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Suppose that you get a prank call, not once but 100 times. Is their frequency good reason to think that the evidence they have been faked (it's someone else) is less convincing and/or the evidence that you have been prank called (by who you think it is) is greater?

If I can prove (at least as convincing as the prank call) where I was for one call, lack a motive (means to trick anyone, am honest, etc.), and someone else has motive and means to fake the prank calls, surely I have proven my innocence for that call and by extension likely all of them?


Supposing each of the calls are authentic if and only if the others are (which is more or less the case/for the sake of argument: if one is faked it hugely increases the chances of the others being likewise), then in assessing their reliability I think you only need analyse one recording (the most convincing, i.e. frequency doesn't come into it) in comparison to the alibi recording.

By analogy: you know the same person is committing a lot of burglaries; if have a good enough alibi for one of them, you've proven your innocence for all of them, and the fact there's been many need not figure in that judgment.

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    You're on the right track, mon ami. Bonam Fortunam Sep 12, 2023 at 19:56
  • Goodman criticized Hume’s colloquial regularity as habit of mind forming from observed constant conjunction missed the point, as you rightly suspected, of course it’s easy to be skeptical that not all such frequent degree of confirmations can be correctly and absolutely generalizable. The key, however, lies in law-like projectible predicates vs unprojectible ones such as grue/bleen, and they definitely correlate with their accuracy rate in the past… Sep 13, 2023 at 3:10
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    Frankly speaking, I cannot understand... "Scientifically, it doesn't matter how many white swans you've seen: one black swan is sufficient to falsify the claim that all swans are white. ... that this swan is indeed black. The swan could be covered in tar or misidentified (a cormorant), but you definitely take that on a case by case basis in science." This is not "induction" (whatever it is) but skepticism: how much reliable are our observations? Science does not work that way: experiment are clearly designed, then executed and checked and repeated. Sep 13, 2023 at 7:22
  • truly, i do not understand what you mean @MauroALLEGRANZA what is not induction?
    – user67675
    Sep 13, 2023 at 20:10
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    If you are satisfied with one of the received answers, please accept it. Sep 14, 2023 at 6:52

4 Answers 4

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100 dice rolls that deliver all 6s is not evidence of an unfair die. It is an improbable event that may require further examination. Evidence of an unfair die is a failed float test.

BTW. This question has been asked on this site numerous times by a user named Thinkingman. Ad nauseum.

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  • yeah this seems right. someone pointing to how many times they've been called is like rolling the dice again and saying "look, it cannot be unfair, i got a 6 again"
    – user67675
    Sep 13, 2023 at 23:49
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I'm afraid I don't understand your example at all. I would rather ignore the text of your post and try to answer the question in the title.

If you have a theory that makes statistical predictions and you wish to test it against data then it is broadly a question of whether the data matches what your theory predicts. There are different ways of measuring how good the match is.

If your theory predicts that all Fs are Gs, then a single counter observation of an F that is not a G is sufficient to falsify it. No amount of positive observations will prove it true, though if you repeatedly attempt to find counter observations and fail, you may say that your theory is corroborated.

If your theory predicts a particular proportion of Fs are Gs, the closer the observed proportion is to your prediction the better, though as before it is does not prove the theory is correct. It merely gives results that are expected in accordance with the law of large numbers.

There are other kinds of distributions which yield more complex comparisons. If a theory predicts that you will always observe one of two possible results then a Haldane distribution Beta(0,0) might be appropriate. Suppose a chemist synthesises a new pure compound and wishes to check whether it is soluble in water. One test is enough to tell you whether the compound is soluble or not. There is no evidential value in making repeated observations, unless perhaps you think you made a mistake.

In the case of prior probability distributions in Bayesian theory, a Beta(1,1) distribution is commonly used. In Bernoulli trials a Beta(0.5,0.5) might be more appropriate. In other applications, distributions such as Poisson, Erlang, or the old favourite Normal might be used.

Making observations does not always tend to increase the probability of future similar observations. Suppose you live next to a forest and every day you go foraging for mushrooms. You wish to form a statistical theory about how many mushrooms you will find and pick each day. It would be reasonable to suppose that there is a finite quantity of mushrooms in the forest and hence the more you pick the fewer remain. So the more observations (and pickings) you make, the less likely it is you will make future observations.

So there is no simple one-size-fits-all inductive procedure that tells you that some general proposition is more likely the more observations you make. You need to formulate specific models and test them. Ideally, testing them involves actively seeking out sources of sample bias, and comparing against rival models.

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If something keeps happening, is it better evidence?

No because the frequency of an occurrence does not necessarily entail that one or more characteristics about the occurrence can be derived from the frequency of the occurrence.

To think otherwise is probably some type of fallacy. I cannot figure out what.

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I can barely believe anyone could disagree.

Suppose there is an illusionist who has made his lovely assistant float 100 times. One time, you notice some pulleys and wires, and the illusionist agrees and says

yes, but all those other times it was true magik

The example of checking your watch should suffice. It doesn't matter how many times you look at your watch (assuming you can tell the time) and it says you are 10 minutes early, if you check it once against a reliable timepiece and it comes back as ten minutes slow.

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