First of all, in my opinion it is easy to show why MBTI is not a scientific theory: it does not make falsifiable statements. It says a lot about what people tend to do, but it never makes a statement which can be used to prove the theory wrong.
There has also been a misconception that a lack of data is what stands between us and the corroboration of MBTI. This is giving MBTI a lot more credence than it deserves: the critique is that it cannot, by its own nature, even generate statements which can be tested by data.
Here are the self-selection ratios that Myers reported for a study involving 705 Cal Tech science majors:
INTJ 3.88
INFJ 2.95
INTP 2.92
INFP 1.97
ENTJ 1.56
ENTP 1.42
ENFP 1.09
ENFJ 1.08
ISTJ 0.68
ISTP 0.50
ISFP 0.49
ISFJ 0.43
ESTP 0.22
ESTJ 0.12
ESFJ 0.18
ESFP 0.02
Stat spectrums that tidy are what you call a personality psychologist's dream. What they indicate (and the sample size was pretty large, at 705) is that the MBTI factor that has the greatest influence on somebody's tendency to become a Cal Tech science major is an N preference, and the MBTI factor that has the second greatest influence is introversion, with the result that the spectrum tidily lines up (from bottom to top) ES-IS-EN-IN.
That's the kind of evidence that psychologists have been using to establish the "validity" of personality dimensions for many years now. And that's just one example pulled from 50 years of MBTI data pools that have respectably established the validity of all four of the MBTI dichotomies.
Keeping in mind that twin studies indicate that the MBTI is tapping into four substantially-genetic dimensions of personality, the results of that sample suggest that there are relatively hardwired dimensions of personality that can make a person of one type (e.g., an INTJ) something like
30 times more likely than another type (an ESTJ) to end up as a science major at Cal Tech.
Hopefully needless to say, no personality typology aspires to be able to reliably predict what career
any particular individual is going to choose, but whether a typology has validity in the first place is a very different issue from that. One of the things that makes personality typology a "soft" science is the fact that, regardless of how valid any particular typology might be, it's hardly going to cover the waterfront when it comes to possible influences on someone's personality or behavior. That's one reason type can't be used to make "falsifiable" predictions about what any particular individual is going to do in any particular circumstance — and that's just one of several serious complications that come into play when you're trying to apply a (valid) typology to a particular person.
Another complication is middleness. As I understand it, there's quite a lot of data (Big Five especially) that suggests that a large percentage of the population may be close to the middle on one or more of the Big Five and MBTI dimensions.
Another complication is the fact that the aspects of personality that tend to co-vary in the kinds of broad "clusters" reflected in the MBTI and Big Five dimensions may not cluster all that tidily. Biological males are sexually attracted to biological females, right? Well, except when they're not. And there's currently no reason to think that the substantially genetic underlying dimensions that the MBTI is tapping into are any tidier than the substantially genetic "biological maleness" cluster.
Contrary to what you sometimes hear, and notwithstanding that there are important distinctions to be made between "hard sciences" and "soft sciences," the four MBTI dichotomies now have decades of data in support of their validity and reliability — and a combination of meta-review and large supplemental study in 2003 concluded that the MBTI was more or less in the same category (if not on a par) with the Big Five in terms of its psychometric respectability.
Anyone who's interested can read more about that — and about several other issues often raised by people claiming to "debunk" the MBTI — in
this PerC post.
Among the issues discussed in that linked post is the "bimodal distribution" red herring you mentioned in your last post.
Carl Jung — mystical streak notwithstanding — was a believer in the scientific approach, and Myers took
Psychological Types and devoted a substantial chunk of her life to putting its typological concepts to the test in a way that Jung never had, and in accordance with the psychometric standards applicable to the
science of personality. Myers adjusted Jung's categories and concepts so that they better fit the data she gathered from thousands of subjects, and by the start of the 1960s (as the leading Big Five psychologists have acknowledged), she had a typology that was respectably tapping into four of the Big Five personality dimensions — long before there really was a Big Five.
Buuut it's also worth noting that, contrary to what some of the function aficionados would have you believe, the scientifically respectable side of the MBTI is the dichotomy-centric side — and the dichotomies differ greatly from the so-called "cognitive functions" in that regard. The functions — which James Reynierse (in
"The Case Against Type Dynamics") rightly characterizes as a "category mistake" — have barely even been studied, and the reason they've barely been studied is that, unlike the dichotomies, they've never been taken seriously by any significant number of academic psychologists. Going all the way back to 1985, the MBTI Manual described or referred to somewhere in the neighborhood of 1,500 MBTI studies, and as I understand it,
not one of the many study-based correlations reported in the manual were framed in terms of the functions. The third edition of the MBTI Manual was published in 1998 and, as Reynierse notes in that same article, it cited a grand total of
eight studies involving "type dynamics" (i.e., the functions model) — which Reynierse summarizes as "six studies that failed, one with a questionable interpretation, and one where contradictory evidence was offered as support." He then notes: "Type theory's claim that type dynamics is superior to the static model and the straightforward contribution of the individual preferences rests on this ephemeral empirical foundation."