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Suppose I predict that John will get into a fight tomorrow and he does. Almost noone will think I can read the future. It seems to be "within" the bounds of chance.

Suppose I instead predict the result of every single sporting outcome in the world tomorrow and get it correct, and I do this for one straight week. Most will believe that I am a prophet. However, let's assume that noone is ever able to figure out exactly how I might be doing this. Without this explanation but with enough predictions, can we be sure that I am a psychic?

Logically, I fail to see how a successful string of predictions by themselves would prove anything. All it would prove is that a certain set of outcomes are extremely unlikely to have occurred by chance or without mind reading powers. However, one would have to show that the likelihood of me being a psychic is higher. Without one being able to show this, how could you possibly say that me predicting 10, 50, or even 100 straight events are enough to show that I am a psychic? Sure, it might feel very psychologically intuitive to start believing that I am psychic after many guesses, but that does not imply that me being a psychic is more likely than me just getting them right by chance.

If instead, we had an actual explanation, or some sort of way that describes how I'm doing this, would this change things? Would this make it more reasonable to believe me being a psychic?

thinkingman
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    Suppose I predict that there will be a question about hypothetical unlikeliness tomorrow. – Boba Fit May 16 '23 at 21:54
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    @BobaFit we need a pool to bet on the likelihood of thinkingman ever being at peace with probabilities. – Frank May 16 '23 at 22:26
  • Broad outline provided by **thinkingman**. I wonder if he'll edit in the devilish details. I'm a man with a big fat zero in experience. – Agent Smith May 17 '23 at 01:23
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    @Frank the struggle of being a thinking man! – Reine Abstraktion May 17 '23 at 14:42
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    I upvoted, because I wish to support the man who thinks in his ultimate question to come at peace with probability – Reine Abstraktion May 17 '23 at 14:43
  • Somebody usually wins the NCAA bracket pool. Do you presume they're a psychic? – Barmar May 17 '23 at 16:27
  • This brings to mind an old scam: Send out, say, 32 letters to 32 people. In 16 of them you say the Dow Jones will go up over the week and in 16 you say it will go down. Then you wait and whichever comes true, you send another letter to the 16 who got the 'right' prediction, 8 up, 8 down. Then after a week, 4 up, 4 down and so on. Then, at some point you send out a letter the people who received all 'correct' predictions and offer to invest money for them. – JimmyJames May 17 '23 at 19:12
  • On a side note, the term 'explanatory power' with respect to a hypothesis has a specific technical meaning that I don't think you intend here. I think you mean how important is it to know how you came to your results. This ties into another possibility that you don't mention: you have some inside knowledge or ability to cause a particular outcome. If a gambler is paying boxers to throw fights, we should not be surprised that their predictions about the outcomes of those fights is correct and it's much more likely than psychic powers. – JimmyJames May 17 '23 at 19:21
  • "Suppose I instead predict the result of every single sporting outcome in the world tomorrow and get it correct, and I do this for one straight week. Most will believe that I am a prophet." Not me. I'll believe you are cheating. –  May 21 '23 at 15:53
  • @TrystwithFreedom. I agree and upvoted as well. Thinkingman is forcing me to review my own knowledge of applied statistics and I am better for it. –  May 21 '23 at 15:56

4 Answers4

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In cases such as this, the probability of a correct prediction made using a model is to be compared with the probability of a correct prediction caused not by the operation of the model but instead by random chance.

This is called (among other things) comparison to the null hypothesis and it can be calculated using the equations of descriptive statistics. If the outcome probability is indistinguishable from that furnished purely from chance, then the model is invalid.

niels nielsen
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  • Do you have an opinion on the random walk theory for playing the stock market? I think human beings have expert knowledge and skill which alters or counteracts what we might also recognize as random events. I do not think our statistical models are sophisticated enough to deal with human knowledge and skill applied to intentional events. The odds of my coffee cup existing as a glass on my desk are zero in the absence of human imagination and 100% given the history of human progress. Waves break at random within a bounded range and surfers use skill to catch and ride waves. Skill reduces risk. – SystemTheory May 17 '23 at 00:21
  • I guess what it means is: (x +/-y)%. Someone please ask a question on *The Null Hypothesis*. – Agent Smith May 17 '23 at 02:16
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    Random chance is one option, but you should also consider other explanations. Beating random chance in predicting sport outcomes doesn't mean you're psychic. You may have spotted some pattern in the outcomes, you may have some insider knowledge of match fixing, the Flying Spaghetti Monster may have decided to just mess with you for a while by aligning reality to your predictions, etc. In the context of philosophy and epistemology, explanatory power would typically relate to comparing different explanations with one another. – NotThatGuy May 17 '23 at 09:36
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I would say that without explanatory power a hypothesis is rather meaningless. Let's take the example you cited. You predict n sporting outcomes correctly, where n is a phenomenally unlikely number. I say you must be psychic. But what does that mean? If you unpick it you will eventually reach the conclusion that 'he must be psychic' is synonymous with 'I have no idea how he does it', which is either meaningless or entirely true.

Marco Ocram
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  • One down, how many ta go? – Agent Smith May 17 '23 at 06:46
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    Yesn't. What about medication where studies show they work, but the mechanism HOW is not yet understood. The psychic who can predict sports events is kind of meaningless if that's the only thing he does, but there are other, more meaningful, examples where you know the effect but don't know the cause. One thing they do is show areas where are still ignorant. Also you can start working with the effect while you figure out the cause. – kutschkem May 17 '23 at 13:45
  • @kutschkem you are raising an objection to something I haven't said! I'm not denying the effect- clearly Thinkingman is able to predict the outcomes of sporting events, so by all means take advantage of it and place bets etc. But to hypothesise that he is 'psychic' is meaningless if you don't define and explain what psychic means. You might as well hypothesise that the effective but unexplained drug is 'magic'. – Marco Ocram May 17 '23 at 14:52
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How important is explanatory power when it comes to assessing the likelihood of a hypothesis?

I want to focus on one particular comment:

Logically, I fail to see how a successful string of predictions by themselves would prove anything.

This observation is correct, and for reasons having to do with logic.

You have run into the same problem as every other philosopher, notably David Hume, who denies the validity of the Uniformity Principle. The Principle says that the relationships of the future will resemble those of the past. Without that assumption, a collection of observations produces only simple enumeration, or the accumulation of unrelated data.

Enumeration does not produce a valid generalization. The fatal problem is that the underlying syllogism is invalid. In enumeration, the syllogism is AAA in the second figure:

If something is a swan, then it is white.

This particular swan is white.

Therefore: All swans are white.

Here, the middle term (white) is undistributed in both premises. In a valid syllogism, the middle term must be distributed in the premises at least once.

Without a distributed middle term, nothing links the major and minor premises; nothing supports a conclusion that is larger than each premise standing alone. However consistent each observation might be with the desired result, it simply produces another invalid conclusion; a lot of such confirmations is no confirmation at all.

Mark Andrews
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Suppose I instead predict the result of every single sporting outcome in the world tomorrow and get it correct, and I do this for one straight week. Most will believe that I am a prophet. However, let's assume that noone is ever able to figure out exactly how I might be doing this. Without this explanation but with enough predictions, can we be sure that I am a psychic?

This is just another version of divine fallacy replacing God with a mystic.

By the way, how do you know what most people believe? I think most people, would believe that your "prophet" is a fraud and a very clever cheat. Which one of us is correct?