Is it the same knife?

There is that old philosophical question which goes like this: “You buy a knife with a wooden handle. After a year, the handle breaks and you replace it with another wooden piece but retain the same blade. After another year, the blade or the cutting part of the knife gets bent and you fix a new one on the same wooden handle. Now that you’ve changed both the parts of the original knife, can you call it the same knife or is it a different one?”

I was reminded of that when I read this interesting story on Douglas Adams (source)

On visiting the Gold Pavilion Temple in Kyoto, Douglas Adams was impressed at how well the 14th-century structure had weathered the passage of time. His Japanese guide told him that it hadn't weathered well at all; in fact it had burned to the ground twice in the 20th century.

"So this isn't the original building?" Adams asked.

"But yes, of course it is."

"But it's been burned down?"

"Yes."

"Twice."

"Many times."

"And rebuilt."

"Of course. It is an important and historic building."

"With completely new materials."

"But of course. It was burned down."

"So how can it be the same building?"

"It is always the same building."

"I had to admit to myself that this was in fact a perfectly rational point of view, it merely started from an unexpected premise," Adams wrote. The essence of a building is its design, the intention of the builder. The materials may decay and be replaced, but these are only instantiations of a persistent idea. "I couldn't feel entirely comfortable with this view, because it fought against my basic Western assumptions," Adams wrote, "but I did see the point."

If at a point in the future, medical science is able to change all the organs in the body, one at a time, including the brain would that person be the same one as before?