Understanding your own ideas is hard work

More recent strata lie on top of older strata, except when they lie beneath them. Radiometric dates obtained by different methods always agree, except when they differ. And the planets in their courses obey Newton's laws of gravity and motion, except when they depart from them.

There is nothing that distinguishes so clearly between the scientific and the dogmatic mindset as the response to anomalies. For the dogmatist, the anomaly is a "gotcha", proof that the theory under consideration is, quite simply, wrong. For the scientist, it is an opportunity. If an idea is generally useful, but occasionally breaks down, something unusual is going on and it's worth finding out what. The dogmatist wants to see questions closed, where the scientist wants to keep them open.

All well and good.

This is perhaps why the creationist denial of science can often be found among those professions that seek decision and closure, such as law and theology.

Umm, what ? Is there an anti-science agenda in the law courts that no-one's told me about ? And throwing theology in there is just asking for trouble... but we may dismiss this careless throwaway comment, because the rest of the article is very nice.

No theory exists on its own, as the philosopher-scientist Duhem pointed out over a century ago, and when a theory fails an observational test there are two kinds of possible explanation. The fault may lie with the theory itself, or with the assumptions we make while testing it. More specifically, as Lakatos pointed out in 1970, every application of a theory involves ancillary hypotheses, which can range from the grandiose (the laws of nature are unchanging) to the trivial (the telescope was functioning correctly). When a theoretical prediction fails, we do not know if the fault is in one of these, rather than the core theory itself. Much of the time, we are not even aware of our ancillary hypotheses, which is one reason why we need philosophers of science.

I don't like the term "ancillary hypothesis". I'd have gone with something like "underlying / hidden / implicit assumption." But I digress.

No scientific theory is rejected simply on the basis of its anomalies. It is rejected only when a superior theory is put forward, and the new theory is superior if it explains as much as the old theory, and more besides. Thus we should not even see theories as existing in isolation, but as part of a sequence or research programme. You are bound to be wrong, but don't let that worry you unduly, because error is opportunity, and the way science progresses is by being less wrong about more things. I find this viewpoint liberating.

... The anomaly in the orbit of Mercury, however, could not be resolved in this way, and remained unexplained until the formulation of Einstein's General Theory of Relativity. In the case of Uranus, the anomaly was associated with the ancillary hypothesis that we had a complete list of planets, and it was this ancillary hypothesis that was overthrown. In the case of Mercury, however, the shortcoming was in the theory itself.

... From the perspective of this essay, Rayleigh's initial thinking included the ancillary hypothesis that all the components of air had been identified. This was not true, and (as readers with our knowledge of chemistry will be aware) the additional component was to play a vital role in explaining chemical bonding.

Well, this explains a lot about why ongoing research is so messy. It's because when a researcher formulates an idea, they only consider a limited number of parameters that have drawn their attention to something interesting. They want to suggest some mechanism to explain the data. During that process, it's the mechanism itself that they're interested in - not in the implicit assumptions it requires. Those may well be interesting in themselves, maybe more so than the theory. But not at that particular moment. The point is that for a complex problem, the researcher will not even be immediately aware of the assumptions they're making. Figuring out what those are takes time - usually, years. And this is why it can often look as though scientists are flogging a dead horse, adding yet more and more adjustments to an "obviously" broken idea; adding more crystal spheres and epicycles. They're not. What they're actually doing is figuring out (and testing) the assumptions behind the idea that they already made years ago, but were unaware of at the time.

http://www.3quarksdaily.com/3quarksdaily/2018/02/in-praise-of-fallibility-why-science-needs-philosophy-.html