William M. Briggs

Statistician to the Stars!

Hume on Miracles

It’s Memorial Day, and it is not an abuse of the word “miracle” to suggest that it applies to the volunteering of the soldier who gives his life so that we might live in freedom.

Here is what I would consider a miracle: a generous, exceedingly wealthy patron decides, after reading this blog, that this man William M. Briggs deserves financial independence so that he is able to continue his curmudgeonly investigations of science and philosophy without having to worry about procuring his rent; and thus the patron provides this man Briggs a sack full of (tax free) gold.

I hope you agree with me that this event is possible It is also is extraordinarily unlikely—winning the lottery three times in a row has a better chance—but it is not impossible.

David Hume would not have labeled this glorious occurrence a miracle. To him, events which are possible, no matter how improbable, but which occur are not miraculous, just rare.

Here is what Hume would have called a miracle: the laws of physical science are suddenly altered in ways unknown and unknowable, such that the stack of newspapers at Briggs’s feet are transmuted into gold (also tax free). And immediately after this just award appears, the laws spring back to their former state.

To Hume, “a miracle is a violation of the laws of nature.” But that word “laws” is tricky. Few doubt that the universe is set up to work on certain inviolable guidelines, we just don’t know what all the guidelines are. So how can we say when and if these sacrosanct rules have been broken?

Discrete (quantum) mechanics being what it is, or the, as yet, true but unknown laws that govern the workings of the universe being what they are, it is possible that a complex mass and energy transfer could result in this worthless paper turning to gold.

All of us are willing to say that this event is improbable, but how many would claim that they could deductively prove that it is impossible? Remembering, of course, that the soundness of all premises used in that proof must also be demonstrated with certainty.

We might guess, but guessing means probability, and we’re after certainty here. Can we, with certainty, say when the laws have been violated and a miracle has occurred? Again Hume:

A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event. In other cases, he proceeds with more caution: he weighs the opposite experiments: he considers which side is supported by the greater number of experiments: to that side he inclines, with doubt and hesitation; and when at last he fixes his judgement, the evidence exceeds not what we properly call probability. All probability, then, supposes an opposition of experiments and observations, where the one side is found to overbalance the other, and to produce a degree of evidence, proportioned to the superiority. A hundred instances or experiments on one side, and fifty on another, afford a doubtful expectation of any event; though a hundred uniform experiments, with only one that is contradictory, reasonably beget a pretty strong degree of assurance. In all cases, we must balance the opposite experiments, where they are opposite, and deduct the smaller number from the greater, in order to know the exact force of the superior evidence.

Now, it is obvious that “a pretty strong degree of assurance” is not certainty. So we seem stuck: we cannot always know—with absolute, utter certainty—whether the strange event before us was merely the result of a confluence of improbable circumstance, or that it obtained from a transient shifting of the laws of nature.

But there’s something wrong with our language here. If we say that a “law” is an “inviolable rule”, then, by definition, the law cannot be violated. This says that if we know with certainty that a law holds sway, any seeming violations of it must be due to other causes, such as a mistaken measurement, or false testimony (note that “false” does not necessarily imply “malicious”). And with what authority do we claim that inviolable rules must exist?

Hume famously argues that our knowledge of physical “laws” is so strong that we would always say that a purported miracle is more likely the result of mistaken or false testimony than the result of temporarily shifted governing rules.

Experience is on Hume’s side: most reports of extraordinary events are later found to be the result of mundane forces or false testimony. And those events that cannot be verified, we suspect can also so be explained.

But, and here’s the meat, “suspect” is not “know.” We cannot prove miracles impossible, nor will we be able to prove certain reports of miracles false. We have to settle for something less than certainty.

17 Comments

  1. First start with the knowledge that most physical “laws” are really models that are assumed true because no counter example has been discovered, for example the first law of thermodynamics. Some “laws” (say the law of cause and effect) would lead to a tumbling of physics as-we-know-it if a violation is discovered.

    Hume got it right. After N–>infinity of supporting examples, finding a counter example should be viewed with suspicion. If the oddity can’t be explained away by existing laws then the next step would be to find which physical “laws” need modification thus incorporating the “miracle”.

    I think by definition, a true miracle would imply all of physics, if not all of science, is hogwash and in need of serious overhaul.

