The Doctor, in all his incarnations, leads with Ne and backs it up with Ti -- not the other way around.
If the Doctor were an INTP, he would be sitting around, theorizing, only venturing out to collect the evidence he needed to prove a theory. Again, the closest we ever get to this is latter-day McCoy, where he wanders around with his head in the clouds, planning, plotting, working out systems that nobody else can see, to the extent that he often misses what's right in front of him.
Otherwise, the Doctor is typically out there in the world. His motivation is to gain knowledge, experiences. To see the universe is to truly understand it. He left Gallifrey because it was too boring; all anyone did was sit around and watch and theorize and pontificate. Typically he only stops to think and process all the information he's taking in when he runs into a problem that needs solving.
Step one: take in as much information as possible.
Step two: slot it together, and see what you can make out of it.
The Doctor is an inventor, not an architect. He doesn't write thousand-pages theses on the ideal resolution to a problem; he works with what he has at hand, and builds brilliant things out of it. He doesn't obsess over a few subjects; he takes an interest in everything he sees. He doesn't plan everything out in advance; he improvises.
The Doctor is about as archetypically an ENTP as you get.
