In Treasure Island, why does the doctor come to the block house and what does this tell you about his character?

In Chapter XXX of Treasure Island,
Dr. Livesey showed that he lived up to his doctor's code in the highest fashion. Livesey
voluntarily entered the blockhouse in order to tend to the wounded pirates, uncertain
whether he would be allowed to leave freely
afterward.

He
seemed to me under no apprehension, though he must have known that his life, among these
treacherous demons, depended on a hair... His manner, I suppose, reacted on the men, for
they behaved to him as if nothing had occurred—as if he were still ship's doctor, and
they still faithful hands before the
mast.

He treated their wounds
and spoke with them in kind words, making sure that certain sailors had taken their
prescribed medicine. Afterward, he managed to convince Long John Silver to speak with
Jim, who the doctor feared had gone over to the pirates' side. But Jim told the doctor
that he had recaptured the ship, and that it was hidden in the North
Inlet.