Yes there is a difference between rational and correct

There's no shortage of idiots pouring their idiocy in written form all over teh interwebs. The idiots themselves are not particularly remarkable but rather trite, and so we'll eschew reference. The idiocy they produce may be amusing, so let's reproduce some :

Sometimes experimental psychologists uncover human reasoning that seems very strange - for example, someone rates the probability "Bill plays jazz" as less than the probability "Bill is an accountant who plays jazz". This seems like an odd judgment, since any particular jazz-playing accountant is obviously a jazz player. But to what higher vantage point do we appeal in saying that the judgment is wrong?

Experimental psychologists use two gold standards: probability theory, and decision theory. Since it is a universal law of probability theory that P(A) ≥ P(A & B), the judgment P("Bill plays jazz") < P("Bill plays jazz" & "Bill is accountant") is labeled incorrect.

There are many differences between "rational" and "correct"ⁱ, such as for instance that statements may be correct while inferences may be rational. The terms apply to different types of things, much like a battery that's powerful (ie, can provide a high instantaenous Intensity * Voltage) is not the same as a battery that's energetic (ie, can produce a high total Intensity * Voltage).

Strictly speaking, discussion of the correctness of a process is all about that process' conformity with an arbitrary (and hopefully aforestated) template, which has absolutely nothing to do with any right or wrong ; nor with any rationality. It may not be right for a Red Army private to wear his pants under his butt like a wanna-be black thug ; it may also not be rational for him to do so. These considerations are however orthogonal to whether it is correct for him to do so or not, a point established by reference to the Red Army Uniform Code and nothing else.

For this reason, it is only possible to apply the correctness attribute, to establish whether something is correct or incorrect, in situations where templates actually exist. Should one claim that from a > b it then follows that a² is also larger than b², it would be proper to call that claim correct, for as long as a and b are limited to real numbersⁱⁱ that are larger than 0. For the case of negative numbers, the claim is incorrect ; for the case of complex numbers the claim is indecidable - it lacks the possibility of being either correct or incorrect for lack of the required template.

Meanwhile whether something is rational or not hinges on whether that something can be stated in terms acceptable to a group. The same item will appear rational and irrational to different groups, depending on considerations unrelated to the item itselfⁱⁱⁱ, and the important difference is that while templates for correctness are always written, group criteria for rationality are always unwritten.^iv There necessarily isn't any way to remedy the gap between written and unwritten^v, and consequently correctness and rationality must remain unrelated attributes, misguided efforts of idiots to soup them together notwithstanding.

As a direct result the various mixes may all be encountered in practice - and in fact are. For instance the person who lies under threat is engaging in making incorrect, but rational statements - both while applauding Hitler's genius under the eyes of the SS, and then while wondering at Hitler's evil, under the eyes of the US. The person arguing with idiots, in any capacity, may well be making correct statements, but can't escape their irrationality. On it goes.

In the actual example given, any sort of correctness is out of the question. While it's correct to say that since there's no such thing as a negative probability, then therefore the probability of a simple statement is always higher than the probability of a compound statement containing the simple statement, this has absolutely nothing to do with the problem of the jazz musician versus the accountant-jazz musician. There's no statement of equal samples, nor any good reason to suspect equal samples would be involved. The question is phrased about a single item, labeled Bill - and while it's true that the particular sort of idiot that ends up fascinated with statistics dependably manages to bungle up this fact, there's actually very little statistics can say about individual cases.^vi

Moreover, the question, like any question, is fundamentally a work of fiction. All fiction relies on a high-level cognitive behaviour called "willing suspension of disbelief"^vii, and the rule there is that it's acceptable to ask the audience to believe the impossible, but not the improbable. For this reason, the abstractly less likely construction is judged as more acceptable, which is what the respondents are saying.

The choice of "someone" is therefore perfectly rational, as per the definition of rationality. It may or may not be correct - thanks to idiots flattering themselves with wholly delusional notions of participating in some sort of scientific process that nevertheless forgot to put all the required template bits in their soup, we don't actually have enough information to make this determination. It may also be "strange", whatever the author may mean by the term - I suspect the behaviours of nubile young women appear just as strange from his particular vantage.

