- First Principles is also the title of a work by Herbert Spencer.
In
philosophy, a
first principle is 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 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.
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 or simulation of
stereoelectronics using
Schrödinger's equation directly is an
ab initio approach, since the equation is just a
definition of energy on the
quantum level.
See also
External links
Herbert Spencer (27 April 1820 – 8 December 1903) was an English philosopher; prominent classical liberal political theorist; and sociological theorist.
Spencer developed an all-embracing conception of evolution as the progressive development of the physical world,
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Philosophy is the discipline concerned with questions of how one should live (ethics); what sorts of things exist and what are their essential natures (metaphysics); what counts as genuine knowledge (epistemology); and what are the correct principles of reasoning (logic).
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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axiom is a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation.
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The term postulate, or axiom, indicates a starting assumption from which other statements are logically derived. It does not have to be self-evident (constancy of the speed of light in a vacuum is not self-evident, however it was used as a postulate in the special theory of
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proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the of communication.
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A syllogism (Greek: συλλογισμός — "conclusion," "inference"), (usually the categorical syllogism
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Euclid
Born fl. 300 BC
Residence Alexandria, Egypt
Nationality Greek
Field Mathematics
Known for Euclid's Elements Euclid (Greek:
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Euclid's Elements (Greek: Στοιχεῖα) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC.
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Aristotle (Greek: Ἀριστοτέλης Aristotélēs) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great.
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Metaphysics is the branch of philosophy that investigates principles of reality transcending those of any particular science, traditionally including cosmology and ontology. It is also concerned with explaining the ultimate nature of being and the world.
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a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively. Attempts to define clearly or explain a priori and a posteriori
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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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The Latin term
ab initio means
from the beginning and is used in several contexts:
- when describing literature: told from the beginning as opposed to in medias res (meaning starting in the middle of the story)
..... Click the link for more information. model is used in various contexts to mean a physical representation of some thing. That thing may be a single item or object (for example, a bolt) or a large system (for example, the Solar System).
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Fitting can refer to:
- Any machine, 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.
- The process of applying regression analysis to data.
..... Click the link for more information. Stereoelectronics is the study of the electron distribution within a molecule. Electron distribution affects the stereochemistry of the reactions of different diastereomers.
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Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1926, describes the space- and time-dependence of quantum mechanical systems. It is of central importance in non-relativistic quantum mechanics, playing a role for microscopic particles analogous to
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Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry.[1]
The simplest type of ab initio electronic structure calculation is the Hartree-Fock (HF) scheme, in which the Coulombic electron-electron repulsion is
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A definition is a statement of the meaning of a term, word or phrase. The term to be defined is known as the definiendum (Latin: that which is to be defined).
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“Quanta” redirects here. For other uses, see Quantum (disambiguation).
Development of quantum theory
Quantum theory, the branch of physics which is based on quantization, began in 1900 when Max Planck published his theory explaining the
..... Click the link for more information. axiom is a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation.
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The Latin term
ab initio means
from the beginning and is used in several contexts:
- when describing literature: told from the beginning as opposed to in medias res (meaning starting in the middle of the story)
..... Click the link for more information. Metaphysics is the branch of philosophy that investigates principles of reality transcending those of any particular science, traditionally including cosmology and ontology. It is also concerned with explaining the ultimate nature of being and the world.
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