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".
This website is a place for people who want to move past shady thinking and test their ideas in a
court of people who don't all share the same biases. Our goal is to
optimize for light, not heat; this is a group effort, and all commentators are asked to do their part.
The weekly Culture War threads host the most
controversial topics and are the most visible aspect of The Motte. However, many other topics are
appropriate here. We encourage people to post anything related to science, politics, or philosophy;
if in doubt, post!
Check out The Vault for an archive of old quality posts.
You are encouraged to crosspost these elsewhere.
Why are you called The Motte?
A motte is a stone keep on a raised earthwork common in early medieval fortifications. More pertinently,
it's an element in a rhetorical move called a "Motte-and-Bailey",
originally identified by
philosopher Nicholas Shackel. It describes the tendency in discourse for people to move from a controversial
but high value claim to a defensible but less exciting one upon any resistance to the former. He likens
this to the medieval fortification, where a desirable land (the bailey) is abandoned when in danger for
the more easily defended motte. In Shackel's words, "The Motte represents the defensible but undesired
propositions to which one retreats when hard pressed."
On The Motte, always attempt to remain inside your defensible territory, even if you are not being pressed.
New post guidelines
If you're posting something that isn't related to the culture war, we encourage you to post a thread for it.
A submission statement is highly appreciated, but isn't necessary for text posts or links to largely-text posts
such as blogs or news articles; if we're unsure of the value of your post, we might remove it until you add a
submission statement. A submission statement is required for non-text sources (videos, podcasts, images).
Culture war posts go in the culture war thread; all links must either include a submission statement or
significant commentary. Bare links without those will be removed.
Jump in the discussion.
No email address required.
Notes -
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".
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link
More options
Context Copy link