Is the idea of a supernatural explanation incoherent?

1. Your question about supernatural explanations enlights in a striking way the explanatory power of the scientific methods.

Oberserve, develop a theory, check, if necessary correct and repeat the loop.

2. But concerning supernatural, i.e. trancendent speculations, there is nothing to observe. Corresponding thoughts neither have a basis nor can their conclusions be checked. In particular, one cannot improve our knowledge in this field.

   Therefore, so called "supernatural explanations" are no explanations at all.

It's misleading to say that supernatural explanations are "apriori incoherent". They are perfectly "coherent" -- if taken at their own terms. Just like SF or SteamPunk stories with magical techniques are "coherent". It's just that a reference to supernatural causes does not explain anything. At least not in terms of any scientific, empirical-evidence-based, falsifiable theory.

The proces by which the Catholic Church determines whether a miracle has occurred gives a perfect example of this. The Church is rather careful in trying to rule out any possible physical explanations for a miraculous event. But that's also where it stops. The conclusion of the process is that at best we do not know what happened or what actually caused the event. It is never that now we got positive evidence that the laws of physics were broken or something like that (not even if we specify those as "the laws of physics as currently known").

So, supernatural explanations at best only indicate the limits of current knowledge (assuming the reported events themselves are credible, which may also be rather dubious). They have no further relevance for physics.

This question has an equivocation fallacy embedded in it, and if one recognizes the fallacy, then it is easily answered.

There are two usages for "supernatural". Under the epistemological usage, then something is "supernatural" if it is not subject to investigation or evaluation using our tools of empiricism and reasoning.

Under epistemology, there are three primary methods to gain knowledge:

1. Direct and immediate intuitive knowing
2. Knowledge acquired through reasoning
3. Knowledge acquired through empirical investigation

It is the first category, intuition, that is a "supernatural" method of gaining knowledge. It is outside methodological naturalism.

Note that both empiricism, and reasoning, are only established through intuition-based rationales, so even methodological naturalists resort to "supernatural" justifications.

The OP question tries to equate supernatural epistemology with an ontic category -- implicitly assuming that physicalism does not depend on supernatural epistemology, and that non-physicalist ontology can ONLY be established with supernatural epistemology. Both assumptions are false.

For physicalism, as noted above, it cannot be justified without resort to intuitions -- hence physicalism ultimately is grounded in supernatural epistemology. Additionally, physicalists can and have resorted to unverifiable claims in principle -- Mysterianism in philosophy of mind is a claim by physicalists that consciousness is epistemically supernatural, and can never be understood using methodological naturalism. These examples show physicalism can be and is epistemically supernatural.

Relative to non-physicalism being subject to methodological naturalism -- humans have been reasoning about souls and Gods for millennia -- AND performing test cases on them. All citations of contradictions in a holy text, or arguments based on the Problem of Evil, are empirical test cases of ontically non-physicalist claims. Examples showing that such testing has been done for millennia very effectively refutes any claim that non-physicalism cannot be evaluated using methodologic naturalism.

The OP question is therefore based on a fallacy, and presumes two major errors relative to epistemology.

As a wrap up to answer the question, neither the epistemic meaning of supernatural—knowing things intuitively — nor the ontic meaning of supernatural — things that are not physical — are logically incoherent. Therefore there is no feature of either meaning that would require explanations using that meaning to therefore be logically incoherent.

For something to count as an explanation you have to end up with more information than you would have had otherwise.

If your explanation is more mysterious than the event it tries to explain then it tends to be counter productive.

Supernatural things could effect the world around you in theory, but in practice "a God did it", or "it was a miracle", tend to tend to make the world less predictable than more so even if true.

Knowing whether the world around you is more or less chaotic and unpredictable is more information than you would have otherwise had. So, if you could know that a supernatural thing happened it would count as an explanation.

Now whether you can actually demonstrate that supernatural things happen is a whole other can of worms which I would usually say that we likely can't "know" that a supernatural event occurred. They can usually only be ruled out by showing a natural explanation instead because the supernatural can explain any state of affairs.

