Rationality quotes are self-explanatory.  Irrationality quotes often need some context and explication, so they would break the flow in Rationality Quotes.

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Background:

Despite being dentist-recommended since the early twentieth century, researchers have yet to conduct sufficient, reliable studies to support the claim that flossing effectively prevents cavities and gum disease.

Since doctors began saying that a string-based tooth scraping was good for oral health, a handful of studies have been conducted. However, they all fall far short of what’s needed to make a convincing argument. A 2011 review of a dozen randomized controlled studies concluded that, “Overall there is weak, very unreliable evidence which suggests that flossing plus toothbrushing may be associated with a small reduction in plaque at 1 or 3 months.”

Quote:

Still, many dentists will continue to recommend flossing for removing debris between your chompers. "It's low risk, low cost," National Institutes of Health dentist Tim Iafolla told CNBC. "We know there's a possibility that it works, so we feel comfortable telling people to go ahead and do it."

Source

For what it's worth, the situation isn't really that we've established that it isn't clear flossing helps, it's that we haven't established with the kind of evidence HHS requires that flossing helps. Those sorts of studies are hard to do reliably with things like flossing.

Do you think the evidence we do have, which doesn't rise to the level required by the HHS, is in fact strong enough and that we should rely on it?

The quote doesn't sound encouraging:

Overall there is weak, very unreliable evidence which suggests that flossing plus toothbrushing may be associated with a small reduction in plaque at 1 or 3 months.

Quite possibly.

The epidemiological studies, as I understand it, make the association between claims of flossing and improved tooth health unambiguously exist (though not huge). HHS didn't analyse them and find them too week, exactly; they simply want controlled studies for this purpose (for good reason, of course). Nonetheless, everything we know makes it sound like flossing is at least a little effective.

Whether the effect justifies spending minutes every week, who knows.

From the International Craniofacial Institute's web page on cleft palate.

What they say:

Statistics reassure us that having a child with a cleft does not mean you’ll have other children with the same condition. In fact, your chances only increase by 2 to 5 percent compared to couples with no cleft-affected children.

What they mean:

The chances that your next child will have cleft palate increases from 0.15% to about 4%. Your odds ratio multiplier is 25.

Why should people care about the odds ratio in this case instead of caring about the absolute risk?

It seems to me that if a patient get's a child with a cleft palate they care about the absolute risk of their next child also getting it.

I didn't click-through and there might be more context than this, but "chances only increase by 2 to 5 percent" is ambiguous between "percent (as an absolute probability)" and "percent (of the chance it was before)". I'm not sure if it qualifies as an "irrationality quote", it's just unclear and could be confusing, but /u/PhilGoetz's version is a step up.

(I'd maybe not use "odds ratio multiplier", because we're not just concerned about clarity, but clarity to people who might be statistically illiterate)

Meta question: are there 'gray area' quotes that can fit both rationality and irrationality?

Let's take 'You miss 100% of the shots you don't take" for example. On the positive side, it means that you should definitely do X, because otherwise you could never get it. The gray area is that it's abstract and situation specific, there's nothing that guaratees success or failure. The negative side could end up you making a fool of yourself.

I'm not really sure where I'm going with this. It seems like rationality quotes provide wisdom, and things to consider. Irrationality quotes provide the opposite: they have faulty reasoning and should be things to avoid. This binary situation reminds me of the part of GEB where it discusses if machines are ultra-flexible or ultra-limited. Can a (ir)rationality quote have the paradox of being both useful and harmful at the same time?

Seems similar to the "motte and bailey" concept -- ideas having both rational and irrational interpretation.

Except that in the typical "motte and bailey", the rational version is supposed to be boring, while in what you describe, the rational version is also interesting.

Probably any rational advice can be horribly abused, so I'm not sure if there is a specific category of those that are specifically "asking for" being abused, or whether just some forms of abuse accidentally become popular.

i remember few quotes which i really like here are few which i will tell quotes: " let go your earthly tether enter the void empty and become wind" "The secret of life is not to do what you like, but to like what you do." "The greatest obstacle to discovery is not ignorance; it is the illusion of knowledge." http://www.dissertationclub.co.uk/