Perhaps the fourth letter could be used to tell us whether or not the individual likes dogs (D) or cats (C), or is left handed (L) or right handed (R). Or perhaps it could be used to indicate whether the person has a tendency toward closure or not. To indicate a tendency toward closure, we could use the letter 'j' as the fourth letter, and to indicate a tendency toward non-closure, lets use 'p' as the fourth letter. And lets further specify that the 'J' and 'P' scales on the MBTI are to be used to test for 'j' and 'p'.
If a particular inF, then, turns out to have a tendency toward non-closure, by testing as a 'P' on the MBTI, we would signify this accordingly - by saying he is an 'inFp'.
'But how does this differ from the MBTI?', you might ask, perhaps a little bit frustrated at this point with all the detail that seems to be getting us nowhere. 'Aren't you still just saying the same thing as the MBTI?'
No. Not exactly. Granted, in the case of the inFp there is no difference - call the person an inFp or an INFP and it doesn't really matter - both amount to the same thing: an introvert (I) with F-N-S-T preference order and a proclivity toward 'p' (non-closure). But now consider this: to the first three letters in our new nomenclature, 'inF', you could also theoretically add a 'j' as the fourth letter - a possibility that isn't allowed in the MBTI!
This possibility isn't allowed in the MBTI because, according to the ASSUMPTIONS underlying the MBTI, since the orientation is 'I' and the preference order is F-N-S-T, one MUST add a 'p' to the first three letters, inF. If we want to act according to this assumption - that all Introverts with F-N-S-T preference order have 'p' traits (preference for non-closure, etc) - we'd have to say that every inF is an inFp.
But is this assumption TRUE? That is the $64,000 question!!!
If it indeed IS true, than the 'inF' must necessarily be equivalent to the inFp; and the 'p' in our new nomenclature would simply be redundant. Insofar as it is redundant, it would be best to simply drop it from the name and revert to the three letter characterization that we speak of in Section One above - inF.
But if it is not true that everyone who has an I orientation and a 'F-N-S-T' preference order is 'p', then some of those who are inF would in actuality turn out to also be 'j' !!! This would result in a new label, the inFj - standing for the person who is an introvert, with F-N-S-T preference order, but a 'j' disposition (prefering closure, etc). It would also result in 15 other previously unrecognized new type-labels. The new four-letter nomenclature would thus not be redundant at all, nor trivial. For it would open up 16 new possibilities that are by DEFINITION outlawed by the assumptions according to which the MBTI works.
So the fact that nobody has ever scored inFj on an MBTI test really tells us nothing about whether inFjs in fact exist. It just tells us that the MBTI, as a test, is based on a theoretical assumption that prevents it from even conceiving of the inFj, let along identifying one.