"Pure reason" <-- what does this even mean? A bunch of if/then statements? I don't see why you couldn't apply that to human behavior. It'd be pretty complex, sure, but it's not like humans are physically made up of anything different than any other object.
Yes, it's true that I focus some of my logical analyses on people (making inferences about what their assumptions are, etc.) But so do NTs. I probably focus on people more than most NTs, but definitely not all of them.
I excel more at math, computer science, physics, etc. than in other subjects in school. I have a math mind. (= a logical mind?)
I've also been typed as INTP multiple times.
My point is essentially that MBTI is quite a limited system, and people should be careful generalizing type characteristics.