At which point does a meaningful coincidence call for a supernatural explanation?

Question

Every time we've ever come across a seemingly marvelous coincidence that was repeatable and testable, it turned out to be representative of a law. It was a coincidence that turned out to be a real pattern, but a pattern that could be represented as a natural law. In some other cases, those coincidences turned out to be fabricated stories.

In all other cases, coincidences are singular or consist of a series of events that seem, to many, to not have been tested enough. This is either because the coincidence was simply a meaningful event that occurred unexpectedly (such as someone calling me after I thought about them), or something that although was "expected/tested for" in some manner, stopped being tested for (such as me correctly guessing a number between 1 to 10 three times from another person, and then stopping). In the latter case, the tests always stop and don't continue.

We've never tested something repeatedly that turned out to be a pattern where the explanation was not natural. Now, clearly, we can conceive of scenarios, where even if we can't identify a natural cause, it would go against our conception of how natural laws work. For example, if I correctly guessed a number between 1 to 10 that Adam was thinking of, and then repeated this experiment with hundreds of people, with enough protocols to ensure fraud was avoided, sooner or later, we'd be convinced that it was not happening by chance. It would cry for a better explanation. But this never happens.

This seems to beg the question though. How many times would I have to guess a number before it begs for an alternative explanation to chance? Intuitively, it seems that certain numbers beg this question more obviously. For example, if I guessed it 1000 times, the chance would seem too low.

But by its very definition, there is no such thing as the probability of an event being too low for chance to not have caused it. If an event E = guessing a number 1000 times, and C = chance, P(E|C) seems low. But this says nothing about P(C|E). One must look at alternative explanations to determine this, but let's consider supernaturalism as a whole here. Even though we don't have any apriori predictions of what kinds of events supernaturalism would entail, the event of me guessing a number 1,000 times seems to beg for an explanation. If we ruled out fraud and my guessing continued, what should our philosophical position be? And at what point should we be skeptical that intentionless naturalism is all that is at play here?

Answer 1

Simply, it depends how willing you are to risk being wrong.

Note this is not any different than any other experiment. You collect data, you do some analysis and you find: "This data is less than 5% likely to have occured by chance, let's publish." (this is p<0.05 which in some fields is enough for people to publish papers, but also means 1 in 20 might be wrong). => statistically significant is the term you are looking for

In particle physics, this threshold is very low, 1 in 3.5 million chance of being a random result.

So, if it's absolute certainty you are looking for, you won't find it with statistics. But you can quantify your uncertainty and then (have to) decide at what point you start believing.

Answer 2

What is a meaningful coincidence?

I have a vacuum cleaner and the last time I turned it on an earthquake started. That's an incredibly meaningful coincidence isn't it? Now I can state that my vacuum cleaner has supernatural powers and it can never be used again since that would cause massive destruction and death.

So from one meaningful coincidence, I have shown that my vacuum cleaner has supernatural powers and provided an excellent reason for avoiding any attempt to disprove it.

In general, it is best to avoid drawing any conclusions from meaningful coincidences. Better instead to perform controlled experiments.

Answer 3

The wording of your question implies that the alternatives to chance are supernatural, which is clearly a non-sequitur. The underlying question has two parts therefore- the first is at what point might one question whether a coincidence is just chance, and the second is whether one is ever justified in looking for a supernatural explanation.

Firstly, there is no single threshold of improbability beyond which one is obliged to rule out chance, having happily entertained the probability of chance up to that point. It is a matter of degree. There is a spectrum of probability, at one end of which you will feel pretty sure that correct sequential guesses of a number are pure luck, and at the other end of which you will be very confident that something other than luck is at play; but there is no hard cut-off between those two regions.

As for the supernatural... suppose you had correctly guessed 1000 times in succession which number I was thinking of between 1 and 10. I would be pretty sure it wasn't luck. However, based on probabilities alone I would not assume the explanation had to be supernatural, if by that you mean some effect that had no possible basis in science. I would be happy to conclude that it was inexplicable- as lots of things in the universe currently are, such as consciousness, dark matter, why a gullible public continues to elect reprehensible politicians, and so on- but I would not imagine it had to be supernatural.

Answer 4

Supernatural explanations have zero explanatory power.

The best example of that is the God explanation. The concept of omnipotence is logically inconsistent so this leaves only ordinary gods like Zeus and Thor. The problem, then, is that we could potentially think of an infinity of ways such gods could be: two eyes? three eyes? Eager to intervene in human affairs? Reluctant? What powers exactly? Whatever we may fancy is not going to be based on empirical observation so anything goes and we end up with an infinity of possible gods and as many possible explanations, by definition each one no more likely than the others, meaning that the probability of each being true is infinitely close to zero. And as a rule, we do not like that sort of odds.

