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Could simply sort comments by pending criticism first, creation date second. (Variation of #4274.)
This has been implemented, sans page at /:username/bounties, which seems unnecessary.
Done, mostly as of 346fb25, then polished in 6dbf721, 5381525, 9f0f936, and 91e6f27.
Making alcohol illegal has been tried and was disastrous. Drugs are already illegal, which is arguably also disastrous. Those who advocate MAKING most drugs illegal but not alcohol are, I think, people who want to outlaw weed.
Drugs are too broad of a category. Is widespread cocaine use the same as occasional magic mushrooms? The latter is suggested to have neuro-protective benefits.
Subjectively applies to every good product that makes its purchasers want to buy more of it. Like good food, video games, comfortable chairs.
In today's society they only have this ability to a limited degree, and would still have to deal with the drug users in public.
Violating the rights of other people depends on whatever their rights are. If we replace it with "desires", or use a libertarian way of saying "aggress on", then it's really just up to the people. I'd rather not live around drug users (depending on the drug), even if none of them physically assault me. I.e. "violation" is subjective, and ultimately decided by the polity that creates the laws.
Knowledge can exist outside any mind. A book contains knowledge whether or not anyone reads it.
Use frame layout for turbo frame requests? https://discuss.rubyonrails.org/t/the-right-way-to-override-render-method/84765/2
Is there a way to teach user-built helpers how to process Hiccdown? Or maybe intercepting capture already took care of this?
Could the application layout live in ApplicationHelper#layout?
The Popper-Miller theorem works by splitting any prediction h into two pieces…
I wonder if your revision from hypothesis to revision was a bit sweeping.
Do they really argue predictions can be split into two pieces? That doesn’t sound right. But I could see hypotheses being split in two.
The Popper-Miller Theorem
In 1983, Karl Popper and David Miller published a paper in Nature titled "A proof of the impossibility of inductive probability" that used Bayesian math to prove something uncomfortable: the part of a theory that goes beyond the evidence never gets supported by that evidence. It actually gets negative support. In their words: "probabilistic support in the sense of the calculus of probability can never be inductive support." (Popper & Miller, 1983)
They expanded on this in a second paper: "although evidence may raise the probability of a hypothesis above the value it achieves on background knowledge alone, every such increase in probability has to be attributed entirely to the deductive connections that exist between the hypothesis and the evidence." (Popper & Miller, 1987)
Here's what that means concretely. Say your theory is "swans are white because the genes controlling feather pigmentation in the swan lineage produce only white melanin." This is an explanation: it tells you why swans are white, not just that they are. It also predicts that the next swan you see will be white.
You see a white swan. Your overall confidence in the theory goes up. But Popper and Miller split the theory into two pieces:
- The deductive piece: "this particular swan I'm looking at is white." The evidence directly confirmed the theory's prediction for this case.
- The inductive piece: "and the reason it's white is a genetic mechanism that applies to all swans, including the ones I haven't looked at." This is the actual explanation — the part that would represent learning something new about the world.
They proved mathematically that piece 2 — the explanation, the part that matters — always receives zero or negative support from the evidence. The only work the evidence ever does is confirm the prediction it directly touched. It never reaches the explanation behind it.
The Math
What follows is a simplified sketch of the proof. For the full formal treatment, see the original paper.
Step 1: Define "support."
The support that evidence e gives to hypothesis h is defined as the change in probability:
s(h|e) = p(h|e) − p(h)
If this number is positive, the evidence raised the probability of the theory. Bayesians call this "confirmation."
Step 2: Decompose the hypothesis.
Popper and Miller split h into two components:
The deductive component: (h ∨ e), meaning "h or e." This is the part of h that is logically connected to the evidence. If e is true, then (h ∨ e) is automatically true, so evidence trivially supports it.
The inductive component: (h ∨ ¬e), meaning "h or not-e." This is the part of h that goes beyond the evidence — the part that would still need to be true even if the evidence hadn't occurred.
The hypothesis h is logically equivalent to the conjunction of these two components: h ⟺ (h ∨ e) ∧ (h ∨ ¬e).
Step 3: Calculate the support for each component.
Using standard probability rules, the support for the deductive component is:
s(h ∨ e | e) = 1 − p(h ∨ e)
This is always ≥ 0, since p(h ∨ e) ≤ 1. The evidence always supports the deductive part. No surprise, the evidence is logically contained in it.
The support for the inductive component is:
s(h ∨ ¬e | e) = −(1 − p(e))(1 − p(h|e))
Both (1 − p(e)) and (1 − p(h|e)) are ≥ 0 (assuming we're not dealing with certainties), so their product is ≥ 0, and the negative sign means the whole expression is always ≤ 0.
Step 4: The result.
The total support decomposes as:
s(h|e) = s(h ∨ e | e) + s(h ∨ ¬e | e)
The first term (deductive) is always non-negative. The second term (inductive) is always non-positive. The evidence never positively supports the part of the theory that goes beyond the evidence. Whatever "boost" h gets from e is entirely accounted for by the deductive connection between them. The inductive component — the explanation, the mechanism, the part that would represent genuine learning about the unobserved — is always counter-supported.
Implication
The implication is devastating for Bayesian epistemology: the entire framework of "updating beliefs with evidence" is an illusion. The number goes up, but the going-up is entirely accounted for by deduction. There is no induction hiding inside Bayes' theorem. The Bayesians' own math proves it.
David Deutsch, who has been working with colleague Matjaž Leonardis on a more accessible presentation of the theorem (Deutsch on X/Twitter, 2020), puts it this way: "There's a deductive part of the theory whose credence goes up. But the instances never imply Ahe theory. So you want to ask: 'The part of the theory that's not implied logically by the evidence – why does our credence for that go up?' Well, unfortunately it goes down." (Joseph Walker Podcast, Ep. 139, "Against Bayesianism")
You have moved the goalposts from "isn’t it just down to other people subjectively valuing the asset you are buying" to "isn’t it just down to other people subjectively valuing the product/service the business produces” (paraphrasing).
Of course it is all subjective in a sense. My point is that you can disagree with the entire market about what an asset is worth and still have it turn out to be a good investment.
How would you suggest I rename it?
Instead of “Say your theory is "all swans are white."”, write ‘Say your prediction is "all swans are white."’
I don’t know if that replacement works for “But Popper and Miller split the theory into two pieces…” and similar parts, because those may or may not need to be about a theory rather than a prediction.
It's still a testable hypothesis.
No, it’s a prediction. “A hypothesis … is a proposed explanation for a phenomenon.” https://en.wikipedia.org/wiki/Hypothesis (links and formatting removed)
Again, ‘all swans are white’ is not an explanation.
Yeah explanations answer ‘how’ or ‘why’ questions. Popper wrote:
In seeking pure knowledge our aim is, quite simply, to understand, to answer how-questions and why-questions. These are questions which are answered by giving an explanation. Thus all problems of pure knowledge are problems of explanation.
‘All swans are white’ is like saying 2 + 2 = 4. It predicts a result given a theory of addition. It does not state the theory.