Den BBC-webbplatsen täcker detta mycket grundligt;
The Doctor has made many conflicting statements about his
qualifications. He certainly studied human medicine, and in The
Moonbase he says that he gained a doctorate under Joseph Lister in
Glasgow in 1888. However, Lister left Glasgow years before that date,
so the Doctor is either being vague or is lying.
He can carry out such basic tasks as resetting dislocated fingers (The
Smugglers), but perhaps the archaic nature of his knowledge (he gives
incorrect advice on fever treatment in The Ark and can't so much for
blood poisoning in The Myth Makers) leads him to deny being a doctor
of medicine (An Unearthly Child, The Krotons). His advanced medical
efforts in The Sensorites rely largely on chemistry skills, and he has
local medics to help him.
The other possibility is that he failed to get an attempted medical
degree (as stated in The Rescue) and, knowing the condition he was
treating in The Moonbase, exaggerated his achievements. In Robot,
knowing he has a doctor on board, he renounces all claims to a degree
save a 'purely honorary' one, which turns out to have been acquired
from St Cedds, Cambridge, in 1960 (Shada).
However, at some point the Doctor does gain the advanced medical
knowledge he uses in The Twin Dilemma and The Trial of a Time Lord.
Perhaps the gap between The Deadly Assassin and The Face of Evil (see
The Doctor's Age) is the most likely place for this to happen, as he's
uncertain about a broken arm in The Seeds of Doom, but familiar with
50th century medicine by The Invisible Enemy. By the time of
Remembrance of the Daleks he's learnt to diagnose by touching
someone's ear.
Before leaving Gallifrey, the Doctor gained a doctorate of some sort
from the Prydonian Academy (The Hand of Fear, The Deadly Assassin),
qualifying, with Drax, in the class of '92 (The Armageddon Factor).
His teachers included Borusa and Azmael (The Twin Dilemma), the latter
possibly being the tutor who understood artron energy (Four to
Doomsday). Since he knows so much about law (The Deadly Assassin, The
Stones of Blood) it is possible that he qualified in this area.
However, on many occasions the Doctor has called himself a scientist
(Planet of Evil) and engineer (The Aztecs, The Mind of Evil). Perhaps
he's telling the truth about a combined degree when he calls himself a
doctor of many things (Revenge of the Cybermen).
I den moderna serien är doktorn mer vag, bara hänvisar till sig själv som en "doktor i allt", som specialiserat sig på "att göra människor bättre".