An Example of a “Best Theory” Without Refuting Competitors

The following is a seeming example of an explanation that is a “best explanation” yet we never actually refute any of the competing theories. How would you explain this in terms of Popper’s epistemology of “conjecture and refutation”?

Example 1

The police are investigating the disappearance and possible murder of Mrs. Smith. They have two theories they are comparing:

  1. Mr. Smith committed a murder
  2. A previously unknown serial killer (or someone that didn’t know Mrs. Smith) committed the murder

None of Mrs. Smith’s friends or family know of her whereabouts. The police are not aware of anyone that has it in for Mrs. Smith. Mr. Smith, however, had a motive to kill her due to an inheritance. Mr. Smith has no alibi for the night of the disappearance.

Clearly, neither of the above theories is refuted at this point, but just as clearly theory #1 is the best current theory — to the point where the police will likely only investigate Mr. Smith at this point. Why?

As an additional question, this isn’t enough evidence to convict Mr. Smith yet, just to investigate him. That is to say, Mr. Smith isn’t considered guilty ‘beyond reasonable doubt’ yet. The entire court system works off of two different standards of evidence: 1) “reasonable doubt” (for criminal cases), and 2) “preponderance of evidence” (for civil cases.) What do these phrases mean within a Popperian epistemology? Or are they meaningless and misguided ideas?

Example 2

Now consider this scenario:

Suppose a scientist is investigating if Tom Jeffs (not in any way to be confused with Thomas Jefferson! [1]) – a famous historical figure – is the father of the daughter of a slave he owned. DNA of Tom Jeffs and the potential daughter are not available. But there are people known to be descendants of each. Further, Tom Jeff’s had no siblings and no other local extended family.

Due to the way DNA works, there is no way to directly test for paternity. However, there is a rare marker in Tom Jeff’s descendants that can be used to look at the probability of being related:

  1. If the descendants of the daughter have the rare marker, it might come from one of her other ancestors (that isn’t Tom Jeffs), but this is unlikely. If we assume a random distribution of the genetic marker, the odds would be one in a million that the marker came from an ancestor that wasn’t Tom Jeffs.
  2. If the descendants do not have the marker, than there is no chance she’s Tom Jeff’s daughter.

The DNA is checked and she has the marker.

Given #1, we have not refuted the idea that she is not a descendant of Tom Jeffs. Yet clearly the theory that she is the descendent of Tom Jeffs is the better theory now. Why? And how can this be explained in terms of Popper’s epistemology of “Conjecture and Refutation” when neither theory is refuted?

Incidentally, I believe Deutsch gave a pretty good answer to the second one in his paper The Logic of Experimental Tests if you care to look it up. It may also apply to the first one.

Footnote

[1] I mean that quite literally. Yes, this example was inspired by the Thomas Jefferson case. But that case is less clear cut than the fictional example I’m using here.

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