because they have evidence for them”? This would make it clear that evidence is involved. Or what about saying “No-one believes things just because they believe them to be true”? This would at least make it clear that it is not the truth of a person's belief that is under consideration but the person's conviction that it is true.

Both of these clearer expressions would avoid the rhetorical sleight-of-hand that is involved in saying “No-one believes things just because they are true” when what you mean is “No-one believes things just because there is evidence for them.” The former claim is obviously true. The latter claim may be true, but not obviously so. The ambiguity has the effect of making the intended claim (if the intended claim is indeed the latter one) more obvious than it really is.

But all this may be moot, since I doubt that my charitable reading is correct. I suspect that Shapin et. al. really are accusing past historians and philosophers of thinking that the truth of a scientist's belief (and not just the scientist's conviction of its truth) can be a good explanation of that belief.

One reason for my doubt is that, in the passage quoted above, Shapin includes “truth” and “evidence” as separate items in his list of candidate explanations for the beliefs of past scientists. This suggests that he is not implicitly including “evidence” under the rubric of “truth.” If he were, then it would be redundant to include evidence as a separate item.

Another reason to be skeptical is that, as I understand them, even sociologists of science have trouble making sense of the idea that people can believe things without first being convinced of their truth. That is, sociologists would probably not say “Newton believed his inverse square law because, although he withheld judgement about the truth-value of the law, he thought that this belief would protect his reputation as a national hero.” Rather, their explanation would be something like: “Newton believed his inverse square law because he thought the law was true, and an important source of this conviction was (not the evidence but) his desire to protect his reputation.”

At least, that is what I imagine they would say. And if that is right, even sociologists think that people “believe things just because they are convinced of the truth of those things.” So that cannot be the allegedly false view that Shapin et. al. are attributing to past historians and philosophers of science. The view they are attributing must be the one I assumed in the above post, viz. that people believe things just because those things are, in fact, true. Expand post.

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