Let's focus on Jung. See below.
External vs. internal is also problematic. For example, Ni provides internal (i.e. inner world) information. Te uses it and makes a judgement. (N.B. a judging function is "blind" ... it doesn't provide/produce any information). In what sense is Te about the outer world here?I think that extraversion is focused outside in tangible and objective reality while introversion is focused inwards primarily,in how the external things affect the individual in several ways (in own feelings, inner world, sensations, etc).
Yes, I agree with you ... Ti (or actually Ti-), structural logic, is the most important function in math... hence, mathematicians are usually LII. But Jung claims that any information in math textbooks is about Extroverted Thinking. That doesn't make any sense! Furthermore, if objective vs. subjective is true, then Te must include structural logic as well. But we don't see any obvious structural logic in LIE and LSE. We see organizational skills, but that is about efficiency (not categorization / classification).About the LII question, I think is because the nature of elements, being Te bussiness or pragmatic logic, while Ti is system or structural logic, which is needed in maths. Actually most of the Ti dom I know are good in maths while Te are not very good at it and don't care about it because they don't see a practical daily use for it.
Again, Jung: "The rationality of both types is orientated objectively, and depends upon objective data. Their reasonableness corresponds with what passes as reasonable from the collective standpoint."