In math or philosophy, it is the initial statements or propositions upon which the rest of the system is based. They’re not deduced from anything else, but are the assumptions you’re starting from.
Its also used more colloquially, usually in the context of problem solving or learning something new, like “let’s take it back to first principles”. In that case it basically means taking it back to basics. Let’s say you’re a business trying to figure out what your next product should be. You could base that off recent market trends, what your last few products have been, or what’s easiest to make based on the equipment you already have. If you take it back to first principles, you start asking fundamental questions about the product. What specific problem does your product solve? What exact market are you trying to target? What’s the best way to solve that problem, irrespective of how its been solved in the past? Often that can provide more innovative solutions because you’re sweeping away all the assumptions and historical inertia and trying to come at the problem totally fresh.
In terms of learning, same sort of thing. Say you want to learn more about car maintenance. You could read your car’s repair manual and have a pretty good idea to go about changing the oil, replacing spark plugs, swapping belts and so on. Or you could go to the first principles of how an internal combustion engine works, how all the systems of the car work together, and then when you get some weird, out-there problem or funny noise you can use that knowledge to diagnose it rather than having to throw your hands up because its not in the manual.
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