When a function is differentiated, it is abstract. That is, it is differentiated and operating in a way that is independent from other functions, where it is highly refined and efficient, able to work smoothly and separate irrelevant components from its key activities. Consider it analogous to writing an essay for an exam: when you write your essay in a manner that is clear, comprehensive, contains all the necessary details, but doesn't have any irrelevant points or "borrow" from unrelated themes, you can usually be sure that your professor will give you an "A." However, as your grasp of the material slips, more irrelevant details slip in, your topic gets combined with other topics, you may try to "shotgun" by incorporating anything that can be brought up into conscious recollection in the hopes that something hits. Well, an abstract function is like that "A" essay. By contrast, when a function operates in a concrete manner, it tends to combine with other functions. It "pads" its activity with tendencies from other functions in an effort to try to get the job done.
Concrete feeling tends to be caught up in the sensuous. When feeling is triggered, it is most commonly experienced as something that happens outside the self. For example, pulling off the road to see cliffs over the ocean and suddenly hit out of nowhere with this wave of emotion would be an example of concrete feeling. Another would be to watch a very moving play and have the experience of catharsis: one is overcome by emotion, tears come to their eyes, feeling is vulnerable, and the experience leaves a profound impact on the person. The sensuous experience of sitting on a rooftop in Malta, sipping a fine wine and eating a good dinner, warmed with all kinds of good feeling, would also be an example.
You may notice a similar thread in all of the above examples: the feeling experience is coupled with emotion and is involved in something sensory. Crying, for example, is a physiological response, which Jung is very clear on as being unrelated to feeling as a differentiated function. When feeling is well differentiated, the feeling values operate smoothly, and in a manner that is separate from emotional reactions.
Additionally, feeling precedes the encounters with the world when differentiated. The values selected or drawn upon are firmly in place and they precede the experience of the outer stimuli. The outer stimuli is therefore subordinated to the judging faculty, and it is only then that it is determined whether the experience is to be accepted or rejected. However, when feeling is concrete, it doesn't operate so efficiently. Rather than the value being in place and the world being judged in that way, these sensory phenomena (apprehension of something beautiful in nature, the satisfaction of a good meal) take on a sudden, mystical power that overpowers the person and fills them with emotion. When this happens, one can conclude that the feeling function most likely does not predominate and is not differentiated, as it is too bound up with sensory experiences.
Concrete feeling can be quite emotional, and can at times deteriorate into mere moodiness, which is different from the mood of the feeling type.
Abstract feeling, on the other hand, is more efficient. Relying on a pre-existing criteria based on religious, moral, aesthetic and intellectual sentiment, it is able to operate smoothly without an emotional response. This isn't to say that the feeling type is never emotional--anyone can be--but the emotions are not tied up with the evaluations. So, for example, the same play as mentioned before will be first evaluated in terms of how it accords with the values and insofar as it is consistent with those values, it is determined to be good or bad. Remember, values means something much broader than the colloquial definition: if my value is that a "good play" follows the formula presented in Aristotle's Poetics, and I then judge the play on those grounds, that would mean judging it in accordance with my values. A rational (but not logical) determination is then made. Similarly, if nature is valued by the person, then these things may be concluded to be good, and then accepted by the individual, but if some other pre-set criteria intervenes (such as determining nature to be something that takes the person away from all the refinement and culture she enjoys, and not in accord with her values) the person may conclude she would rather be in Paris and express dissatisfaction with the current environment.
This brings me to an important point. Jung says that abstract feeling covers religious, moral, intellectual and aesthetic sentiments. Now, there is nothing to say what form these take. They will follow a rational pattern for the individual, so, if the feeling type has a value, their analysis will conform to that value. For example, suppose I hold the value that art should in some way express something of the human condition. My aesthetic experience will be predicated on the art doing this. If I go to MoMA and see an exhibit of inflatable chairs, not only will I be left cold, but I will determine this to be bad art. However, that doesn't mean that my values will remain static. It might be that I, at 39, have values that exclude the inflatable chair. Perhaps at 19, though, due to other intersecting beliefs or the values of my social group, I thought the idea of inflatable chairs as art was deeply profound (thankfully, that was never the case) I might have made a different determination then. That doesn't mean it isn't rational: an evaluative principle can change over time, as things touch upon these abstract ideas and impress upon them the need for certain values to be modified, altered or adapted.
