If all knowledge is based on assumptions, can first principles truly exist?

That's an excellent question, one that immediately hits upon a core contradiction.

My understanding is that it depends on how we define "first" in "first principles." Is it "first" in an absolute sense, or "first" in a relative sense?

From the perspective of an ordinary person solving problems, the "first principles" we use are actually relative, and "first" within a specific system.

For example, let's consider playing chess. What are the "first principles" of chess? They are the basic rules like how the knight moves, how the bishop moves, and that pawns can only move forward. Within the "chess" system, these rules are absolute, unquestionable truths, forming the foundation for our strategies and game thinking. You can't tell your opponent, "According to quantum mechanics, my rook can be in two places at once." How would you even play then?

But are these rules the ultimate truths of the universe? Clearly not. They are merely a set of axioms that we "assume" and "mutually abide by" for the game of chess.

Elon Musk building rockets is an excellent example.

• The previous assumption was: "Rockets are very expensive." This was an "assumption" based on historical experience and market conditions.
• Musk's first principles thinking was: "What are the most fundamental components of a rocket?" He went back to the physics and chemistry level: raw materials like aluminum, titanium, copper, and carbon fiber. Then he looked up the market prices of these raw materials and found that their cost accounted for only a tiny fraction of a rocket's selling price.
• In this problem, "the cost of a rocket depends on the cost of its raw materials" was the "first principle" he discovered.

Is this principle a universal truth? Not really. It also rests upon a series of even more fundamental assumptions, such as "efficient market economy" and "relatively stable metal prices." But for the question of "how to reduce rocket costs," it was already fundamental enough, "first" enough. He didn't need to question "why aluminum atoms have this structure"; that wouldn't help solve his problem.

So, you can understand it this way:

First principles thinking is not a philosophical tool for pursuing "ultimate universal truths," but rather a way of thinking. This approach requires us, when facing a complex problem, not to be constrained by existing "common sense," "experience," or "assumptions" given by others.

What you need to do is, like peeling an onion, dig down layer by layer until you reach what you consider to be the most fundamental, defensible, and almost indivisible core element or rule within the current problem domain. Then, starting from this "foundation," rethink and rebuild, to see if you can arrive at different, or even better, conclusions.

Therefore, even if all knowledge ultimately rests on certain ultimate assumptions, first principles thinking can still exist and be extremely useful. Because it's not concerned with that "absolute foundation" we might never reach, but rather ensuring that when we build our own house, we start solidly from the deepest "bedrock" we can reach, instead of continuing to build directly on the second floor of someone else's already constructed, or even shoddy, building.