Let's look at the Thinking function. Te would mean thinking that is exerted on the external world correct? Applying objective logic to to situations that are happening or could happen. So the inverse, Ti, would meaning thinking that is exerted on the internal world, i.e. the self, right? Logic in Ti would therefore be subjective, but still logic.
Also, Ne is intuition exerted on the external world and Ni would be intuition exerted on the internal world.
So TiNe INTP would be a archetype that applies logic internally and is externally intuitive.
Now we're cooking with fire. I'm not sure I would choose these exact words, but this is agreeable enough. Perhaps I wouldn't say that Ne "exerts" itself on the external world, more just that it deals with the external world. I also wouldn't say Ti necessarily "applies logic internally" but rather logic is applied more to internal ideas and concepts. Still - close enough.
Ok, we know this, but what does it mean to apply logic internally and to be externally intuitive?
Introverted-ness is concerned with the self, so if you are dominant Ti would not that mean you subject your own thoughts to logic? In other words, you are primarily concerned with logic. Ne, being that its energy is focused outward, would be objective, since it originates from the external world. So Ne receives objective information.
I'm not 100% sure that I would say Ne is always objective. Supposedly, one of the primary processes of Ne is to infer consequences, possibilities, and effects from external stimuli. These inferences may or may not be objective, but would likely be derived from objective sources.
So now we have a person who is primarily concerned with personal logic and receives secondary objective information from the world. It's judgment focuses on the subjective self and it's objective perception flows into the subjective self. Any energy that is exerted on the external world would have to be objective and impersonal then, no? Because it's judgment, Ti, is exerted on the self, while it's perception, Ne, is exerted on the world.
No, I do not agree with this. Just because you receive objective information, that does not mean that your interactions with the world will be objective. If Ti is the dominant function, then it is very likely that interaction with the world will have been influenced by a personal, subjective factor. Ne develops the
desire to move from one domain to another, but interaction with those domains is still largely Ti. The information to process likely just comes through Ne.
Ne picks up the information, Ti analyzes it and makes the decisions (generally).
This paints the picture of a character who sees the world from his logical self, which is built upon subjective, irrefutable truths,
No, this character sees the world through Ne, which is more likely to be objective insight.
but who interacts with the external world in an objective way.
It seems like you switched Ne and Ti somewhere in here. Most of the decision making (which I suppose is what I would call interaction) is Ti. The "seeing the world" part is perception or Ne.
A theory proposed by such a character would then take in objective information(Ne) and focus judgment on matters of the self and the self's truths(Ti) and not external matters such as society and society's behavior.
I think you have to be careful with how you're describing Ti. Ti doesn't necessarily stand for thinking about things that only involve the self. It means thinking of ideas and concepts that are mostly subjective in nature, as opposed to thinking about things and people that are largely objective in nature.
Would not such a theory that concerns external matters be proposed by a character who perceives information from the self but judges on external objective information? NiTe.
Sure, I can agree with this.
In other words, this character takes in information from the observations by the self but does not exert judgment on the self, rather it uses the information to make judgments externally.
Still something I can agree with, though I'm a little iffy on the wording again.
To put it more simply this character perceives the internal world, filters the information subjectively and then makes a judgment about the external world.
Ok, here is where I think you've deviated. Why would this character filter the information subjectively? Filtering involves a decision making process, which is a process of the judging function. This character would judge via Te, so filtering information would be in an objective, externally oriented manner.
Would not this character be the one to tend to make objective theories(Te) about the world based on personal observation and subjective introspection(Ni)? Now, is this not the INTP character?
How can you make an objective theory about something when you start from a subjective premise? Ni's are often described (even by Jung himself) as sort of the "prophet" type. Many of their ideas just seem to come from thin air, because they are extremely subjective and based on intuition. This can manifest as anything from a cult leader with an innovative dogma or a brilliant scientist with an innovative theory. In the former case, the subjective and intuitive idea produced an erroneous and subjective dogma. In the latter case, the subjective and intuitive idea produced an objective and scientifically sound idea.
I would argue that the INTP makes subjective theories about the world based on objective observation. This is why an INTP's ideas will many times seem outlandish and subjective, but will be grounded in objective truth. Consider a debate in the two cases:
INTP: Theory seems wacky and offbeat, but the INTP always manages to come back with sound evidence and sources to support the point. The steps to get to the theory/conclusion sometimes seem muddled and arbitrary, but when you really question the premise you discover that it comes from an objective truth.
INTJ: Theory seems logical and all the steps used to create the theory check out, but when you really question the premise the INTJ falls back on "that's just how it is...it's obvious!"
That's my two cents, anyways.