Rather than being incoherent, supernatural explanations are explanations without any explanatory power.

If you insist that an explanation must be in physical terms then a supernatural explanation is by definition an oxymoron. However, your definition of an explanation would be a rather exclusive club to which only physically real members were allowed entry. The doorman might also be puzzled when presented with purported explanations relating to concepts such as 'dark matter', since they seem to be similar in appearance to the supernatural would-be entrants.

Moreover, suppose one day a dazzling entity appeared over Trafalgar Square announcing 'I am God', picked up Nelson's column with a giant hand, and replaced it having converted it into a huge diamond. You would have no way to explain in physical terms what happened, but you would be considered pedantic if you refused to accept 'God did it' as an explanation.

The wording "supernatural" is a bit tendentious here. A better term would have been "extranatural" or simply non-empirical.

Most people, in my impression, believe in some non-empirical truths (both atheists/agnostics and religious ones). In fact a view like Quine's, that we should treat logic and mathematics as subjects to be determined by evidence just like any other sciences, is quite rare even among philosophers (Quine did expect logic and mathematics to change the least).

If you are against all non-empirical arguments, you may end up calling loads of traditional philosophy incoherent...

In science, every time we find an explanation for something, it usually implies that we have a) discovered a step by step process leading from the cause to the effect, and b) have essentially "summarized" the otherwise disparate data into a shorter form.

Science posits theories that are consistent with the evidence and retains those that have predictive validity.

Now, if something is supernatural, then it at the very least is not physical.

I accept this as a premise of your question.

But if something is not physical, it seems as if we can never arrive at how exactly something supernatural would do anything.

That's correct.

Even in the case of evidence that "seems" to make it 100% obvious that god exists (DNA strands having the words "God is real" written on them), we would still be clueless in regards to a complete causal chain that leads from God to that physical effect given the fact that God is not a physical being Himself.

Without us conducting further investigation, that is probably correct.

Does this make the idea of a supernatural explanation incoherent even apriori?

It means that supernatural explanations (in the sense you've described) can't do the things that natural/physical/scientific explanations can do for us.

It is straightforward to scientifically involve supernatural explanations.

In computer science there is the concept of a halting oracle. The halting oracle is not computable. On the other hand, everything in the universe is based on quantum physics, and quantum physics is computable. Therefore, if we detect the activity of a halting oracle, then we can infer non physical intervention in our world. Visa versa, we can also use the concept of a halting oracle to characterize one form of non physical intervention in our world.

How do we detect such a thing? Good question.

The halting oracle induces a certain probability distribution of bitstrings with certain properties, e.g. highly compressible and with deep, complicated structure (DNA and language), which is different than the probability distribution induced by only computation and randomness, which is either highly random (diffused gas) or trivial structure (crystals). See Solmonoff induction an a formalized example of this kind of theory.

Why is this useful?

We can compare these theoretical distributions with what we observe in the world, and from that infer the kind of causal source that created the empirical distribution. We can also reverse the direction and based on inferring the causal source infer what kind of further distributions we expect to see in nature, e.g. tells us where to look and what to look for.

This method can be used in a practical environment like network intrusion detection, or a more scientific environment like biology.

In other words, yes supernatural explanations are scientifically tractable, and there are many untapped application areas with low hanging fruit today.

Addressing some potential objections:

Some might say an uncomputable concept is not usable. However, Kolmogorov complexity is an uncomputable concept that is quite usable. There is a thick book title "An Introduction to Kolmogorov Complexity and Its Applications" that has many applications of this uncomputable concept.

Others might object that theoretical distributions based on theory and math are not grounded in physical reality, so can't be used scientifically. However, John Bell came up with a theoretical distribution of how quantum particles behave if quantum entanglement is a real thing, and his distributions was not confirmed empirically until many decades later. Another example is Claude Shannon's channel capacity theorems which theoretically calculate the upper limit of a channel's lossless bandwidth, but we've only started to approach now 80 years later.

