-J as in "MBTI J"?
Being certain and "correcting" people can also come from having the idea that you are objective. [Granted, the INTP is more likely to be "objective" than other types] For example, 1 + 1 = 2. Doesn't that seem unquestionable? Also, adhering to certain social traditions doesn't really make sense if you apply "sense" to it, does it?
True. I myself have done this often.
But I, and I believe all Ps, tend to rather explain WHY 1 + 1 = 2. If you don't agree with their reasons, then they'll tend to explain their reasons in more detail.
I believe that Js just say that it is, and you have to accept it. or they say that you are crazy. If you ask them why they think that it is so, they will normally give you a short explanation. It's usually one that either makes everything clear, and you agree, or that doesn't make any sense, but that they think is obvious, and expect you to accept it unconditionally.
On reflection,Sheldon DOES actually explain his reasoning for things. But usually, only when asked by Leonard. Leonard sometimes says "Oh. That actually makes sense". But mostly, it still doesn't make any sense. Leonard points this out to Sheldon, and again, Sheldon just dismisses his points.
The INTP has personally sorted through the logic(TiNe) and the assumptions(Si), how can this person be wrong?
I don't claim to understand the Ti system. But I can build on what you've written so far:
I have read before that INTP = Ti-Ne-Si-Fe, and INTJ = Ni-Te-Fi-Se.
If I read you right, that Ti-Ne is logic, and assumptions are Si, then:
Ti = step-by-step logical thinking, following lines of reasoning.
Ne = insights about the external world.
Si are assumptions, sensory 'facts', that only exist in your internal simulations.
INTPs use Ti-Ne-Si thinking, with Ti being dominant. Everything else must fit in with their Ti.
They start with Ti, by thinking things out. Those lines of reasoning, being the dominant function, force them to update their Ne insights into the external world. Then they correct their Si assumptions to fit in with their Ne insights about reality, that were generated by their dominant Ti.
However, because they have reached Si, their internal world, they can now go back to the start point, and use Ti, to again follow lines of reasoning, to reach more insights about the external world, that again allow them to correct their Si assumptions. So they get a feedback loop: Ti-Ne-Si-Ti-Ne-Si-.... This feedback loop continually refines their internal world, that makes it slowly converge to match the external world.
By the same principles:
Se = sensory facts about the external world,
Ni = internal insights, ones that fit with our internal simulation, but are not yet connected with the real world. We can call these subjective insights.
Te = external thinking, either in planning out how to implement one's ideas, or in planning how to test one's ideas in the real world, via experimentation.
INTJs use Ni-Te-Se thinking, with Ni being dominant. Everything else must fit in with their Ni. They start out with Ni, their own views on how things are, subjective insights. They then use Te to test the external world to fit in with their ideas. They then use Se observations to check if it fits.
However, because it starts with i, and ends with e, the loop cannot complete. So they start out with their own insights, based on how they see the world in their internal simulation, and then put it into application, and then, the thought process ends. The judgement is made, and it cannot be changed.
So, from that point on, they have to use Se-Ni-Te thinking, with Ni being dominant. They then take their observations, and go back to their internal world, to evaluate if Ni is correct. However, because Ni is dominant, Se and Te are forced to fit in with that. So they either change their Te, by changing their attempts to change the world to fit in with their Ni, until their Se observations agree with that, or they change their Se observations, until their Se agrees with their Ni.
As a result, INTJs will either keep trying to change the world, until the world acts in accordance with their beliefs, or they re-interpret the data, until the data looks like it agrees with their Ni.
If both are totally impossible, then they will be forced to change their Ni. However, because it is Ni, subjective insight, they will merely pick another way to look at the world, that is still totally based on the way they already see the world, and again try to make the world fit in with the way they see things.
INTPs are effectively, people who change the way they think, until the way they think, agrees with reality. INTJs change the way the world is, until it agrees with the way that they see the world.
In your system, INTP is TiNe=logic and Si=assumptions, the equivalent for INTJ is Ni=hypotheses, and TeSe=keep changing the world until the objective is achieved.
A good example of this, is how Leonard and Sheldon approach dealing with Penny. Leonard's approach is to try to change himself, until Penny likes him. Sheldon's approach is to use NLP to change Penny, until Penny behaves the way he wants her to, like he did when he fed Penny chocolates in an attempt at behavioural conditioning.