First principles

A first principle is a basic, foundational, self-evident proposition or assumption that cannot be deduced from any other proposition or assumption.

In philosophy, first principles are taught by Aristotelians and a nuanced version of first principles are referred to as postulates by Kantians.

In mathematics, first principles are referred to as axioms and postulates.

In physics and other sciences, theoretical work is said to be from first principles, or ab initio, if it starts directly at the level of established science and does not make assumptions such as empirical model and parameter fitting.

In a formal logical system, that is, a set of propositions that are consistent with one another, it is probable that some of the statements can be deduced from one another. For example, in the syllogism, "All men are mortal; Socrates is a man; Socrates is mortal" the last claim can be deduced from the first two.

A first principle is one that cannot be deduced from any other. The classic example is that of Euclid's (see Euclid's Elements) geometry; its hundreds of propositions can be deduced from a set of definitions, postulates, and common notions: all three types constitute first principles.

In philosophy "first principles" are also commonly referred to as a priori terms and arguments, which are contrasted to a posteriori terms, reasoning or arguments, in that the former are simply assumed and exist prior to the reasoning process and the latter are "posterior" meaning deduced or inferred in the reasoning process. First Principles are generally treated in the realm of philosophy known as epistemology, but are an important factor in any metaphysical speculation.

In philosophy "First principles" is often somewhat interchangeable and synonymous with a priori, datum and axiom or axiomatic reasoning/method.

Terence Irwin writes:

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