The ultimate goal of all this overflowing stupidity is transparently ethical, which is to say the idiot is aiming to derive strict bindings for the future, that'll allow him to decide behaviour (his and others') on some sort of basis within his control. This is not nearly as laudable a goal as it's currently fashionable to regard it among idiots ; but that aside it is also not strictly speaking possible. The inherent tension between different groups' definition of rationality can never be resolved, for reasons that exactly mirror the reasons socialism always fails in any attempt at practical implementation. The "obvious"^viii solution to bridge that unresolvable (but for the idiot also unobservable) gap is the recourse to "corectness"^ix, but this only serves to compound the difficulties : there isn't nor can there be a way to translate from rational to correct, or back again. The Romanian expression is "frectie la un picior the lemn", ie, rubbing the wooden leg. It dun do nuttin!

Actually, that's not really correct : it does do something. It provides the cover of frantic activity, always and everywhere the preferred hideout of impotence. This is why the whole idiotic pile of nonsense seems rational to the idiot in the first place. For him, it is.

1. Let's not even get into discussing the patent idiocy of mixing wrongness, an ethical consideration of the nature of oughts, in a discussion of is-type attributes such as "rational" or "correct".

   It is universally the confusion of different things that distinguishes the idiot from the non-idiot. Contrary to easy if unsubstantiated claims made fashionable by the memetic quality of one paper by D. Dunning and J. Kruger (such as the ineptidudes pouring forth out of a very stiff Stephen Fry), there's a perfectly workable, easily deployed, trivially scored mechanism by which idiots of all stripes and ignoramuses of all types can readily access the plain truth of their idiotic ignorance : list distinct things! The fewer items one can distinguish, the less knowledge and intellectual ability generally speaking at his disposal.

   Supposedly they "don't know" about this. For the same money we could as well believe that their socialist bias is not borne out of a fervent if ultimately doomed desire to paper over their own shortcomings instead of fixing them. No, they just hate distinction in general and unrelatedly to how it is exactly the path out of the stupid cave. How coincidental! Your average "intelligent design"-er couldn't have painted a prettier picture! [↩]

2. You will note that while sorting of complex numbers can work any way you want it to work, unless you provide the way you want it to work in advance there's no way to resolve the truth value of a+bi > c+di type inequalities. [↩]
3. And with intelligent individuals the rationality changes by context. Consider : if you put a chunk of soppressata in the respective drawer of your fridge, is it rational to expect to find some in that same drawer next you open it ?

   Strictly speaking, there's absolutely no good reason for this expectation. Your experience may show that you'll find some, or that you won't find any. Irrespective of this inductive reasoning of yours, there's nothing that guarantees you'll find the колбаса where you left it, conservation of matter be damned. If it decides to no longer be there one day, you won't have anyone to complain to, nor any contracts to stand your complaint on. Physics comes with no promise, past performance is no sort of guarantee for the future, and so no, you have no rational grounds to expect anything in particular. [↩]

4. To further illustrate the difference, suppose you conduct the salami experiment : you open the drawer, place the item, close the drawer and the fridge door, all under the eyes of a witness, let's call her Wanda.

   Once the ritual performed, you put forth to Wanda that you expect there to be some salami in your fridge drawer. She will agree that this is a rational expectation, as it matches her feelers on the topic of how salami behaves when alone in a drawer ; she can not agree that this is a correct expectation, unless she's one of the unintelligent louts who actually keeps a template matching this situation in her list of correctnesses (which is a dumb thing to do - but people do dumb things all the time, which isn't even all that irrational but we'll get to it later).

   You then open the fridge and the drawer, and declare that indeed, the salami is still in its place. Wanda can confirm that this is indeed a correct find - by checking to see how the claim "salami is in drawer" matches the observed salami in the observed drawer. She can't however call your claim rational, but on the contrary - it's a pretty stupid thing to say. Unless, of course, she's the sort of retard that has a cutoff for banality very different from other people. [↩]

5. Please consult proper discussions of semiotics and general theory of representation to edify you on this point, I can't be arsed. [↩]
6. Knowing that women have a 50% lower chance to develop disease X than men, how is Bill's sex change operation going to impact his life expectancy ?

   Knowing that on average humans have one testicle and one ovary, what are the odds that this human's left ovary is a testicle ?

   If you are playing a dice game so that you win ten times your bid every time you roll a six, with the condition that you always wage half your cash, what are your chances of getting rich surviving a few dozen rolls ?

   Statistics is the easiest thing to misunderstand. [↩]

7. You know that it's high level because it involves volition and belief. [↩]
8. The practical solution, meanwhile, is to carefully tailor "user experience" in the manner Google tailors search results. Alienation is first and foremost a coping mechanism. [↩]
9. Recall Ballas' excellent "only the facts" piece ? [↩]