  2. Slightly OT but I have always appreciated Peter Drucker’s observation that “…the problem with miracles is not that they don’t happen, but that you can’t count on them happening.”

    That is, the probability of the occurrence of a miracle is a function of…normal curve..something…something..times 2 standard deviations…something to the fifth power……uhh..umm…

    Guess I’ll leave the statistics to you. I’m more comfortable with Drucker’s application in gerneral life.

  3. Are miracles occurrences that defy the laws of nature and thus are by definition impossible, or are miracles merely highly unlikely events, not impossible ones? The question is difficult to answer, since life itself is the “confluence of improbable circumstance.” The stack of newspapers at your feet is no less improbable than a stack of gold. For that matter, your feet and your very existence are highly improbable events. Nothing in this world can be said to be mundane, including the laws of nature. It’s all a miracle.

    The hair-splitting on this question arises from the anti-religionist tendencies of the Age of Enlightenment. Miracles were (formerly) seen as cases of divine intervention proving the existence of God. Those who rebelled against theocracy rejected the notion of divine intervention for political as much as philosophical reasons. Science then became the religion-substitute, culminating in Darwinism, which rejects divine intervention utterly.

    Science does not reject faith or fanaticism, however. In fact Science invites fervency in it’s adherents, single-minded dedication to the teachings of neo-priests such as we have seen in the Global Warming Alarmist movement and other social Darwinist frenzies. Science has not cured war or other political oppressions — it has made war worse: more inhumane and horrific. The rejection of religion-based ethical restraints on behaviors has not been enlightened or pragmatic. So-called “progressive” philosophies are as oppressive as those of the Inquisition.

    In that light, Hume’s strict definition of miracles may be seen as a failed attempt to free mankind from oppressive superstition. Anti-divine-interventionism (aka Darwinism) has not resulted in any evolution of humanity — we are still brutishly inhumane to each other, maybe even more so.

    Which is why I have adopted a more expansive view, that life is hugely improbable, that it is all a miracle, that divine intervention may be seen in all of Creation, and that nothing is certain. I don’t desire adherents, however. Keep your gold, free your spirit. And try to be nice to your neighbors. They are miraculous creations of divine will, after all, and deserve your kindness — if you can muster any up. God gave you the capacity for compassion; try exercising it.

  4. Mike D.,

    ” Anti-divine-interventionism (aka Darwinism) has not resulted in any evolution of humanity”

    And why should it? Since when do explanations cause a change in the explained or explanations of a cause of an effect result in more the effect?

  5. I must confess that I witnessed a true miracle once. I dropped a peanut butter and jelly sandwich that landed jelly-side up — a mriacle.

  6. Since we don’t know what the “laws of nature” are, Hume’s concept of a miracle is just another philosophical straw man. “Miracle” is a folk concept, not a scientific or philosophical one, and therefore no rigorous definition will fit. A Carnappian explication is of no interest.

    Regarding the prospect of a miracle happening to the mortal Briggs, the Wizard of Dissolved Gas (same species as the Wizard of Oz, with similar capability of granting wishes) has a crude approximation in mind. The wise will understand.

  7. Current (April) odds for winning the Super Bowl in 2011 are apparently:

    Cleveland Browns 80/1
    Detroit Lions 80/1
    Oakland Raiders 80/1
    Buffalo Bills 100/1
    Kansas City Chiefs 100/1
    St. Louis Rams 100/1
    Tampa Bay Buccaneers 100/1

    Personally, I think if Detroit or Cleveland won, then a miracle will have occurred.

  8. JJD,

    FYI, Miraclesat the Standford Encyclopedia of Philosophy.

  9. Since the post on Martin Gardner, I have pondered the idea of a theist who accepts Thomistic arguments of metaphysics and who would restrict God to the physical laws of nature. With this post, I have a glimmer of understanding that definition of “inviolable” and one’s thoughts about God’s nature shape this concept, and that my own bias regarding both could keep me from seeing common ground.

    Personally, I do not believe that the First Mover or the First Cause was subsumed by His own creation such that He is now subject to the laws of nature that He created. However, I can see an argument that He also would not be inconsistent with what He created and that it is our lack of full understanding of creation that keeps us from seeing that God works in our physical universe in a way that does not violate the laws of Creation.

