First principles, as I mean it here, is a way of slowing down at the start. What is the job? What is actually constrained — time, money, regulation, physics, a person's attention? Which parts of the usual product are there because they solve that job, and which are there because the last product in the category had them?
I associate the public version of this habit with engineers who talk about reasoning from constraints, and with product work that refuses features which do not change the experience. Elon Musk and Steve Jobs are two of the people I study for that. I am not borrowing a quotation, and I am not saying their companies are a template for mine.
Zero to One, by Peter Thiel with Blake Masters, pushes a related question: are you making something new, or competing as a variation? I think the question is worth sitting with. I do not think the book is a machine that produces a successful company. A clever distinction can still be aimed at a problem nobody has.
In practice I try to write three sentences before I design a screen. Who is stuck? What do they do today? What would have to be true for a new tool to be worth the switch? Restro20 started from everyday restaurant operations, not from a desire to have a POS in a portfolio. Focus20 Labs starts from a business workflow, not from a model I want to demo. Those are intentions. They are not case studies with outcomes attached.
The failure mode I watch for is using "first principles" as a performance. If the decomposition does not change a decision, it was a preface. The point is the constraint I am willing to design around, and the assumption I am willing to drop.