I'm curious . . . I've noticed that I tend to black/white things when I learn about them. Learning about parenting, for example, I might simplify to the point of "A is all bad, and B is all good," and then use that as a starting point from which to categorize different parenting practices. Only later, when I have them all categorized, do I start to take them out and re-assess with a less black and white perspective. I always start with an all or nothing attitude, and then adjust later. Or I take on labels in a serious way (labels such as, for example, radically politically liberal), then as soon as that begins to feel comfortable, I start deliberately shedding it as I re-assess and refine what I had rejected before since it didn't fit the label.
Am I creating INTJ boxes? Is that what you mean when you talk about boxes? (Or am I just weird?)
It's close. The INTJ becomes more precise by obtaining better and better perspectives (Ni). We try to come up with the absolute best box to hold the facts as we know them. We
know that a "black and white" box is going to be replaced once we have enhanced our understanding. Subsequent boxes gradually gain more colors and shades and hues, coming up with an underlying ruleset that allows one to almost immediately be able to classify things (in Te terms). For that matter, even our really good boxes tend to be upgraded in one way or another as time goes on. There are some very few boxes that are rather "solid", so solid that they feel more like Si than Ni. An example of such a "box" would be the physical law of energy conservation. While there is an outside chance of energy conservation being violated in some way or another by some unknown mechanism, it's so very unlikely that an INTJ is unlikely to entertain the possibility that energy conservation isn't real. Other boxes are intentionally provisional: we know we don't understand a topic, and we'll fill in that understanding as we get there.
The main thing is that we always rethink the rules (upgrade to better boxes). Every box we adopt is inherently limiting, but without the box, we can't really analyze things. By choosing boxes of varying types, we analyze things rather quickly, by switching between various boxes and seeing which fits best.
Indeed, if something is totally brand new, the boxes start off rather black and white, and one can see this in the posts by young INTJs, who talk as if they've figured everything out, when they really haven't. As we age, however, our initial boxes become less and less black and white. Our experiences shade our thoughts, and we have gained a great deal of practice in choosing what boxes are applicable and which are mostly nonsense. An INTJ with a very sharp Ni will choose the "correct box" from the get-go; exposure to many different ideas allows the INTJ to select the best-fitting box from a wide variety.
The benefits of the "box analogy" are twofold. It reminds us that any context is inherently limiting, and it helps us to understand why it's so hard to describe INTJ thoughts in detail. Communication requires a context, a box: if the INTJ necessarily swaps around boxes in order to understand something, how does the INTJ choose a box to explain how one's understanding?! We don't reason within one box, and thus our reasoning cannot be contained within a single box.
[Note that INFJs have a similar problem. Both INTJs and INFJs complain about being misunderstood, precisely because there is no single box with which to explain the full understanding.]
Thus, in communication, we end up selecting the box we believe to be the "best fit." As a consequence, we often sound far more rigid than we really are, underneath. I've also described it as a gem with many facets: the INTJ can show any single facet at a time, but explaining all facets at once ends up sounding like contradictory nonsense.
The INTPs have a similar dilemma, in that their logical understanding of an idea is as deep as the INTJ intuitive understanding: it's impossible to actually
explain the interplay of all the ideas, ironically because the INTP's understanding is so complete. To explain any single piece of that understanding feels woefully incomplete to the INTP, because there is so much more to it. It plays out differently because their Ne is the extroverted function, and thus it seems outwardly unfocused, even though inwardly Ti is very focused.
For the INTJ, the outward Te seems to be very focused, but the inward Ni is much less focused: the Te gives the illusion to others that the INTJ has only one box, when the reality is that there are many boxes.