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Are all arguments against miracles circular?

Update: InspirePhilosophy posted a reply to this text on his blog.
The InspiringPhilosophy YouTube channel has produced numerous wonderful videos about the foundation of quantum mechanics – and many more, equally visually wonderful yet much less sensible videos defending naive and literal Christian beliefs. The latest, 14-minute video was posted on Friday

and it argues that there are no valid arguments against miracles. The narrator has the same voice in all these videos, the linguistic perfection permeates every minute of the monologues, and the videos are always fun to watch. Nevertheless, some of them – the quantum ones – provide us with totally sensible and relevant arguments about the deepest discoveries of the 20th century physics which many people including physics PhDs misunderstand even in the 21st century; while the arguments about the miracles may be described as the rationalization of its religious beliefs by an 8-year-old schoolkid.

The narrator basically agrees that one may define miracles as a violation of the laws of Nature. And the first half of the video is dedicated to the assertion that no one has presented a valid argument against miracles because all such arguments are circular. The structure of the anti-miracle arguments is described as follows: Miracles don't exist, and therefore the uniform human experience says that they don't exist, and therefore violations of laws don't occur, and therefore miracles don't exist, or something like that.

We also hear that one can't be right if he says that there are no miracles just because they would contradict his experience. The reason why this argument is wrong, we hear, is that other people have other experiences. And because many people in the world believe in miracles, they must have a nonzero probability. Also, an Arab prince has never seen the ice so he may conclude that ice – a miracle – doesn't exist but this conclusion is wrong. And so on.

All these pro-miracle arguments are cute and make me smile but they are just totally silly. They have nothing to do with the actual arguments against miracles. The actual arguments against miracles involve the scientific method i.e.
  • observations of phenomena in Nature, patterns in them, and the formulation of candidate hypotheses that may describe these patterns
  • comparison of the hypotheses with the observed data and elimination of the falsified ones (or the gradual suppression of the disfavored ones)
The first subtlety we must realize is that while we may define miracles as violations of the laws of Nature, we don't immediately know what the "exact" laws of Nature are. Instead, we are learning about the character of the laws of Nature by accumulating the knowledge by the scientific method.

At a finite moment of this process, we must always distinguish miracles in the sense of
  • hypothetical events violating the "actual" laws of Nature that we don't perfectly know yet
  • hypothetical events violating the "approximate" laws of Nature as we currently know them.
These are two things that are different in general and I believe that the narrator fails to distinguish them. At the same moment, there may exist evidence (or overwhelming evidence) that for a given class of questions, these two categories are basically equivalent.

A funny thing is that if we talk about miracles as events that violate the "most accurate laws of Nature" that one may conceivably formulate, such miracles don't exist by definition! You know, if Jesus Christ was turning water into wine, it follows that the possibility (if not certainty) that Jesus Christ may have turned water into wine is a part of the exact laws of Nature. If Jesus can or could do such things, the exact truth about the behavior of Nature obviously cannot say that Nature can't allow such phenomena. So we can't decide whether Jesus was turning water into wine yet. But we can say that miracles don't exist if they're defined as violations of the (typically unknown) exact laws of Nature! They can't exist; this claim is a tautology. It doesn't matter a tiny bit whether these violations are described in terms of God, supernatural agents, or anything else – they're just technicalities. What matters is the truth about the existence of certain phenomena or events and the truth just can't contradict itself.

So this part is easy. The less trivial part of the reasoning arises when we ask about particular miracles. Has Jesus been turning water into wine? Now, let me destroy your Sunday before the Christmas: He hasn't. How do I know that? I haven't observed Him. His daily life was as inaccessible to me as ice is inaccessible to the aforementioned poor Saudi prince (who, probably thanks to the falling oil prices, doesn't have enough money to buy a fridge or fly to the North and see the ice LOL).

One may use arguments against the "water to wine transmutation" based on different kinds of scientific thinking or laws. They have various risks. I would use the most modern scientific theories. Wine is defined as a liquid that contains ethanol and many other compounds, aside from water, and satisfies some additional conditions that may be approximately defined. Nevertheless, the presence of ethanol is a necessary condition for something to be wine; and 13% is the minimum in the wine that I am allowed to buy for family parties LOL. Now, ethanol contains (a huge number of) carbon atoms. Water doesn't.

(The argument involving ethanol and carbon isn't the only possible one. There exist similar arguments but one representative is enough to settle the question.)

To turn water into wine therefore requires, among other things, to produce the carbon atoms out of something that has no carbon atoms. It's possible but only through nuclear reactions – pretty much by the definition of nuclear and non-nuclear processes. Non-nuclear reactions conserve the number of nuclei of each type so they can't turn water into wine. It follows that if Jesus were turning water into wine, he must have been using a nuclear device, too. Given the heat and unhealthy radiation that these gadgets have to produce and given the history of nuclear physics, it seems very unlikely that Jesus was using a nuclear device of this form. So he was almost certainly not turning water into wine.

