How Skeptical Are We Allowed to Be?

What Paranormal Challenges Say About the Probability of the Supernatural

Do psychic powers exist? Do ghosts flutter around castles? Are miracles real? Most readers of this probably have a strong sense of what they think the answer is. There are people who will go to their graves asserting that the probability of a genuine miracle is zero and plenty of people who are completely confident that God will yank them out of their graves because the probability of certain miracles being real is one hundred percent.

What is the probability that a given supernatural or paranormal power or phenomenon exists? One approach is to consider all the scientific principles that paranormal claims might violate^[i][ii]). Or when it comes to the biggest philosophical claim of all- is there a God- philosophers bring out all kinds of considerations such as the principle of indifference, simplicity, parsimony, and elegance^[iii].

This question is very hard. An easier question might be to ask how low can we reasonably set the probability of a particular supernatural or paranormal claim? What is the maximal level of skepticism we can have before we are rightly accused of absurdity? Some skeptics might rush to say zero- these things simply do not or cannot exist. But if we want to be able to update our beliefs in the face of new evidence, we must assign a non-zero probability for the supernatural or paranormal powers. This is because as Bayes’ Theorem says, our current credence in a proposition is our previous credence in a proposition multiplied by other factors. If our past credence or belief in a proposition is literally zero, our current or even future belief in a proposition should be zero.

 If we think, say, witchcraft has a probability of zero, that means we would have to insist that there is no such thing as witches even as we dangle off a flying broomstick in front of a gibbous moon and see our un-christened nephews turned into magical ointments. Setting a probability of zero is statistical bigotry.

So how close to zero can the maximum level of permissible skepticism I am proposing get us? Pretty darn close.

Admission Against Interest

In American law, statements outside of court generally are not allowed as evidence. One important exception comes from the concept of “declaration against interest” where someone makes a statement so harmful to themselves that it’s assumed that it is probably true^[iv]. A similar principle from history is the criterion of embarrassment, where for instance, New Testament claims about Jesus of Nazareth are held to be more likely to be true if they make Jesus or the early Christians look bad^[v]. We take statements or admissions more seriously when they go against the interests, personal or ideological, of the speaker.

Skeptics of the paranormal and the supernatural have produced several paranormal challenges, probably the best known one being a defunct million-dollar challenge created by James Randi. These challenges promise a monetary award to people who can demonstrate a paranormal ability.

The sponsors of these challenges are generally not just skeptical about specific individuals who claim mysterious powers but are committed atheists and naturalists. The Center for Inquiry which sponsors a paranormal challenge which dares people who think they have a paranormal ability to “prove it” for $500,000^[vi] also promotes atheism. If groups committed to the non-existence of the supernatural argue that the probability of a supernatural or paranormal phenomenon existing is X%, it’s reasonable to think that the group is not overstating the probability of the phenomenon existing. So, the probability of the phenomenon existing is probably at least X%. Secular, skeptic, and atheist organizations do not, as far as I know, produce extensive charts laying out the probability that various claims are true. But every paranormal challenge that demands a specified strength of evidence for a paranormal phenomenon corresponds to an implied level of probability that the phenomenon exists before any new evidence is presented or any test is performed.

This is because the odds form of Bayes’ Theorem tells us that the posterior odds of two claims are equal to the prior odds times the strength of the evidence (also called the likelihood ratio)^[vii]. Imagine a mystery investigation where Sherlock Holmes is completely certain that the murder was committed by either Lucrezia Borgia or Jack the Ripper. Initially, Sherlock thinks there’s a 50% chance Borgia is the murderer, and a 50% chance Jack is the murderer. The odds are 1:1. After finding an empty bottle of hemlock in Borgia’s purse and the autopsy says the victim died of hemlock poisoning, Sherlock thinks that evidence is 100 times more consistent with Borgia being the murderer than Jack being the murderer. Since 100:1 to 1:1 is 100:1, Sherlock now thinks the odds that Borgia is the murderer are equal to 100:1. This reasoning can also be applied to paranormal challenges.

Implicitly, in a paranormal challenge one claim is that the power exists, and the other claim is that the power does not. This means that if you know how strong the evidence would have to be to prove that a paranormal power exists, you would be able to calculate the so-called prior odds that a paranormal power exists (the odds that a power exists before any new evidence is presented).

