TezlaKoil

In a topological space, defining

1. X ∨ Y as X ∪ Y
2. X ∧ Y as X ∩ Y
3. X → Y as Int( X^c ∪ Y )
4. ¬X as Int( X^c )

does yield a Heyting algebra. This means that the understanding (but not the explanation) of /u/cousin_it checks out: removing the border on each negation is the "right way".

Notice that under this interpretation X is always a subset of ¬¬X.:

1. Int(X^c) is a subset of X^c; by definition of Int(-).
2. Int(X^c)^c is a superset of X^c^c = X; since taking complements reverses containment.
3. Int( Int(X^c)^c ) is a superset of Int(X) = X; since Int(-) pre

You can get a clearer-if-still-imperfect sense from contrasting upvotes on parallel,

I'm fairly certain that P(disagrees with blargtroll | disagrees with your proposal) >> P(agrees with blargtroll | disagrees with your proposal), simply because blargtroll's counterargument is weak and its followups reveal some anger management issues.

For example, I would downvote both your proposal and blargtroll's counterargument if I could - and by the Typical Mind heuristic so would everyone else :)

That said, I think you're right in that this would not have received sufficiently many downvotes to become invisible.

Thanks for giving a name to this phenomenon.

Indeed, it would not surprise me if some people actually want hedge drift to occur. They don't actually try to prevent their claims from being misunderstood.

It's much worse. In my experience as an academic, most departments simply pre-hedge-drift their press releases. Science journalists don't - and are often not qualified to - read and comment on the actual papers, all they have to work with is the press release.

I mean nationalized, as in the distribution of tobacco products (imports, wholesale, retail) is handled by companies that may or may not have been private at some point, but are now property of the state.

What do you mean by nationalizing?

The weight of evidence best demonstrates that control measures have thus far been quite uniformly positive.

I see. The black market effects are well-documented, but I am not familiar with evidence which shows that control measures have any measurable effects on public health. Where could I find that data?

Dagon's points are very good. There's another aspect as well:

Tobacco import and distribution (and in some cases, production) are already nationalized in many countries, especially in the EU. National governments try to impose artificial scarcity (winding down operations, tax increases, fixed pricing), and this makes the statistics look better - officially monitored tobacco sales decrease.

Artificial scarcity cannot last: a black market of RYO tobacco, and home-made cigarettes of dubious origin is always ready to serve customer demands. In the end, the healt... (read more)

I bet if you phrase the question as "your brain is destroyed and recreated 5 minutes later", most people outside LW answer no. I guess this might be another instance of brain functions inactive vs lack of ability to have experiences.

In row 8 of the table, P(D) should be replaced by P(~D).

Location-specific advice

Libgen is blocked by court order in the United Kingdom, but if you're a student, you can usually access it through Eduroam.

Yes.

In a sterilized and sealed jar, jam made without sugar can last for years. Once you actually open the jar, you have about 7 days to eat it, and you better keep it refrigerated. You don't need the sugar for thickening - the pectin in the fruit thickens jam just fine.

However, if you don't add any sweetener, the result will be very sour.

Source: been making my own jam for years, had plenty of time to experiment.

In my experience, acid reflux can cause similar sensations.

I'm not sure that my paradox even requires the proof system to prove it's own consistency.

Your argument requires the proof system to prove it's own consistency. As we discussed before, your argument relies on the assumption that the implication

If "φ is provable" then "φ"
Provable(#φ) → φ 

is available for all φ. If this were the case, your theory would prove itself consistent. Why? Because you could take the contrapositive

If "φ is false" then "φ is not provable"
¬φ → ¬Provable(#φ) 

and substitute "0=1"... (read more)

It is not that these statements are "not generally valid"

The intended meaning of valid in my post is "valid step in a proof" in the given formal system. I reworded the offending section.

Obviously such statements will be true if H's axiom system is true, and in that sense they are always valid.

Yes, and one also has to be careful with the use of the word "true". There are models in which the axioms are true, but which contain counterexamples to Provable(#φ) → φ.

Now here is the weird and confusing part. If the above is a valid proof, then H will eventually find it. It searches all proofs, remember?

Fortunately, H will never find your argument because it is not a correct proof. You rely on hidden assumptions of the following form (given informally and symbolically):

 If φ is provable, then φ holds.
 Provable(#φ) → φ

where #φ denotes the Gödel number of the proposition φ.

Statements of these form are generally not provable. This phenomenon is known as Löb's theorem - featured in Main back in 2008.

You use these inva... (read more)

From Falsehoods Programmers Believe About Names:

anything someone tells you is their name is — by definition — an appropriate identifier for them.

There should be a list of false things people coming from common law jurisdictions believe about how choice of identity works on the rest of the globe.

Should this be surprising? I briefly worked at a French school in Hungary: the guy who taught Spanish was Mexican, the girl who taught English was American, and so on. A Korean living in Guatemala still needs to learn English.

looked up monotone voice on google, and found that it has a positive, redeeming side – attractiveness.

My friends tell me that my face is pretty scarred. Research shows that facial scars are attractive. By the word scar, researchers mean healed cut. My friends mean acne hole.

Not all monotone voices are created equal. I'd be really surprised if "autistic" monotone and a "high-status" monotone would refer to the same thing.

I believe that an ultrafinitist arithmetic would still be incomplete. By that I mean that classical mathematics could prove that a sufficiently powerful ultrafinitist arithmetic is necessarily incomplete. The exact definition of "sufficiently powerful", and more importantly, the exact definition of "ultrafinitistic" would require attention. I'm not aware of any such result or on-going investigation.

The possibility of an ultrafinitist proof of Gödel's theorem is a different question. For some definition of "ultrafinitistic", ev... (read more)

Sure, that's exactly what we have to do, on pain of inconsistency. We have to disallow representation schemas powerful enough to internalise the Berry paradox, so that "the smallest number not definable in less than 11 words" is not a valid representation. Cf. the various set theories, where we disallow comprehension schemas strong enough to internalise Russell's paradox, so that "the set of all sets that don't contain themselves" is not a valid comprehension.

Nelson thought that, similarly to how we reject "the smallest number not... (read more)