Religious conversions often are of this character. I don't mean the sort of deathbed religious conversion often found among extraverted thinking types with inferior introverted feeling, but rather when some sort of crisis of faith or social value leads one from one religion to another. Religious values can be of any sort: Christian, Muslim, Pagan, Hindu, Buddhist, etc. Even atheism, when infused with all sorts of evaluations about the worth of Christianity, behavior of the Catholic church, and not based solely on the logical arguments, falls under the domain of the feeling function. One example would be the person who is raised as a Christian but, when away at college, discovers Zen Buddhism, and where they once made judgments based on a thing's congruence with Christian values, they now have Buddhist values as their means of making determinations. Now, in our contemporary society, the feeling function gets a bad rap for its religious inclinations: words such as "fanaticism" and "dogmatism" get bandied about. However, that sort of extreme reaction tends to be more the domain of inferior feeling, which has not learned how to "handle" its faith experience, and gets so bound up in emotions it feels compelled to then force it upon others. When operating well, it simply is a system through which one can evaluate where the person stands in relation to the things it encounters.
Feeling function, when abstract, elevates above moodiness and becomes a sort of "mood" a general tone or "vibe" of a place, epoch, or society. Rather than being personal and self-absorbed in its moodiness (as is the case with concrete) it taps into something which has a more universal quality.
Concrete thinking, just like concrete feeling, has a relative inefficiency to it and tends to be bound up in sensation. When concrete thinking is connected to sensation, it becomes slavish to facts. One example of this slavish thinking: the Psychology major who likes to quote statistics, without being able to say anything critical or insightful about the research in question. Another example would be the academic that over-relies on quoted material, while being reticent to declare one's own position or interpretation.
More concrete numerical operations would fall into this category as well. Jung was rather critical of the idea that mathematics could be considered part of logic, and in his essays he says that while it makes use of logic and that it is a separate faculty altogether. In The Gifted Child, he states,
While I am on this subject I must not omit to point out that very erroneous views used to be held at one time concerning the gift for mathematics. It was believed that the capacity for logical and abstract thought was, so to speak, incarnate in mathematics and that this was therefore the best discipline if one wanted to think logically. But the mathematical gift, like the musical gift to which it is biologically related, is identical neither with logic nor with intellect, although it makes use of them just as all philosophy and science do. One can be musical without possessing a scrap of intellect, and in the same way astounding feats of calculation can be performed by imbeciles. Mathematical sense can be inculcated as little as can musical sense, for it is a specific sense. (239)
Higher mathematics is akin to musical ability, though at the lower levels I would assert that it falls under the domain of concrete thinking due to its reliance on sensation. It becomes like the mathematics of the accountant: precise, detail-oriented, a numerical "fact" of sorts that is neither related to the abstract thinking in logic nor the kind of gift or talent required in higher mathematics.
Perhaps it's because this is the easiest for me to understand, but it doesn't seem like there's much to say on the matter. Like the negative theologian who defines God by what he is not, my explanation of what abstract thinking is not seems to illuminate what it would be to the point where I think I'd just be (over)stating the obvious here. Still, I'll say a few words on in in the event that it isn't as obvious as I think it is.
Abstract thinking, of course, is going to be efficient, focused thinking which doesn't get caught up in extraneous details. At the risk of being too self-referential, consider the following analogy: at the start of this summer, I decided I wanted to figure out what the key features of Jung's system of psychological types were. I read Psychological Types, and some key sections I read over more than a few times. I also read Von Franz and Hillman. Where things seemed baffling or contradictory, I looked at some of Jung's other works (ranging from dreams and archetypes to educational methods) to get a picture of his overall project. From there, I parsed out what the key features were and wrote various notes and drew various diagrams to get to the essence of the system. Well, that's pretty much what abstract thinking does: it takes the wealth of information and logically organizes it, slicing out what is unnecessary to form categories and draw conclusions.
Now, abstract thinking doesn't mean that someone who has differentiated thinking necessarily creates great intellectual works. There may be variabilities in terms of ability which are distinct from the role it plays in the personality. Just as a person can be highly intelligent but simply have some other function hold dominance, a person can have thinking more differentiated than the other functions but not utilize it to its fullest capability for whatever reason (background, opportunity, life choice etc). What indicates abstract thinking is that the person predominantly has this efficient use and habitually employs it when making judgments.
In Conclusion: So, you have what should be a fairly detailed picture of what each of the two judging functions look like when either abstract or concrete. The examples I gave should be taken as exemplar situations. The effects of concrete thinking and feeling may be much more subtle than is depicted here. Since there are degrees of development of the functions, the placement will influence how clearly concrete or abstract a function is. A very differentiated dominant function will look fairly abstract, similarly the inferior function will tend to be quite obviously concrete, but the middle functions may be less obvious, and may even have traits, to varying degrees, of both the abstract and concrete aspects of that function.
This is my last week before the semester starts. I may try to get a couple more posts in, if I'm feeling inspired. Or I might get my last bit of leisure reading in. I'll probably be writing more sporadically after that, since I'm going to be crazy busy this term.