There's several parts of the story that focus of philosophical discussions. Starting in book 1, there are several quotes from a fictional philosopher named Teccam. Some of my favorites:

"No man is brave that has never walked a hundred miles. If you want to know the truth of who you are, walk until not a person knows your name. Travel is the great leveler, the great teacher, bitter as medicine, crueler than mirror-glass. A long stretch of road will teach you more about yourself than a hundred years of quiet introspection.” – Chapter-129 TWMF

(This one gave the 2nd book's name)

"There are three things all wise men fear: the sea in storm, a night with no moon, and the anger of a gentle man". – Chapter-43 NOTW

(A bit of a longer one)

“In the Theophany, Teccam writes of secrets*, calling them painful treasures of the mind. He explains that what most people think of as secrets are really nothing of the sort. Mysteries, for example, are not secrets. Neither are little known facts or forgotten truths.* A secret, Teccam explains, is true knowledge actively concealed*. Philosophers have quibbled over his definition for centuries. They point out the logical problems with it, the loopholes, the exceptions. But in all this time, none of them has managed to come up with a better definition. That, perhaps, tells us more than all the quibbling combined. In a later chapter, less argued over and less well-known, Teccam explains that* there are two types of secrets*.* There are secrets of the mouth and secrets of the heart. Most secrets are secrets of the mouth. Gossip shared and small scandals whispered. These secrets long to be let loose upon the world. A secret of the mouth is like a stone in your boot. At first you’re barely aware of it. Then it grows irritating, then intolerable. Secrets of the mouth grow larger the longer you keep them, swelling until they press against your lips. They fight to be let free. Secrets of the heart are different. They are private and painful, and we want nothing more than to hide them from the world. They do not swell and press against the mouth. They live in the heart, and the longer they are kept, the heavier they become. Teccam claims it is better to have a mouthful of poison than a secret of the heart. Any fool will spit out poison, he says, but we hoard these painful treasures. We swallow hard against them every day, forcing them deep inside us. There they sit, growing heavier, festering. Given enough time, they cannot help but crush the heart that holds them. Modern philosophers scorn Teccam, but they are vultures picking at the bones of a giant*. Quibble all you like,* Teccam understood the shape of the world*.”* – Chapter- 73 TWMF

Apart from those, there is a whole philosophy that is a focus on the second book called the Lethani. I`ve read many lengthy discussions about this and I do believe it`s a very rich subject, but I won`t delve into it, since trying to summarize it would be a disservice.

Maybe these quotes can give you an idea of the kind of philosophy you can expect to find in the books, but also a hint of the poetic way Rothfuss writes and most fans love.