Why can't it be algorithmic? If the brain uses the same process on all information, then that is an algorithmic process. There is some evidence that it does do the same process to do things like consolidating information, processing the "world model" and so on.

Some processes are undoubtedly learned from experience but considering people seem to think many of the same things and are similar in many ways it remains to be seen whether the most important parts are learned rather than innate from birth.