The Center for Inquiry’s Investigation Group, as do other paranormal challenge sponsors, understands that it’s possible to pass some challenges just by luck. A psychic who successfully predicts three coin tosses in a row is not that impressive. So, the CFI challenge demands that an applicant pass an initial test at 5,000:1 odds and a second test at 1,000,000:1 odds which is equivalent to a single test at five billion to one odds^[viii]. While the challenge dares applicants to prove their power, the most reasonable interpretation is that they are using “proof” in the colloquial sense as strong evidence. If strong evidence is evidence that makes a claim is at least 50% likely to be true (or 1:1 odds), then the level of evidence demanded by that challenge implies that the probability that their applicants have a paranormal power is one to five billion. This is because five billion to one multiplied by one to five billion equals one to one odds.

Other challenges set by skeptics have required less impressive evidence for the existence of paranormal powers. At one point, James Randi’s challenge required beating cumulative odds of one billion to one^{[ix] [x]} before allowing applicants to replace passing a difficult preliminary challenge with press clippings, academic backing, or video demonstration^[xi]. That means the Randi challenge implied that the probability that their applicants have a paranormal power is one to one billion.

Since it is hardly possible that these groups would overestimate the probability that such powers are real, a reasonable lower bound of probability for a claimed paranormal power or supernatural feat is one to five billion. These odds may be too extreme, maybe far too extreme, but they provide a reasonable non-zero estimate for the existence of a given paranormal phenomenon. Since this is the odds of a given phenomenon existing, the odds of at least paranormal or supernatural phenomenon must be higher.

What if instead of taking the odds of one to five billion as the lower bounds of whether a paranormal claim is true, we just treated that as a reasonable figure and acted as if we were just as skeptical of paranormal and supernatural claims, as the committed skeptics that organize these challenges? What are the implications?

Epistemic Considerations

Odds of one to five billion implies that any given paranormal claim is almost certainly false. Yet, it’s not infinitesimal odds. In academia and research, scholars do produce evidence so strong that claims that seemed initially just as unlikely to be true end up well-supported. So paranormal and supernatural claims could in theory be vindicated. Supernatural or paranormal claims do not exist in some ethereal realm, or some separate magisterium that’s somehow exempt from normal investigation.

Mediums can be investigated by magicians. Paranormal claims can be tested by parapsychologists (and then psychologists can see if they replicate). Some alleged miracle claims that occurred in the past could be corroborated or debunked by normal historical investigation or archeology. Contemporary claimed miracle healings have medical records that could be examined. Certain prophecies could be tested by waiting. Normal academic disciplines, not just theology and philosophy can assess these claims.

It would be strange to be a New Testament scholar one’s entire life and never develop an opinion on whether the resurrection of Jesus of Nazareth occurred. Likewise, it would be strange to be an Egyptologist with no opinions on the book of Exodus.

Practical Considerations

One to five billion odds are small. These odds let you simply ignore many paranormal claims. The odds of a reiki healer fixing your knee are low enough to ignore and so are astrological stock tips and $10 psychic cleansings offered by a local psychic. Skeptics should feel free to buy that strangely affordable mansion with a legacy of mysterious deaths and unspeakable midnight gathering.

The size of some claimed supernatural rewards and punishment are so large, that even dividing them by five billion still leads to expected gains or losses too big to ignore. Pascal’s wager claims that any chance of infinite reward offsets any finite cost. His argument is complicated by the existence of multiple potential routes to the infinite  e.g. Christianity,  Islam, etc., and there is no consensus on how to treat infinite outcomes when making decisions^{[xii] [xiii]}although choosing the route most likely to yield an infinite pay-off offers a straight-forward rule^{[xiv] [xv]}.

Yet setting aside claimed infinite payoffs, there are some finite supernatural claims which matter a lot in cost-benefit terms, even with five billion to one odds against them. Take Buddhism. Buddhism, in at least some forms, has the possibility of reincarnation in a hell realm that can last over three quintillion years^[xvi].

A one in five billion chance of that occurring is terrible. Luckily, Pure Land Buddhism says if you chant the name of the bodhisattva Amitābha just ten times you will be reborn in a heavenly realm instead^[xvii]. That’s a great deal in cost-benefit terms and it seems hard to rationally turn down. Or take the thought experiment inspired by Pascal’s Wager called Pascal’s Mugging^[xviii]. Bostrom asks us to ponder what one should do if they are accosted by an unarmed man who demands one’s wallet and claims to have magic powers and offers to use them to offer a monetary reward large enough to offset the cost of the lost wallet, even when discounted by the victim’s skepticism of magical money conjuring. While Bostrom intends that the apparent absurdity of the situation would let anyone hold on to their wallet, the upper bound of skepticism implied by paranormal challenges would not let one turn down such an offer if the promised reward was large enough.

