My definition of when something is "scientifically explained" is when the laws of science (a set of axioms) can be used to deduce behavior of said phenomenon quantitatively/qualitatively.
With this definition it seems that in principle, nothing is "unexplainable".
My reasoning is as follows: Suppose person A comes up with some phenomenon at some point of time that he claims is not explained by the science of the time. All scientists realize he's right. They have two options now to "explain it":
- The standard approach: Tweak the laws a bit so that all that was previously "explained" still remains so (more or less) but this new phenomenon is also deducible from the new laws.
- The desperate trick: Add this phenomenon with its quantitative details into their laws of science (axioms).
So, in principle this can continue forever. It seems like everything can be explained in principle.
The reason I ask this here at PSE is coz, to me, it opens up some philosophical questions:
- Is there any essence to a "scientific explanation"? Does it mean anything at all for a phenomenon to be explained?
- Can science ever "fail"? It seems like failure is ill-defined for science. Science can only either succeed or do nothing.
- If all of this is true, it seems like there is a blur between "natural" and "supernatural" explanations to a phenomenon. We can consider a "scientific explanation" to also be a "supernatural" one, expect that the scientific explanation is more mathematical.