In mathematics, first principles are referred to as axioms or postulates. Gödel's incompleteness theorems have been taken to prove, among other things, that no system of axioms that describe the set of natural numbers can prove its own validity - nor perhaps can it prove every truth about the natural numbers.
In philosophy, a first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption.
Other articles related to "first principle, first principles":
... In physics, a calculation is said to be from first principles, or ab initio, if it starts directly at the level of established laws of physics and does not make assumptions such as ...
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“I ... observed the great beauty of American government to be, that the simple machines of representation, carried through all its parts, gives facility for a being moulded at will to fit with the knowledge of the age; that thus, although it should be imperfect in any or all of its parts, it bears within it a perfect principle the principle of improvement.
—Frances Wright (17951852)