It's much more likely that this story is being told because some people were fooled or some people have actively deceived others or some naive people were trusted more than they should have. These possibilities seem much more likely. The scientific approach to the answering of questions simply does require us to compare what is more likely and what is less likely. And – even though the narrator tries to pretend otherwise – people are not infallible and 100% honest and 100% able to see everything correctly etc. It's normal for them to be fooled, for them to actively lie, and do other things. So there is nothing implausible about this explanation of the "water into wine" story. The story has made many people happy and many other people powerful.

One may question all steps in my chemistry-based argument. How do we know that the number of carbon nuclei is conserved in non-nuclear reactions? Well, with my definition of "non-nuclear reactions", it's a tautology. But you may adopt a more informal definition of "non-nuclear reactions" as those that might have been available to Jesus Christ, or reactions at low temperatures. With these informal definitions, there is still extremely strong evidence that the number of nuclei is conserved in all "mundane enough" processes. We have observed lots of very diverse processes and this law has always been valid. And we actually claim to have a theory that in principle predicts not only that new nuclei can't arise from different ones or from nothing. We have a theory that claims to calculate all the probabilities of any conceivable event – a much stronger statement. There is a huge body of evidence that this theory works across the Universe, or at least on Earth. ;-) And one of the consequences of the theory is that carbon atoms do not arise from water under room temperature.

As Dr Herod implicitly told Jesus, one may and one should search for and collect evidence both for and against miracles. Can you walk on Herod's swimming pool? Or can you miraculously fix the wrong aspect ratio of the video above? Just prove it! ;-) You may check how the Czech edition of the song [by Bohouš Josef of Pilsen] from the musical sounds. For more pro-religious songs from the musical, check e.g. this one.

I want to stress that the actual scientific arguments against "the transmutation of water into wine" are way more reliable and sophisticated than the "argument" by the Saudi prince who has never seen ice. Physics has understood the phenomena around us to such an amazing depth that it may boldly make many claims about many objects that no human has ever seen – or will never see; about events that took place billions of years ago; billions of light years away; at length scales much shorter than the atomic radius; at temperatures of trillions of degrees etc. This could have been an impossibly ambitious goal a few centuries ago but it has become a reality.

Nothing about these actual scientific arguments is anything like circular reasoning. We accumulate evidence about processes involving \(10^{50}\) atoms of the Earth and other things and all of them are nontrivially consistent with a detailed theory that also implies that one can't change the number of nuclei of various types at low temperature. So one can't turn water into wine, either. The idea that someone has lied or sloppily observed Jesus Christ is vastly more likely.

At the end, he does mention quantum mechanics again. Improbable things may happen in quantum mechanics. Right. But quantum mechanics still predicts many things to be so wonderfully improbable that for all practical and most impractical purposes, we may say that they're forbidden. For example, if the probability of something is much smaller than \(10^{-125}\), we may say it will never happen in our Universe. And be sure that the calculable probabilities easily sink under this threshold because the expressions often have the exponential form and the exponent may easily drop beneath –125.

If something that was similarly insanely unlikely to occur according to the theory T does occur, then the theory T has been falsified. This is how the truth value of hypotheses is treated by science. This is the very point of science. Because most probabilities predicted by realistic theories are never "strictly" zero, we must choose some "threshold" at which it becomes OK to eliminate the hypothesis. There are different standards reflecting the people's and disciplines' readiness to be wrong. But be sure that if the probability is below \(10^{-125}\), the thing just couldn't have occurred between the Big Bang and now, anywhere in the Universe according to anyone who looks at the world from any scientific viewpoint. If it did happen and a theory predicted a probability that was this low, the theory is dead.

Now, chemistry or the Standard Model aren't dead in this sense yet. These theoretical frameworks are by far the most convincing tools to approach the question whether water may be turned into wine at room temperature and the answer is No.

Around 11:50, a guy says that "there is a difference between a very low probability and a violation of the law of Nature". Well, there may be a difference but the difference goes to zero when the probabilities go to zero, too. Morally speaking, the difference just isn't there for tiny probabilities and this operational equivalence between "tiny probabilities" and "impossible" is the very reason why we use the concept of probabilities! What the man says is "fully" right for probabilities "comparable to 50%". But the probabilities like \(10^{-125}\) are much closer to zero than to 50%. Their implications for our understanding of the truth is therefore also closer to the consequences of \(p=0\) than to consequences of \(p=1/2\). So his implicit assumption that all non-zero, non-one probabilities should be treated just like \(p=1/2\) is simply not a rational way to think.

