The question asked and the one described are different. You asked if it is possible to define "the supernatural." The answer to that question is, yes. It has been done in many dictionaries, and the word very simply is used to cover all things which have no cause in nature or causality.
Within the description you changed the question with the caveat that the definition is "from the naturalistic perspective," which has the obvious answer, "no." It is impossible to claim something you cannot define does not exist (naturally it is impossible to prove a negative). So is this question actually asking if supernatural phenomena are "physically real?" Can any physical qualities of the supernatural be predicted by experimentation?
Let's first define what it means to be physically real. In 1935 after the bizarre observations of quantum entanglement Albert Einstein wrote a "criterion of physical reality" in the Einstein-Podolsky-Rosen paper to define this:
if without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. - Albert Einstein
So is it "yes" or "no?"
This is not actually a dilemma because science abhors the truth - a final and unyielding philosophy. Many have faith in spiritual truths, yet science cannot investigate this truth at all — or even tell us whether it exists. (U.C. Berkeley) Scientists strive to build knowledge about the natural world that corresponds to the way the natural world really works (what is physically real and predictable). This will forever be changing.
In science, truth is, by definition, a malleable and perfectly revisable thing.
(Berkeley Science Review)
If science is not seeking absolute truth then what is it?
Consider the laws of Newtonian physics - at one time they were scientifically true. Due to the discovery of quantum mechanics, we know it is a general and conditional fact of reality. His relations are only good for objects that have a constant mass, and nothing except an object at rest has a truly constant mass. "f = m x a" is therefore not actually true, and it cannot be used to perfectly predict any momentum; only very very closely so. The difference doesn't change the usefulness of f=m*a in calculating physical phenomena such as orbits and fuel loads. True or not, Newton's laws are useful, and therefore they are science.
Why are scientific facts not truths?
Officially, the definition of science at The Science Council is:
Science is the pursuit and application of knowledge and understanding of the natural and social world following a systematic methodology based on evidence.
The most important word is at the very beginning: "Science is the pursuit." Science is not an end and will not produce an end - a truth. The book on what is real and what is not will never be closed - it will always and forever be willing to rewrite itself. If you omit the tolerance for revision and assume some natural explanation is "the truth," then you have just created a religion.
The scientific method awards the best solution to a problem among competing theories. It never tests if the theory is "true," it is simply a better explanation than the other offers. One of the key tools to measure which is best is Occam's razor Every law and principle of nature is and always will be the most parsimonious solution given all known evidence. Every single scientific fact MUST have that caveat: "Given our current evidence." As new evidence which challenges any scientific principle arrives, it becomes necessary to re-test our scientific knowledge. Every natural law and theory must bend to it.
Evidence is defined as:
Empirical evidence is information acquired by observation or experimentation. Scientists record and analyze this data. The process is a central part of the scientific method.
Obviously any thing which cannot be repeated, cannot be observed; thus it is not evidence. If I do X, and I get Y as a result, it becomes evidence if and only if that process is repeatable. On the other hand, if I create cold fusion in a jar in my kitchen, that only becomes science when someone else can repeat it. Also, if it can be observed, it is evidence.
The fact that no one else has not repeated the cold fusion experiment does NOT proclaim that it did not happen. It states the following:
- Cold fusion in a jar was not observed - it is not evidence
- The process to create cold fusion in a jar cannot be repeated, it is not evidence
- The cold fusion in a jar is not science - it has no useful purpose
- Because it can't happen today, it most likely (but not absolutely) did not happen then.
The exact same is true of supernatural phenomena. Can we repeat a miraculous healing? A divine calling to serve in Africa? The parting of the Red Sea? If we can repeat it, then it becomes "physically real" and can be called "natural."
A definition of Supernatural as "unreal"
Consider you have observed something happen. By the definition above, that makes it evidence to everyone who observed it. Now let's describe what needs to be true for this happening to be supernatural:
The happening cannot be repeated (If it could be repeated, it would be real)
We cannot predict the value of any physical quality without disturbing the system (we cannot predict the color, temperature, size, weight, volume, darkness, speed, or any other physical quality of the happening)
Under the above conditions, the thing which was observed to happen (the evidence) is classified as supernatural. It happened, it was observed, and it is not physically real.
This DOES mean that a supernatural event can never be predicted
This does NOT mean supernatural events are only ghosts and illusions
Give an example of what is and is not supernatural:
A Hindu Yogi meditates and practices yoga until he achieves anima. Several people are surrounding him and witness him shrink away to nothingness. Is this a supernatural phenomenon?
- It was observed; there is evidence
- His physical size was reduced, as predicted; the phenomena is real
- If he meditates and does yoga again, it will repeat.
No this is not supernatural. There exists a natural explanation by nature of its repeatability and predictability.
At 8:30pm, April 2, 1968 hundreds of people watch an illuminated woman defying gravity and walk around the dome of St. Mark's Coptic Church in Zeitoun, Egypt. This happened many times on different nights. Ask the same questions:
- It was observed - it is evidence
- The dome was illuminated - a physical quantity was changed, but not predictable
- If the people pray or do other acts, the apparition will not repeat
Yes at this time the apparition would be considered supernatural.
However, science has an obligation to attempt to frame all evidence into natural terms, without care for how rational that attempt is. Again, it is a pursuit. So scientists have tried to explain the lights in natural terms, leading one paper to be published in 1989 hypothesizing that the apparition was a theorized natural luminous phenomena resulting from tectonic strain, or, a kugelblitz. The paper was published without any experimentation, using only a 0.56 correlation between earth lights being reported before tectonic activity.
A Kugelblitz has only been a hypothesis however one was allegedly finally caught on film in 2014 using a slitless spectrograph. It lasted less than 2 seconds.
Thus no matter how absurd and unproven a natural answer to evidence may be, Science will always find "the best" natural answer to any phenomena. But this is not a problem, it has a purpose.
Let's look at what would happen if we allow supernatural answers, even if they were factually true, into our science:
James goes to the hospital with stage 4 cancer throughout his whole body. He is incurable. Some of his family pray for hi, and God heals him (truthfully). He returns to the hospital and is completely cancer-free after only 2 days.
Now, let's assume that even the doctors are religious. Would they write in their report, "James came into the hospital, thorough tests revealed stage 4 cancer throughout his body. Through a miracle, James was healed. Patient released."
Even if that report were completely true, how does it help Suzy with cancer in the next room? It's completely useless in helping other cancer patients. So the religious doctor is going set aside his personal beliefs, come up with the most sensible natural explanation and include that in the report. Can you imagine the world if this did not happen?
Natural explanations do not care if something is true. Only if it works.