I've come up with this idea of the "complementary hypothesis". I don't know wheter it's truly original.
The idea: In a pair of complementary hypotheses, one is the explanatory hypothesis (as in the scientific method), and the other is the negation
of the explanatory hypothesis. Because they are absolute complements, their respective probabilities must always add up to 1, and falsifying one proves the other.
When you take this view, hypotheses seem more testable. The most basic way to judge an hypothesis would be to compare it to its complement, and ask which does the data fit better? For this comparison, I think the bottom-line is the likeliness of the actual observations. Certain observations or sets of observations may be more probable in one condition than the other. For example:"Somebody is sneaking into my room" (A)
and"Nobody is sneaking into my room" (AC)
Somebody ≥ 1 ... Nobody = 0 ... discrete counting using positive integers.
A is unfalsifiable because a really good sneaker will not leave any evidence of their sneaking; no observation would be inconsistent with A. However, there are some observations that would be inconsistent with AC
, such as written messages appearing on the room's walls before I return to it. It's extremely unlikely that written messages would appear on my walls if nobody was sneaking in. In the absence of such evidence, I can at least say that this absence of evidence (B) is more likely given AC
Condition A offers the absence of evidence as a possibility (P(B|A) ≤ 1.0), but only AC
assures that it will be the case (P(B|AC
) = 1.0).https://en.wikipedia.org/wiki/Conditional_probability
Of course, scientists like to collect more information before reaching conclusions.
Any observation that supports A is, in other words, an observation that can be explained by A. But A may not be the only way of explaning the observation. We can't test A, but we may be able to test alternative explanations.
By supporting an alternative explanation, I discredit some of the evidence for A. And remember that the absence of evidence is the advantage that AC
has over A.
Suppose I have no evidence that somebody is sneaking in except that Delilah, who sits in my room 24/7, keeps telling me so. This is unsettling. The fact that Delilah makes this claim is evidence for A, but I still have no way of refuting A, nor does there appear to be any evidence that confirms A. However, I could also explain Delilah's claims as hallucinations, and I can test whether she is delusional. Suppose I test her for delusions and rest on a 0.75 chance that her observations are hallucinations. The possibility of hallucination (D) is represented by the circle labeled "Delilah Delusional", whereas the possibility that her observations are genuine sensory experiences (G) is the rest of what is inside the circle labled "Delilah Claims". To adjust the probability of A with this incoming information:
P(A|D) ⋅ P(D) + P(A|G) ⋅ P(G)
P(A|D) ⋅ 0.75 + P(A|G) ⋅ 0.25