First principles

First principles

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In philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, a first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption. In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, first principles are referred to as axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...

s or postulates. Gödel's incompleteness theorems
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of...

 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
Truth
Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...

 about the natural numbers.

First principles in formal logic


In a formal logical system, that is, a set of proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

s 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
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

, "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
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

's (see Euclid's Elements
Euclid's Elements
Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...

) 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


Terence Irwin
Terence Irwin
Terence Irwin is a scholar and philosopher specializing in ancient Greek philosophy and the history of ethics Terence Irwin (born 21 April 1947, in Enniskillen, Northern Ireland) is a scholar and philosopher specializing in ancient Greek philosophy and the history of ethics Terence Irwin (born 21...

 writes:

Descartes


Profoundly influenced by Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

, 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
Cartesian doubt
Cartesian doubt is a form of methodological skepticism associated with the writings and methodology of René Descartes. Cartesian doubt is also known as Cartesian skepticism, methodic doubt, methodological skepticism, or hyperbolic doubt.Cartesian doubt is a systematic process of being skeptical...

, 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
Cogito ergo sum
is a philosophical Latin statement proposed by . The simple meaning of the phrase is that someone wondering whether or not they exist is, in and of itself, proof that something, an "I", exists to do the thinking — However this "I" is not the more or less permanent person we call "I"...

.

In physics


In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, a calculation is said to be from first principles, or ab initio
Ab initio
ab initio is a Latin term used in English, meaning from the beginning.ab initio may also refer to:* Ab Initio , a leading ETL Tool Software Company in the field of Data Warehousing.* ab initio quantum chemistry methods...

, if it starts directly at the level of established laws of physics and does not make assumptions such as empirical model
Model (physical)
A physical model is a smaller or larger physical copy of an object...

 and fitting
Fitting
Fitting can refer to:* A dress fitting.* Any machine, component, piping or tubing part that can attach or connect two or more larger parts. For examples, see coupling, compression fitting or piping and plumbing fittings....

 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
Ab initio quantum chemistry methods
Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ab initiowas first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene.The background is described by Parr...

.

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