What Constitutes a Scientific Explanation?

I think that is exactly right but think it needs to be clarified what we mean by “explain.” This is a particular term of art which privileges quantitative (and semi-quantitative) and mathematically (and math applied to data) derived explanations.

We are not talking about stringing words together into complete sentences. That doesn’t usually constitute an explanation in science. Those wordy “explanations” are judged by the quantitative models they induce.


I am going to make a conjecture that I invite Ph.D. scientists to correct as needed:

In the absence of a mathematically based model, you don’t have science. Intuitions, maybe, but not science.

Note: my definition of mathematical is fairly broad here. A most likely ordering of events would be mathematical, for example.


Too broad, I think.

Science is systematic. Without the systematicity you don’t have science.

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My definition of mathematics was vague, for sure. What you seem to be saying is that a most likely ordering of events would be systematic rather than mathematical. Am I understanding you correctly?


In some ways, mathematics can be thought of as a theory of systematicity. And I’m inclined to think that’s why mathematics is so useful in science. But I would not say a study area is unscientific just because it doesn’t use mathematics.

This needs to be fleshed out more. I’m reminded of the several instances where people have been accusing of engaging in “numerology” instead of science: one famous example is Dirac’s Large Numbers Hypothesis, where Dirac, Eddington, Weyl and others saw some patterns between fundamental constants and thought they gave evidence to some deeper connections, but this never actually developed into a “real” theory. On the other hand, the periodic table and parts of the Standard Model initially also started out as pattern recognition, but eventually people were able to give deeper, structural explanations for why the objects behaved according to these patterns, also allowing them to make new predictions (new elements or new fundamental particles).

From this, I think a “real” scientific explanation is one that has levels of depth: one is able to explain a numerical pattern produced by a phenomenon by appealing to another observed phenomenon(s) and postulating a well-defined law characterizing the range of behavior of these two phenomena. Usually this involves some sort of reduction, namely:

  1. Postulating that an object/phenomena consists of certain component parts,
  2. Postulating fundamental properties for each of those components and fundamental laws/principles for how those components interact with each other.
  3. Showing that the combination of 1) and 2) give rise to the numerical pattern initially observed.

For steps 1)-3) I don’t think complex mathematics is necessary; you just need logical statements referring to well-defined objects in nature.


Certainly complex mathematics is not necessary, and might even be undesirable compared to simple mathematics. The key point is quantitative or semi-quantitative. This could legitimately, for some claims, be as simple as a comparison between coefficients in a logistic regression.


A general reply on the topic.

Scientific theories are sometimes called “models”. And I think that’s a good term.

A model is abstract. But a scientific model should model part of reality. And that means mapping aspects of reality into the abstract model. The mapping rules – how we map reality into the model – are an important part of the theory.

To take a bad example, we can look at Dembski’s ID theorizing. There’s lots of mathematics there. But it fails to tell us how to map reality into his model. And that why we question whether it is science.


My understanding is that this law by Planck was a very clever curve fit of observations of ovens, and it worked it he added a hypothetical constant called “h”. When I first saw it, my jaw dropped that anyone could concoct it! It won a Nobel Prize, rightly so.

It turned out the curve fit, but especially “h”, became a crucial part of quantum mechanics. The curve fit for the limited data set could be tested for applicability to other data sets, and was vindicated as a predictive “law”, Plank’s Law:

\LARGE B_\lambda (\lambda ,T) = \frac{2hc^2}{\lambda^5}\frac{1}{{e^{\frac{hc}{\lambda k_BT}}}-1}

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5 posts were split to a new topic: Baryon Acoustic Oscillations and Big Bang Cosmology

I’m all about mathematical scientific hypotheses, but no, math isn’t always necessary to science.

The Little Rock Lake studies on effects of acid rain ares a fine example of this. Take a lake, divide it in two, treat one side, observe what happens.

I can’t find it now, but there are before/after aerial photos of Little Rock Lake or a similar study, showing a very clear difference between the two side of the lake.


That’s a rather large subject, but there are several features of good explanations that I have found.

  1. Explanations are unavoidable. Any good argument builds from agreement and ends at an unavoidable conclusion. Good explanations are good arguments. Facts should lead to an unavoidable explanation.

  2. Explanations tie seemingly disparate observations together. For example, we can use GPS to measure the movement of the Hawaiian islands. We can use mass spectrophotometers to measure the ratio of potassium and argon gas in rocks on the Hawaiian archipelago and Emperor seamounts. How can these two things be tied together? The explanation of age, radiometric dating, and tectonic plate theory tie those very different things together in a single explanation.


  1. Explanations make predictions. A good explanation should allow us to clearly say what we should and shouldn’t see if that explanation is true. If any possible observation could be consistent with the explanation, then it isn’t an explanation.

Great example. And that brings back memories of similar “divided lake” experiments in Canada when there were rising concerns about the phosphates in most laundry detergents causing runaway algae growths. (Late 1960’s, I think.)

Found it:

That classic Hawaiian Chain graph has always been a personal favorite. It’s yet another example of data consilience.


The difference can actually be expressed mathematically as the wavelength of light reflected off the water in the two sides, can it not? Alternatively as the density of algae in the water?

I don’t disagree that sometimes science is systematic in a non-mathematical way. This particular experiment does not strike me as the strongest example of that principle, however.



Yet, it is definitely a fun example for illustrating the idea.

I couldn’t find my original example that actually had the photo in the journal article. In that example the photo was literally the evidence.

But yes, nothing stops anyone from using math.

There was a joke …

“The data wasn’t clear, so we has to use statistics.”

And as much as I enjoy sneaking into other people’s research, sometimes the results are so clear that statistics are unnecessary (except maybe descriptively).


I think there just is well researched explanations. The word science is irrelevant. Science is just presumed to be about accurate methodology before conclusions are drawn.
Yet its just weighing the evidence like everything else and then it falls into error. like in evolutionism.

How do you determine if an explanation is in error?

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One is determining if the explanation is accurate. So methodology must be a high standard. Yet because humans standards are related to what we start with knowing THE standard is not high by natures demands. A standard can’t replace lack of knowledge or options for results. The fix is in.
We can draw conclusions on things with limited options likev testing new medicines. However biology or physics options are too many to allow settled conclusions.
In evolutionism I always say the standard was compromised because the evidence for a biological hypothesis was not based on biology. Instead other subjects (Indeed its hard to have biology evidence on past and gone processes and events)
Thars why evolutionism can’t prove its case on biology and also opponents can’t debunk it using biology evidence.
its all not a high standard of investigation on evidence. its not science.

So you reject all conclusions no matter what the evidence or methodology is?

How is genetics not based on biology?