Generalizations I do not like about INTPs? That we are:
1. Cold / Don't care about people.
2. Don't have emotions / are machines.
3. Don't live in the "real" world.
4. Don't have any "common sense."
There are tendencies to these things, true; but they usually are expressed openly only by dysfunctional/extreme INTPs, and the rest of the time it seems to be more a misunderstanding or the results of another type's excess.
For example, we can have "common sense," but there are other concerns that prevent us from just accepting a purely common sense solution. And we see the destructive elements of impulsive emotion, so we tend to detach such things from our decision-making, so we can make a "fair and impersonal" decision that weighs all factors into account rather than just the ones we happen to favor at the time.
We also do not indulge in showy displays of emotion and don't deal well when others "over-emotionalize" around us, it's just too much to deal with. We usually show we care by listening, or giving advice, or sharing information about the world; if we did not care, we would not bother, we just feel uncomfortable with more personal emotional displays of affection.
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As far as me personally, I focus much more on my N and less on my T, and I've developed some more formalized social ability so that I can come across as warm and friendly in a way that most INTPs do not. (It's more like the Fe version of friendliness.)
I struggle between trying to reduce life down to one defined equation, versus viewing life as an infinite number of viewpoints depending on where I place my feet.
I also enjoy isolation, but at the same time desire very intimate personal relationships in terms of "knowing" someone deeply [it's more the exchange of personal information than spending time together that interests me... so I suppose that is more an INTP approach to intimacy].
I'm also very sensitive to how others might be feeling and consider that a factor to take into account, rather than to be dismissed as irrelevant to the question at hand (especially if we are talking inter/intrapersonal matters).
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The generalizations are such because they help define the extremes. But few people are at the extremes. No one will ever fit perfectly into a generalization. That's simply to be expected and accepted. It doesn't mean the concepts are useless, they just give a starting point from which to individualize.