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Before moving on with my question, I want to note that by supernatural I mean anything that would be considered a cause not known to be operating under known natural laws. Sure, if pigs started flying tomorrow, there may be an unknown natural explanation for this. But nevertheless, a cause that was considered impossible under currently known physical laws would still be operating.

Now, unless a literal violation of a known physical law occurred, what kind of evidence can one have that would reliably indicate that natural processes are not at work and a designer or some other intentional process that isn’t blind is at work?

As long as a certain observation is possible under natural processes, regardless of its probability or plausibility, no matter how small or hard to intuit, can one ever conclude that a designer causing that observation is more likely or more reasonable to believe in?

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    "by supernatural I mean anything that would be considered a cause not known to be operating under known natural laws" by this definition wouldn't light rays bending around a massive celestial body like a star have been supernatural in the XVIIIth century and natural after the discovery of special relativity?
    – armand
    Commented Jun 2, 2023 at 2:29
  • I wrote that comment so we don’t get caught up in semantics and the whole supernatural vs natural distinction debate. If we all started having the ability to fly, it would break currently known natural laws, and may have a natural explanation. But the point is that we would know for sure that our previous knowledge of natural laws was wrong. The question is more about when to discount a natural explanation in the cases of when an event under a natural explanation may be very improbable or implausible
    – user62907
    Commented Jun 2, 2023 at 3:57
  • You're on the right track. Sometimes a child-like simplicity can clarify the issue much better than detailed analysis by grown-ups. An interesting proposition presents itself ... one worth a separate, dedicated thread, but who has the time, oui, mon ami?
    – Hudjefa
    Commented Jun 2, 2023 at 4:57
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    If "supernatural" is defined as any cause not known to be operating under known natural laws then establishing its existence is trivial, just check that known natural causes do not explain the phenomenon. Of course, then length contraction, black body radiation, photoeffect, beta decay, etc., were "supernatural" in their time under this 'definition', and even "miracles".
    – Conifold
    Commented Jun 2, 2023 at 7:30

4 Answers 4

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Your question presumes several false things about science, which will make the answer to the first question fairly simple.

1a) You presume that science laws are absolute, and always unbroken. This is an invalid assumption. All science "laws" are only regularities, and even the most "fundamental" of them spontaneously break at times. This is made explicit in this paper on symmetry breaking in physics, and the spontaneous breaking of all the fundamental "laws" of physics: https://www.pnas.org/doi/10.1073/pnas.93.25.14256#:~:text=Symmetry%20principles%20play%20an%20important%20role%20with%20respect,structure%20and%20coherence%20to%20the%20set%20of%20events.

1b) You further presume that science is complete, and there are no known violations of any of the "laws" of science. This is blatantly not the case, all active science fields are incomplete, and there are known violations of nearly every regularity that are called laws in science. Exploring those violations, and trying to figure out if they can be explained by a modified set of regularities, is what science DOES. All active science is therefore a process of studying and providing explanations for "the supernatural" per your definition.

1c) You presume that science "laws" are coherent, and they therefore do not violate each other. This is manifestly false. We do not have a valid reduction structure to fundamental physics, some fraction of physics is not reduced, and only about half of chemistry, and only aspects of biochemistry in biology. Outside of these fields, complete reduction has been unsuccessful in science. PARTIAL reduction remains highly useful, as SOME causes can be found to be explainable at a reduced level, such as chemical poisoning of organisms. But the existence and stability of organisms, for example -- is only understandable at a higher level of biological system theory. And things like species, ecosystems, ecological niches, norms, societal institutions, etc. -- none of these seem to be reducible even in principle. They just don't rely on their substrate in any way, they exist due to logic phenomena and structures at a higher level. The goal of being able to reduce all of science to physics has been abandoned as unachievable in principle by the vast majority of philosophers of science. See the SEP article on reductionism in science, section 5. Science has adopted pluralism -- the subjects studied by other sciences besides physics are real, and their phenomena are causal.

One of the consequences of pluralism is radical incoherence. IF one accepts multiple uncoupled sources of authority, they WILL end up with conflicting predictions in their derived consequences. Hence, pluralist science CANNOT EVER in principle create a network of "this is consistent with science, and that is not".

Your second question is how to provide support for miracles, and in particular for design inferences.

2a) In one respect this question is trivial. There are two sub fields of science that focus on design inference, both anthropology, and SETI. Both reference "naturalism" by trying to distinguish designed objects from natural ones. One need not assume that the "natural" is constrained by unbreakable "laws" to do this, regularities work just fine for both fields. Key to both fields is to presume an agent as goals, and the powers/capabilities of the agent are critical to identify what one will then look for as evidence of artifacts left from accomplishing those goals.