    So, it appears that in this post and in Mike D.’s response we have the range of thought that either 1) nothing is really a miracle because everything God does is consistent with His laws of nature, or 2) everything is a miracle because everything is part of God’s creation.

    tomayto, tomahto

  10. Dear Mr. Briggs, GOOD LUCK!

    I cannot turn paper into gold. Perhaps Moses could do it. I’ve seen a magician turn a piece of tissue paper into real money though.

    Theism was not a major trend in Chinese thought. If it were, maybe the two Chinese characters meaning “miracle” would have consisted of a component of “God”. They simply mean “odd, unusual happening”.

  11. DAV,

    What I meant was that the rejection of divine influence by Hume, Darwin, et al. was really a rejection of traditional religion, but the alleged “enlightenment” of that proposition did not enlighten. Mankind is still mired in unenlightened thinking, maybe even more so than before.

    Rejecting God did not do us any good. Atheism has not proved to be a better way to think. We have not risen above our Medieval superstitiousness. We are still a herd animal mentally.

    Brigg’s point, from which I deviated, was to redefine “miracle” as a highly unlikely event. He based that on the proposition that we do not know Natural Law all that well, and so cannot ascertain with certainty whether an event trancends or not. I don’t argue with his point; I merely appended my own cynical view.

  12. It would seem that any event, once observed, is ipso facto possible. Thus, it would seem that the only possible members of the class “miracles” are events which are never observed.

    Or there’s another view: “A miracle is a change in perception.” It’s not the event that makes it a miracle: its the way observers react to the event that makes it a miracle.

  13. “All of us are willing to say that this event is improbable, but how many would claim that they could deductively prove that it is impossible? Remembering, of course, that the soundness of all premises used in that proof must also be demonstrated with certainty.”
    .
    Interesting subject William .
    First I would say that a stack of lead (easier than newspapers) transforming in gold is far from being any miracle .
    You can do that in a particle accelerator with just a few protons and neutrons .
    Of course you won’t become rich because the accelerator and the energy will cost you much more than the gold produced but it is not a miracle .
    .
    Second is that even if physics is mostly about induction , there are several deductively proven real impossibilities where , indeed , the premises used are sound beyond any reasonable doubt .
    Not surprisingly these deductive pieces belong to the most beautiful pieces of physics .
    3 examples :
    1) The premise is that no interaction can propagate at infinite speed . From that follows that there exists at least one interaction that defines the maximum speed of propagation .
    Call this maximum speed C .
    It is then proven that it is impossible to violate the Lorentz invariance for galilean reference frames (e.g time and space cannot be absolute) . Not improbable . Impossible .
    .
    2) Emmy Noether has proven what is for me the best piece of science ever .
    It is impossible to violate energy conservation if the natural laws are to be invariant by a translation in time . This premise only means that if you do an exactly identical experiment today or tomorrow , you will get the same result . Deductive impossibility .
    .
    3) Again Emmy Noether has proven that it is impossible to violate the momentum conservation if the natural laws are to be invariant by a translation in space . This premise only means that if you do an exactly identical experiment in Paris or in New York , you will get the same result . Deductive impossibility .
    .
    So if one wanted to cut the hairs in 4 , the only lee way left in those impossibilities is to argue that the premises “might” be wrong in some circumstances .
    Good luck to find a sound argument against Emmy Noether’s theorems :)

  14. Tom
    I assume that if you extracted only lead articles from Matt’s newspapers, he could get gold from his pile of newspapers?

  15. Thanks, DAV, for the reference to the Standford Encyclopedia of Philosophy article. I think the article (which I did read) just illustrates my point. It is a demonstration of the absurdity of applying deep and narrowly-focused technical thinking to a folk concept which is inherently vague and pertains to a variety of events in fables. Aquinas and Hume both learned about miracles from stories, and along with legions of other scholars mistook the general concept for something worthy of deep thought.

  16. Bernie well yes .
    Actually lead is just an example because it is just 3 protons and a few neutrons away from gold and pretty common .
    Even easier is mercury – only 1 proton more than gold .
    That’s why if you send electrons on the right mercury isotope and some get captured by a proton transforming it in a neutron , you’ll obtain gold too .
    Newspapers being mostly light elements like carbon and oxygen , it’s not the ideal substance to be transformed in gold .
    Newpapers are much more efficient in transforming gold in s..t … sorry , couldn’t resist :)

  17. Tom:
    Lead articles …I also couldn’t resist.

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