Imagine that the probability of something, like turning water into wine, is some insanely small number like \(\exp(-10^{25}\). It can't happen often but "it can happen", the miracle apologists argue. Could have God done it 2,000 years ago? Well, in principle yes, in practice no. We are allowed to identify these tiny probabilities with zero. If we weren't doing that, we could never conclude anything, we could never make any progress in science. So our reasoning is different: If those de facto impossible events were possible, it's because the exact laws of Nature should imply a much higher, more reasonable value of probabilities. It must be because the laws as we imagine them are not complete and we are ignorant about some effects or features of the initial state that make the "miracle" (e.g. an event in Bethlehem 2,000 years ago) much more likely than we think.

I have picked the "water into wine" transmutation. Obviously, one could present arguments based on modern science that would lead to conclusions about other miracles – Jesus Christ born from a virgin (some cell biology would be helpful), walking on the water (hydrodynamics etc.), and many others. These proofs could be entertaining but at the end, I think that many people understand the elementary enough science that is needed to decide about these matters so these technicalities are not the problem. The problem is really more far-reaching – whether we believe rational reasoning or not.

It's a priori possible that something is seriously wrong about our understanding of the laws of physics that misleads us about Jesus' miracles but this hypothesis – that there is some "really big" bug in our understanding of the laws of physics that dramatically changes the rules and allows some 2,000-year-old tale to be "real" – should be fairly compared with the acceptability of other hypotheses, including the hypothesis that some ancient people 2,000 years ago were just bullšiting or someone has just turned an innocent fairy-tale into a documentary. At least vaguely, one may compare the probabilities of these two explanations and be sure that the latter overwhelmingly wins. I can't prove it rigorously. There is no way to rigorously calculate the probabilities that "the laws as we know them today break down in some imperfectly understood context"; a theory can't quite see everything beyond its domain of validity. This is also the reason why we can't "calculate" the probability that the \(750\GeV\) diphoton resonance will survive. The "exact" probability depends on the prior probability and there's no way to "objectively" decide about the prior probability that particles beyond the Standard Model are allowed in this mass range.

But the theory that agrees with all the tests of chemistry and nuclear physics but that is fundamentally modified just in order to allow Jesus or His hypothetical non-penetrative father to do a few sleights-of-hand is an extremely contrived theory. It violates Occam's razor of any kind that people think about. It's exactly this kind of a "modified theory" that postulates ad hoc exceptions that scientists generally eliminate among the first ones.

The main impression is that I am baffled that someone who reads papers about foundations of QM and extracts the right conclusion out of them much more safely and easily than many people with a physics PhD is also willing to maintain this kind of self-evidently fallacious and childish reasoning about miracles. To see the contrast in the "methods", check e.g. the point 8:45 in the video. The narrator sketches what he imagines under the "laws of Nature" (those notions may have been copied from philosopher David Hume or someone else):
regularity theory

nomic necessity theory

causal dispositions theory
What? By the laws of Nature, I imagine string theory – or the Standard Model combined with general relativity in some way – and their derivable implications for numerous "more mundane" situations. The three "parts of the laws of Nature" listed above sound like some philosophers' superstitions. They have very little to do with science. The narrator must know that he's been fighting against a straw man, right? He's recorded numerous videos about observables on the Hilbert spaces so he simply must know that the actual laws of Nature as understood by science today are completely different than the three philosophical phrases above. What water is able to become is given by physics and chemistry, not the "causal dispositions theory".

Many people are reasonable if not brilliant but they have certain barriers behind which their rational thinking isn't allowed. It's worse than that. The "complete ban on balanced rational thinking" behind these barriers seems to be a very important source of enhanced self-confidence for these people. That's how they become e.g. more spiritual (or, in other contexts, more politically correct) than other people who "just know" the same thing.

But apologies. The laws of physics – even those that we know as incompletely as contemporary physics does – properly account for the "most obvious" phenomena in the European labs as well as phenomena in stars that are over 10 billion light years away. It's silly to think that the same laws broke down e.g. in a cowshed in Bethlehem 2,000 years ago. If some modifications of the Standard Model are needed, they're universalistic new features at the very short distance scales or the LHC-like or higher energies. To postulate exceptions for macroscopic phenomena in Bethlehem violates the whole framework of reductionism; to believe such a thing means to believe that the description (e.g. of Jesus' water and wine) in terms of the smaller blocks is absolutely unusable. There's a huge body of evidence against such ad hoc exceptions.

Now, I know that it's popular to say that it's not right to try to steal people's cute beliefs. But I have several points to say here. First, I am not sure whether these childish beliefs continue to be cute when one is no longer a child. Second, these beliefs will survive this critique – after all, they have survived for at least for 2,000 years before it. Third, you may say that "I believe" in the scientific method and its results in the same passionate ways as some Christians believe in miracles in the cowshed. So you may also treat me as a naive child and don't take this belief from me, either! ;-)

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