One can extend this process to theistic design, and this was usefully done for design vs evolution in the TalkOrigins forum debates. TalkOrigins established that evolution fits our evidence set from species far better than design does, but the result for discussions on abiogenesis, and the origin of the universe were less definitive.

2b) You need to understand how hypotheses and theories are evaluated in science. You tend to think in terms of proofs -- a formal logic process. But science operates of a much looser and more pragmatic methodology. Philosophers of science have characerized how this process works, and the best characterization is by Imre Lakatos, who identified Research Programmes as how science operates. See https://www.liquisearch.com/imre_lakatos/research_programmes#:~:text=Lakatos%27%20model%20of%20the%20research%20programme%20aims%20to,abandoned%20or%20altered%20without%20abandoning%20the%20programme%20altogether. Research programmes are a set of working assumptions, which have core and secondary elements, and the secondary elements may be adjusted as evidence is accumulated in the field. Contradictions to the programme are not disqualifying, so long as there is continuing work to try to resolve them, AND there is useful continuing progress in the field using the programme. But when the field is generating more and more unresolved discrepancies, and rationalizations to try to explain them away become the dominant activity in a programme, it has become regressive, and a new programme needs to be developed in the field.

Accordingly, any design "miracle" programme has to show utility in solving problems, and effort to resolve falsifications. If a design programme does that, then it becomes a credible working model, and it will satisfy what you are asking for.

2c) As an aside warning, there are some trends of thinking in contemporary science that are far less useful than Lakatos' model, and these tend to be adopt Bayesian thinking. Bayes developed consistent and coherent math on how to show the change in validity of a theory in the circumstance of accumulating evidence. Bayes math is fully coherent and supported, unlike the standard statistics approaches used in P tests, T tests, etc.

The standard statistics embedded some judgements into how to do tests, and what thresholds are useful, which are USUALLY useful, but occasionally give whacky results. It is a pragmatically created model, that is not internally coherent.

Bayes model ALSO involves judgment calls, but he makes them explicit, and at user discretion. These involve the determination of the "prior" probability" and the weighting of new evidence. The assumption behind standard statistics is that users can't be trusted to make these judgements, so a standard should be pre-set for everyone, even if the standard can't be formally justified. Bayes statistics allow one to openly specify one's assumptions. The trouble with Bayesian statistics, is that the ANSWER is DRAMATICALLY dependent on these opinion-based judgement calls. If one just sets the confidence in one's "prior" very high, then one can honestly evaluate massive amounts of contrary evidence, and still show that it does not change the conclusion, and that the evidence fails to reach statistical significance.

Bayesian statistics in practice end up being used to rationalize not changing one's views in the face of contrary evidence. All Biblical Creationists, for example, are basically Bayesians who consider the prior evidence for Biblical accuracy to be so strong, that no contrary evidence from any science can shake their conclusion. And the recent tendency in science to adopt Bayesianism gives these sorts of dogmatisms a shield or cover to hide behind.

It is not only Creationists who have adopted this sort of anti-evidence rationalization based on Bayesian thinking. The organized skeptic movement has also adopted it. Susan Blackmore, in her autobiography, notes that she will dismiss ayn and every test done for psi phenomenon, because she considers the "prior" of physicalism to be so likely as to be unquestionable -- while the logical possibility of experimental error or researcher cheating is always be possible, for any experiment, hence her beliefs are irrefutable by any evidence, in principle. Similarly, the creator of the Science Based Medicine web site and movement, Dr Steven Novella, will dismiss any positive results supporting any clinical success for alternative and complementary medicine, because there is always the possibility of experimental error or confounding effects in medical studies. He even more radically advocates for a BAN on funding any medical experiments on CAM, on the assumption that all positive results are experimental anomalies, and lead to confusing both doctors and patients about the uselessness of CAM. The SBM web site explicitly advocates for use of Bayesian statistics, with a prior is so high that it excludes CAM for every showing any statistical validity. Organized skeptics, similarly to creationists, can become immune to evidence and rationalize this dogmatism with Bayesian thinking.

