Definitions

# First principle

First Principles is also the title of a work by Herbert Spencer.
In philosophy, a first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption. In mathematics, first principles are referred to as axioms or postulates.

## First principles in formal logic

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 former 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 of which constitute "first principles."

## Aristotle's contribution

Aristotle, author of the earliest surviving text on logic, formulated a principle (the Aristotelian tautology denoted A=A ) that later achieved the historical distinction of being called the first principle as a proper name. It occurs in those of his writings that have come to be called the Metaphysics. The principle in Greek, and its transliteration, is (Meta ta physica, 1005b):

"τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό"
"to gar auto hama hyparchein te kai me hyparchein adynaton to auto kai kata to auto."

and in English translation:

"For the same (characteristic) simultaneously to belong and not belong to the same (object) in the same (way) is impossible."

This principle is the first expression of consistency in western thought. Any defining and reasoning in any language on any topic assumes it a priori. It cannot be doubted, as all doubting is based on inconsistency, which assumes consistency a priori.

## Descartes

Profoundly influenced by Euclid, Descartes, the "father of modern philosophy", was a rationalist who invented the foundationalist system of philosophy. He used the "method of doubt", now called Cartesian doubt, to systematically doubt everything he could possibly doubt, until he was left with what he saw as purely indubitable truths. Using these self-evident propositions as his "axioms", or "foundations", he went on to deduce his entire body of knowledge from them. (The foundations are also called a priori truths.) His most famous proposition is "I think, therefore I am", or "Cogito ergo sum".

## John Duns Scotus

"A Treatise On God As First Principle" is about the First Cause, or the Prime Mover, that is eternal, and exists, prior to the order of beings, and prior to creation.

## In physics

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 model and fitting parameters.

For example, calculation of electronic structure using Schrödinger's equation within a set of approximations that do not include fitting the model to experimental data is an ab initio approach.