Faced with some fact or occurrence, a supernatural "explanation" is not meant to account for how it came about or subsists but where it fits in the explainer's lifeworld. It's another meaning of the term 'explanation'.

Again, the function is not to make the explanandum available to mental operation but to help acquiesce to it, to get it out of the way of bigger concerns, likely practical ones. So neither is the relevant frame of coherence that with facts and their logic but with prior beliefs, emotional economy, and social embedding.

Even within that frame the bar for coherence may be lowered by humans' ability to hold divergent views comfortably in different life contexts by just never thinking to cross-compare them. I forget the psychological name for that.

Source: observation and involvement.

We don't have a "modern" or retold playbook for metaphysical because not many people venture to that world anymore to tell you about it. One example where you can see, feel and experience is in a secluded cemetery alone in the dead of night. If you can keep your wits about yourself, one of the first, obvious things you notice is Stillness. That Stillness, without any ghost, is very scary by itself ALSO VERY PROFOUND. So that's like a whole different lifestyle and i don't think any such people are active on SE. The people who venture into meta physical for reals.

Ok so I hope it understand question right. Supernatural if it includes metaphysical then PatanjalYogPradeep, a Hindu scripture, has it explained. It gives the Sequence of Events, divides it into various entities and then explains the end state.

Like for Anger, Anger is Bhav, Bhav is State of Soul or Being or Feeling(loosly), then comes Mind(Thoughts) and then Action(Body). So Vrutti is another name for Bhav, VruttiSaroopyaMitrRat, which means when we succumb to Anger, WE BECOME ANGER. So rather than saying, "You have become Angry", it's more technically correct to say, "You've become Anger". You BECOME the Bhav/Feeling you succumb to. And that's True.

This VruttiSaroopyaMitrRat principle is Mentioned in PatanjalYogPradeep. It is considered scripture because of the importance of Knowledge in it, but there us nothing "religious" about it. I personally call it the Technical Manual for Meta Physical and Physical.

By the way lemme just emphasise the importance of that Sootr/Mantra. It clearly and accurately describes how DEATH happens to us at metaphysical level. But i can bet, you couldn't have guessed that in a million years. I couldn't either, i made the connection later when i met Death. Death is also a Bhav, an Experience, it's just that it's so mesmerising that you cannot take your eyes off of it. Like when highly extremely sexually aroused, it's almost impossible to look away from "the object of desire". Now take that thing to ABSOLUTE LEVELS. MEDUSA. So what happens?!!!!! YOU ARE CONSUMED BY IT, YOU BECOME LIKE IT, MEANING DEAD. YOU'VE BECOME DEATH THAT'S WHY YOU LOOK DEAD, BECAUSE DEATH LOOKS COMPLETELY DEAD. That's why when i saw Death I Realised! That ONLY DEAD THING IN THE UNIVERSE IS DEATH ITSELF. There is nothing "dead" in this World that looks as DEAD as death. So a dead body looks like(gives a feeling of) death BUT NOT REALLY. IT LOOKS LIKE IT BUT DILUTED, LESS DEAD LOOKING, APPEARS LESS DEAD THAN DEATH.

All of this in PatanjalYouPradeep.

See metaphysical, people study it mostly on theoretical level but you can perform some very radical experiments to Experience Extreme MetaPhysical Events. Like going to cemetery to meet Ghosts because if you look at it Objectively, Ghosts are the most possible, plausible, metaphysical entities that are available to us. An entity without a physical body. How can you shy away from Ghosts if you are really interested in metaphysical.

BUT THESE ARE RADICAL EXPERIMENTS AND ARE NOT SAFE WITHOUT OBVIOUS OVERT DIVINE HELP. PLEASE EXERCISE EXTREME CAUTION AND BETTER JUDGEMENT BEFORE TRYING THRM.

Please read PatanjalYogPradeep, it'll be helpful to you.