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    "The trouble with Bayesian statistics, is that the ANSWER is DRAMATICALLY dependent on these opinion-based judgement calls." A prior is measured. A statistical inference based on a guess is a guess with extra steps. Representing a guess as anything other than a guess because you took extra steps is a lie. The problem isn't Bayes' theorem, which worked just fine expressing the true correlation between one guess and another, it's lying about your data.
    – g s
    Commented Jun 3, 2023 at 14:41
  • @gs How does one measure the probability of Biblical inerrancy, or physicalism to be true as priors? How does one measure weighting of new data? These assertions appear radically implausible.
    – Dcleve
    Commented Jun 3, 2023 at 14:49
  • For Biblical inerrancy (if we assume that there aren't internal contradictions so the idea of inerrancy means anything - which assumption we need to state clearly in our conclusion), establish a finite countable data-set whose frequency represents or can be directly correlated to the claim, get archeologists to count it, and make sure you propagate your measurement error. I think physicalism is not something that can be empirical, but only because a physicalist with a measurably inerrant Bible would believe in a physical God who did physical miracles through the a physical Holy Spirit.
    – g s
    Commented Jun 3, 2023 at 14:56
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    Spontaneous symmetry breaking is not an example of what you're trying to illustrate. Every time water freezes into ice, the orientation of the bonds in the ice crystal breaks the rotational symmetry of liquid water. That's spontaneous symmetry breaking. Electroweak symmetry breaking works similarly. It doesn't break the laws of physics as you assert; the whole process is predicted and correctly modeled by known laws of physics. You should instead use an example of a scientific theory being supplanted (e.g. Newtonian gravity by general relativity).
    – benrg
    Commented Jun 3, 2023 at 17:41
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    @Dcleve The paper looks fine to me, but you've misread it. You seem to be hung up on the use of the word "break", which doesn't mean what you think it means in this context. Note that the paper says that in spontaneous symmetry breaking "the laws of physics are symmetric but the state of the system is not" (emphasis mine). The SU(2)×U(1) electroweak symmetry remains an exact symmetry of the laws of physics even after the process unfortunately called "electroweak symmetry breaking".
    – benrg
    Commented Jun 3, 2023 at 19:37
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The example i like to use for this kind of questions are healing prayers. So assume a person is sick, in coma even, and their friends and relatives may pray for their recovery, or not. When they do, and the person recovers, the recovery could be attributed to a higher power having listened to prayers. There is no placebo effect possible here (because the patient in question is not aware of the prayers).

The presence of such supernatural influence can still be proven statistically however, if they act often enough consistently. As an example, hospital record could show whether christians recover more often from diseases than atheists or believers in other faiths.

So statistics are a way to prove divine intervention in some form when this intervention is not observable as obvious violation of natural laws like flying pigs. (Note the placebo effect is prone to look like supernatural influence, so some precautions are required. Similar other known research biases can exist.)

Statistics are similarly used by Casinos to find out if any of the gambling customers use techniques or devices to beat the random odds (saying a prayer before throwing the dice would already have been detected as proof of god if it worked, by the Casinos).

However statistical proof requires the supernatural to happen frequently enough. If a god chooses to miraculously heal one person only once every 100 years, this won't be detectable in the records.

Another proof can be to detect the "fingerprint" or "signature" of the supernatural. As one funny example, imagine one day a researcher notices that the unused DNA of humans can be decoded as a message like "Greetings earthlings, this is a letter from your creators. Be nice. Here is a nice recipe for how to make pancakes..."

Such a linguistic evidence in the DNA would irrefutably show intelligent tampering (though not necessarily by a supernatural force, technology could achieve the same in principle).

Apart from linguistic traces, other complex regularities in nature that cannot be explained by natural selection or life (organic copying of molecules) can be evidence of the supernatural. Dunes in the desert, pebbles, rivers, lakes, continents, crystals, snowflakes, suns and planets, are all examples for simple regularities explainable by natural selection. Organic molecules, viruses and cellular life are regularities explainable by life (according to science). Most man-made structures exhibit complex regularity that cannot be explained via natural selection or life.

There can be more methods depending on what kind of non-miracle intervention is implied by the question, so the question is too broad to give a complete answer.

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You ask two questions here. They require different answers.

Comment on the definition of "supernatural". In present usage, any cause that is accepted by science thereby becomes a natural cause.

In reply to your first question - A violation of a natural law on its own would never be regarded as a as evidence for a supernatural explanation. If no natural explanation is available for a given phenomenon, it is labelled "anomaly" and filed in the pending tray. Kuhn has a great deal to say about this phenomenon. See Thomas Kuhn (Stanford Encyclopedia of Philosophy)

In reply to your second question - Archaeologists (especially those working in pre-history) do this all the time. But they know that human beings exist and a great deal about what they are capable of.

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I would suggest the following as a working definition of the supernatural:

A claimed process (including beings, etc) is supernatural if it is:

  • (claimed to be) detectable.
  • resistant to the kinds of observation that are useful for making confident empirical claims, and the reasons for this cannot themselves be explained in terms of processes which are themselves readily verifiable thereby.
  • and substantively unlike anything that is readily verifiable by the kinds of observation that are useful for making confident empirical claims.

This would let us preserve the common use of the word - for instance, bigfoots being natural and werewolves supernatural - without appealing to cultural norms like what genre of movie something is supposed to be in or whether you're supposed to pray to/against it or shoo it away if it shows up in your yard.

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