Very good, although I would quibble with the wording in a few places, e.g. -
"A meta-skeptic should doubt everything"
I would put it as Hume did when discussing miracles: "A wise man proportions his belief to his evidence." Evidence is never conclusive, but it can be stronger or weaker. The coin toss observations favour the hypothesis that the coin is biased towards heads, but not to an extent that can't be easily dismissed as random error.
Professional skeptics tend to focus on easy cases where credulity goes wrong, which encourages the conflation of skepticism and denial that you describe.
I would put it as Hume did when discussing miracles: "A wise man proportions his belief to his evidence." Evidence is never conclusive, but it can be stronger or weaker.
Indeed. This is a point I often emphasize in debates. The quote "absence of evidence is not evidence of absence" is wrong because it is evidence, but people often confuse evidence with proof.
But I don't see evidence as a continuum, I see certainty as a continuum. I would say for example "I believe the coin is biased with 95% certainty". 50% certainty means no belief one way or the other. This is a matter of semantics of course.
In the end what "true skeptics" should agree is that 100% certainty is not characteristic of skepticism.
Yes, and some Bayesians would even distinguish between e.g. 50% certainty in the coin landing heads on the next toss after 50 heads and 50 tails from your rational beliefs before testing the coin at all. They would model the latter with a convex set of different beta distribution priors (some very biased to heads, some very biased to tails) and the former as the beta posteriors after using your observations of the 100 coin tosses to do Bayesian updating on each element in that set. I'm not persuaded by this "Imprecise Bayesianism," but I agree that it's a useful distinction.
Yes, and some Bayesians would even distinguish between e.g. 50% certainty in the coin landing heads on the next toss after 50 heads and 50 tails from your rational beliefs before testing the coin at all.
You can use the beta distribution to calculate the probability that the actual probability is between 45% and 55% given 50H/50T, and it's around 70%: graph. So in that case I would say I believe the coin is fair with 70% certainty. With 0H/0T it's around 10%.
The more tosses the more likely the actual probability is between a certain range, so the more "precise" it should be.
Articles from Stanford Encyclopedia of Philosophy are very interesting, but way too complicated for me. This article is no exception, very interesting, but my point is much more general.
By using probability I'm not trying to find an accurate value of belief, what I'm trying to do is show is that even in simple questions people have an unwarranted level of certainty, even people who call themselves "skeptics".
Yes. I didn't consider it a critique. I think we are talking about the same thing except at different levels, like those Wired videos of explaining one concept "in 5 levels of difficulty".
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Notes -
Very good, although I would quibble with the wording in a few places, e.g. -
"A meta-skeptic should doubt everything"
I would put it as Hume did when discussing miracles: "A wise man proportions his belief to his evidence." Evidence is never conclusive, but it can be stronger or weaker. The coin toss observations favour the hypothesis that the coin is biased towards heads, but not to an extent that can't be easily dismissed as random error.
Professional skeptics tend to focus on easy cases where credulity goes wrong, which encourages the conflation of skepticism and denial that you describe.
Indeed. This is a point I often emphasize in debates. The quote "absence of evidence is not evidence of absence" is wrong because it is evidence, but people often confuse evidence with proof.
But I don't see evidence as a continuum, I see certainty as a continuum. I would say for example "I believe the coin is biased with 95% certainty". 50% certainty means no belief one way or the other. This is a matter of semantics of course.
In the end what "true skeptics" should agree is that 100% certainty is not characteristic of skepticism.
Yes, and some Bayesians would even distinguish between e.g. 50% certainty in the coin landing heads on the next toss after 50 heads and 50 tails from your rational beliefs before testing the coin at all. They would model the latter with a convex set of different beta distribution priors (some very biased to heads, some very biased to tails) and the former as the beta posteriors after using your observations of the 100 coin tosses to do Bayesian updating on each element in that set. I'm not persuaded by this "Imprecise Bayesianism," but I agree that it's a useful distinction.
https://plato.stanford.edu/entries/imprecise-probabilities/
You can use the beta distribution to calculate the probability that the actual probability is between 45% and 55% given 50H/50T, and it's around 70%: graph. So in that case I would say I believe the coin is fair with 70% certainty. With 0H/0T it's around 10%.
The more tosses the more likely the actual probability is between a certain range, so the more "precise" it should be.
Articles from Stanford Encyclopedia of Philosophy are very interesting, but way too complicated for me. This article is no exception, very interesting, but my point is much more general.
By using probability I'm not trying to find an accurate value of belief, what I'm trying to do is show is that even in simple questions people have an unwarranted level of certainty, even people who call themselves "skeptics".
Sorry, wasn't meant as a critique: just something else that is interesting to think about.
Yes. I didn't consider it a critique. I think we are talking about the same thing except at different levels, like those Wired videos of explaining one concept "in 5 levels of difficulty".
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