First principle

In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause attitudes and taught by Aristotelians, and nuanced versions of first principles are referred to as postulates by Kantians.

In mathematics and formal logic, first principles are referred to as axioms or 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. "First principles thinking" consists of decomposing things down to the fundamental axioms in the given arena, before reasoning up by asking which ones are relevant to the question at hand, then cross referencing conclusions based on chosen axioms and making sure conclusions do not violate any fundamental laws. Physicists include counterintuitive concepts with reiteration.

In a formal logical system—that is, a set of propositions that are consistent with one another—it is possible that some of the statements can be deduced from other statements. 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 an axiom that cannot be deduced from any other within that system. The classic example is that of Euclid's Elements; its hundreds of geometric propositions can be deduced from a set of definitions, postulates, and primitive notions: all three types constitute first principles.

In philosophy, "first principles" are from first cause attitudes 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 deduced or inferred after the initial 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" are often somewhat synonymous with a priori, datum, and axiomatic reasoning.

In ancient Greek philosophy, a first principle from which other principles are derived is called an arche and later "first principle" or "element". By extension, it may mean "first place", "method of government", "empire, realm", or "authorities". The concept of an arche was adapted from the earliest cosmogonies of Hesiod and Orphism, through the physical theories of Pre-Socratic philosophy and Plato before being formalized as a part of metaphysics by Aristotle. Arche, sometimes also transcribed as arkhé, is an Ancient Greek word with primary senses "beginning", "origin" or "source of action", from the beginning, οr the original argument, "command". The first principle or element corresponds to the "ultimate underlying substance" and "ultimate indemonstrable principle".

The heritage of Greek mythology already embodied the desire to articulate reality as a whole and this universalizing impulse was fundamental for the first projects of speculative theorizing. It appears that the order of "being" was first imaginatively visualized before it was abstractly thought.