Kyburg's Model of Scientific Theory-Formation
Ronald Loui
Ronald Loui
Ronald Loui
Published May 29, 2026
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Continuing my rush to get some ideas on a more persistently archived platform (LinkedIn is well indexed these days by search and LLM-AI). You never know what access remains to your home page and blogs when no one is around to pay the ISP and domain registration bills... and publication with peer-review seems so passe; are they really your peers?

I have said often that Henry Kyburg's got the best ideas on "scientific" theory-formation and that these were some of his best ideas. But he hid them in books that are very hard to penetrate.

It's so simple, really, but unlike others who try to explain scientific theory revision, his account gives place for error and inferential power, mediated by probability. A whole trinity. You can use his ideas on interval probability in this account, or just point-value probabilities. Just so long as you can calculate them for various sensory inputs, or per assertion-type. You might even be Bayesian and be working with subjective priors. Oddly, for a guy who was very non-Bayesian, his account is perfectly consistent with Bayesian beliefs.

The best way to understand how it all works is, I always thought, to look at axioms of decision used descriptively. Others will want to keep F=ma* or PV=nRT in mind, or other such famous equations from normal sciences. But the transitivity of preference is the one I use to illustrate what's going on: If a > b and b > c, then a > c, where > is read as "is preferred to." In fact we can make it more concrete: Someone is observed preferring Mozart to Bartok, and Bartok to Mendelssohn, so under transitivity, we infer that the person prefers Mozart to Mendelssohn (sorry I dropped an s in the JOURNAL OF PHILOSOPHY paper that used this example!).

*I once asked my Punahou-rank#1-Harvard-summa-Harvard-PhD physics eminent prof friend, way back around 1984, how he measured mass. What did mass mean to him? He said mass is whatever he needs it to be to make F=ma true! This is rule entrenchment.

Now, there may be a dozen such instances of preferring Mozart to Bartok, and preferring Bartok to Mendelssohn. And we keep inferring that the person prefers Mozart to Mendelssohn on the basis of those, and the transitivity of preference. But as we know, people often violate axioms of preference. On one occasion, you observe the person preferring Mendelssohn to Mozart despite showing the other two preferences.

Kyburg would say we now have an error. That error can be ascribed to the observation of preference. Maybe 12/13 such observations seem to produce no contradiction. That's still a good rate. You still retain some confidence in your measurement method that produces claims of preference for this person (you still believe what is reported; you still believe preferences persist over a short time; you still believe that concerto is Mendelsson's). So "at a level of acceptance," say .9, you may still put raw observations of preference into your corpus of working knowledge. At .9, you observe another Mozart> Bartok and another Bartok > Mendelssohn, so at .9 you can use transitivity and infer Mozart > Mendelssohn this Tuesday.

But because your observations of preference are now slightly tainted, imperfect, subject to some non-zero error, there is higher level, say .95, at which you cannot accept the raw observation of preference. Those observations are too error-prone to be accepted at the higher level. There is nothing for the axiom of transitivity to use, to produce inference, at that level because there is no acceptable statement about Mozart vs Bartok, and no acceptable statement about Bartok vs Mendelssohn.

The question then becomes at what level of acceptance you are willing to work. As you lower the threshold for treating something as knowledge, you start to admit observations that form contradictions in large groups (see his LOTTERY PARADOX). You are forced to work with maximal consistent subsets of knowledge, and to seek agreement among them. We never talked about what you might do if .9 of the maximal consistent subsets agree on an inference, q, but perhaps we should have. We talked about wind power and dogs running free on his farm a lot instead.

Now, at some point, the axiom of transitivity produces more errors than you would like, especially at a working level of .9 or higher. So you consider theory revision. You think, what if I drop the transitivity rule? It's causing errors, and that's annoying. If you drop the rule, you lose a lot of inferences about Mozart vs Mendelssohn. But now your raw observations of preference generate fewer contradictions, so raw observations flood back into your corpus at .9.

Which do you want? A lot of preference statements that seem correct? Or a lot of inferences from statements acceptable at a lower level, but not at the level where you would like to do inference? If you can decide this, you can decide whether you like having a theory with transitivity of preference, or not (at least an unqualified statement about transitivity).

Of course, you can make smaller changes to your theory. You could say preferences-involving-Mozart are the ones where transitivity does not apply. Or you could add auxiliary hypotheses, junking up your theory, so preference-on-Tuesdays are not subject to transitivity. Or preference-on-Tuesday is the class of observations that generates errors. An infinite number of revisions possible. But the principle is: inference, error, probability, acceptance, information, in feedback. This is what regulates adjustment of inferential mechanism.

You can see it in PV=nRT. You might have to say it only applies to ideal gases. Or the measurement of pressure is error-prone. Or just say for your lab, for your gases, on this Tuesday, T cannot be calculated from P and V at all well. For some reason. No need to give the reason. Just don't use the formula when it keeps disagreeing with your measurements, or don't keep the measurements if they keep disagreeing with the formula.

This doesn't sound like much, but it connects Hempel and Nagel and Kuhn and coherentism and foundationalism and a lot of prior ideas that were pieces of the theory-formation puzzle. He does not address simplicity. Not surprisingly, Kyburg's teacher was Nagel, whose teacher was Cohen, and Cohen-Nagel is the preeminent lineage in philosophy of science mid-20thC. So if it sounds naive, perhaps i have written it too clearly!

But look how widely you can apply the basic tradeoff.

I think a pitcher likes to throw two fastballs then a curve. He throws three fastballs in a row in this 9th inning. This is a violation of my theory. I either revise the theory to say he doesn't throw the curve after two fastballs in the late innings. Or I say that that last curve was actually a lot faster and straighter than I initially thought, and my id of curve balls needs to improve. As for umpires, time to get glasses.

Since we have a way of assigning probabilities to events based on empirical data across multiple REFERENCE CLASSES in Kyburg's world of inductive logic, this is a fairly straightforward thing to do (see also our new COLVIN DIAGRAMs). If your probabilities are intervals, you use the lower bound to determine acceptability in a corpus of 1-e.

Hank had trouble answering the question of how you decide if you like inferred knowledge at 1-e, or acceptable probably non-erroneous observations at 1-e. He shrugged and said, maybe count them. Some might be more important than others. It's always hard to count p and q, when they could be the single assertion p&q. One can always tag predicates in the object language as the ones you really care about and ignore others or weight them less.

As far as i can tell, no one had come closer to an account of theory-formation (and theory-revision) by 1990. Perhaps someone has since then. I doubt it.

For those who are savvy about science and language, you might recognize the axioms of a theory as the meaning postulates of a language. This is actually standard post-Quinean analytic philosophy. You want to add transitivity to your theory of preference? You have just changed the meaning of "preference". You are now speaking a new language. We hope you find this new language convenient. This seems odd to non-philosophers, but anyone serious after say, 1950, should agree with this. Certainly conventionalists and instrumentalists would. (Kyburg always liked the Quine-Ullian picture of WEB OF BELIEF and the moving boundary of theoretical vs observational terminology, according to people like William Craig and Hartry Field.)

So theory-formation is also revision of meaning.

And you thought you were just fitting a regression line to a scatter plot. Actually, please stop doing that. Linear regression is so misleading, especially when charting data.

At the very least, Winsorize your outliers, which is a bit like rejecting observations as errors, producing an error rate, lowering the confidence level you are working at. And realize that any curve you fit, linear or not, is not just inference, but language shift!