[insonable]

It's based on analytical psychology from the 1920s as Jung laid out in "Psychological Types." The funny thing is MBTI was developed for carbon copy paper and as an instrument to quickly type people. So they created the 4th column because in their scoring and layout, they couldn't indicate whether the person was more perceptive (N or S) or reasoning (T or F) focused by putting one in front of the other as Jung did, and also, in their test I guess they found it easier to figure out which function type you extraverted rather than what the attitude (introversion or extroversion) of your primary function was directly.

This leads to a lot of confusion. Jung for example might call a type "Introverted Intuitive with Feeling", and in MBTI that is INFJ, where the J means they extrovert the Feeling, but are primarily actually perceivers! Then there's Introverted Feeling with Intuition, which in MBTI is INFP, the P here meaning they extrovert intuition, but since they're primarily introverted they are "introverted feelers" foremost. I think this MBTI formulation has really made Jung's ideas unnecessarily confusing.

Also, Jung himself was not fond of people typing others, and thought people ought to learn the ideas and type themselves and of course allowed and discussed that some are not differentiated strongly in some dimensions, although he did view that as being a sort of lack of development.

So is it science? I guess I'd call it an interesting analytical model and leave it at that.