Supernatural by definition means that the explanation is not grounded on empirical observations of nature and this is where the problem is. Anything you fancy will be as good as anything else.

The fact that we are interested in explanations when we think there is a reason for a coincidence comes from our logical sense, which is an innate mental faculty that therefore all humans in good health have. Logic takes advantage of the existence of regularities in nature, what we call "laws of nature". Whenever our observation of nature suggests that there is a regularity in natural phenomena, our logic applies: all cats meow, so if Felix is a cat, then Felix meows. This is as simple as that. Our search for an explanation is triggered when we observe a regularity in nature: All cats meow. This has explanatory powers because once we accept the rule, we can infer that anything which is a cat can be expected to meow sooner or later. However, the rule itself is based on observation of nature (cats), not invented out of thin air.

In the case of supernatural explanations, we eschew observation of nature to rely exclusively on our imagination. And there is potentially no limit to our imagination, hence the infinitely close to zero probability. Utterly uninteresting, except presumably for people who prefer wishful thinking to the hard work of observing nature.

Answer 5

There are a number of thinking errors behind this question.

1. There is not a dichotomy between coincidence and "natural laws". All laws are only consistencies, not logical necessities, and all break spontaneously at times. See this physics paper for a discussion of this for even fundamental physics: https://www.pnas.org/doi/10.1073/pnas.93.25.14256

2. This question seems to presume that non-physical is necessarily supernatural. But abstract objects are not physical, and it is a reasonable inference from the almost 200 year failure for physicalism to solve the hard problem of consciousness, that consciousness is not either. But abstract objects are by their very nature subject to reasoning, and consciousness studies are a very active field of research, so neither are "beyond the scope of reasoning or empirical investigation".

It is a core assumption of methodological naturalism that whether physicalism is true or not of our world, is a question subject to naturalist inquiry. Therefore, by direct and explicit inference, non-physical hypotheses can be natural.

Note also -- science is now pluralist. None of the other sciences reduce to physics. And science does not encompass all of the universe. Scientism is false. With just pluralism and the falsity of scientism, the premises behind this question break down.

3. This question assumes that no investigations with non-physics assumptions, or with explicitly psi assumptions, has succeeded in showing the likely reality of anomalous phenomena. This is untrue. The reference for what is true in science, is the consensus of the relevant scientific professional society, and the Parapsychology Association, the relevant NAAA member society, summarizes multiple that multiple phenomena have been demonstrated beyond any reasonable questions. Here is their summary of these demonstrated phenomenon: https://parapsych.org/articles/36/55/what_is_the_stateoftheevidence.aspx

4. What you seem to be looking for, is what is the criteria to compel you to accept the validity of a non-physical phenomenon. This is a question that philosophy of science has long struggled with. Quine pointed out there can BE no "critical tests" to refute a theory, because all theories are infinitely malleable with ad hoc assumptions. Dismissing all refuting experiments as "mere coincidences" could leave a determined and dogmatic physicalist immune to any evidence.

The standard that has proven most useful, is that of Lakatosian Research Programmes. See here: https://www.telework.ro/en/imre-lakatos-the-methodology-of-scientific-research-programmes-an-overview/ Note, as Papineau spells out in The Rise of Physicalism -- the widespread adoption of physicalism occurred when it proved to be a more "progresive" programme than its rivals.

5. But physicalism is not in the same favored state today as what Papineau describes from a century ago. Current problems include the theoretical and practical inability of physics to ever be "closed", abstract objects, emergence, the problems with all three of our models of time, the failure of reductionism and the incoherence of non-reductive "physicalism", the preference of theoretical physicists to think of MATH as more fundamental even than physics, plus the hard problem of consciousness. GLOBAL Physicalism is trending toward a regressive programme today. This has led to the revival of non-physicalist worldviews today, with pan psychism, neutral monism, and property dualism joining with a revival in physicalism's traditional rivals of idealism and substance dualism.

Answer 6

It's a judgement call.

Just as one person may differ from another about whether an event was caused by human intervention, they may differ about supernatural intervention. Their prior assumptions will, of course, color it on both cases; if one believes that a man's medical problems were known, he would be more willing to believe that the food was intentionally contaminated with something that he would react badly to, and so his death was murder, while the one who believes they were secret would be more likely to put it down to accidental death.