Even if we adopt very extreme skepticism of the supernatural (five billion to one against!), we are still not justified in not begging a bodhisattva for help or refusing to pay a Pascallian mugger.

Another approach that might work better for the five billion to one skeptic would be to bet on infinite reward instead, and either rush off to get baptized as a Christian or quickly recite the Shahada to become Muslim. Once converted to one of these religions, it would be foolish to chant the name of any bodhisattva as apostasy or idolatry risks infinite punishment, or to forfeit infinite reward to take the deal offered in Pascal’s Mugging. Dealing with any type of wizard is frowned upon by Abrahamic religion. Pascal’s Wager solves Pascal’s Mugging.

The stakes of the supernatural claim determine the practical implication. Skeptics can be skeptical enough to ignore things that go bump in the night but should not be skeptical enough to ignore things that go bump in the afterlife.

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^[i] Steven, P. (2022, July 26). ESP debate: Is belief in ESP irrational? Steven Pinker vs. Brian D. Josephson. Skeptic. https://www.skeptic.com/reading_room/debate-is-belief-in-esp-irrational/ 

^[ii] Reber, A. S., & Alcock, J. E. (2019, July). Why parapsychological claims cannot be true. Skeptical Inquirer. https://skepticalinquirer.org/2019/07/why-parapsychological-claims-cannot-be-true/ 

^[iii] Miller, C. (2018). The intrinsic probability of theism. Philosophy Compass, 13(10). https://doi.org/10.1111/phc3.12523 

^[iv] Legal Information Institute. (n.d.). Declaration against interest. Legal Information Institute. https://www.law.cornell.edu/wex/declaration_against_interest 

^[v] Meier, J. P. (1991). A Marginal Jew: Rethinking the Historical Jesus, Volume One: The Roots Of The Problem And The Person. Doubleday. 

^[vi] The CFIIG Paranormal Challenge. CFI Investigations Group. (n.d.). https://cfiig.org/paranormal-challenge/ 

^[vii] Downey, A. B. (2012). Think Bayes: Bayesian Statistics made simple. O’Reilly Media, Inc. 

^[viii] Lewis Rees. CFI Investigations Group. (2012, February 1). https://cfiig.org/lewis-rees/ 

^[ix] Society for Psychical Research. (n.d.). The One Million Dollar paranormal challenge. The One Million Dollar Paranormal Challenge | Psi Encyclopedia. https://psi-encyclopedia.spr.ac.uk/articles/one-million-dollar-paranormal-challenge 

^[x] Taylor, G. (2008, February). The myth of James Randi’s million dollar challenge. The Daily Grail. https://www.dailygrail.com/2008/02/the-myth-of-the-million-dollar-challenge/ 

^[xi] Crabtree, S. (2011, March 9). JREF’s $1,000,000 Paranormal Challenge Now Easier Than Ever. https://web.archive.org/web/20110312070220/http:/www.randi.org/site/index.php/jref-news/1239-mdc-changes.html 

^[xii] Bostrom, N. (2011). Infinite ethics . https://nickbostrom.com/ethics/infinite.pdf 

^[xiii] Nick, B., & Teruji, T. (2021, July). A paradox for tiny probabilities and enormous values. https://globalprioritiesinstitute.org/wp-content/uploads/Beckstead-Thomas-A-Paradox-for-Tiny-Probabilities-and-Enormous-Values-Version-2.1.pdf 

^[xiv] Jackson, E., & Rogers, A. (2019). Salvaging pascal’s wager. Philosophia Christi, 21(1), 59–84. https://doi.org/10.5840/pc201921110 

^[xv] Amanda Askell. (2012, August 10). Common objections to Pascal’s wager. https://askell.io/posts/2012/08/pascal 

^[xvi] Malik, A. (2007). Survey of Buddhist temples and Monasteries. Anmol Publications. 

^[xvii] Huntington Archive. (n.d.). The Sutra on the Buddha of Eternal Life. https://huntingtonarchive.org/resources/downloads/sutras/04amitabhaPureland/SV%20Long.doc.pdf 

^[xviii] Bostrom, N. (2009). Pascal’s mugging. Analysis, 69(3), 443–445. http://www.jstor.org/stable/40607655