different between principle vs axiom

English

Etymology

Borrowed from Old French principe, from Latin pr?ncipium (“beginning, foundation”), from pr?nceps (“first”); see prince.

Pronunciation

• IPA^(key): /?p??ns?p?l/, /?p??ns?p?l/
• Hyphenation: prin?ci?ple
• Homophone: principal

Noun

principle (plural principles)

1. A fundamental assumption or guiding belief.

   • Let us consider ‘my dog is asleep on the floor’ again. Frege thinks that this sentence can be analyzed in various different ways. Instead of treating it as expressing the application of __ is asleep on the floor to my dog, we can think of it as expressing the application of the concept
          my dog is asleep on __
     to the object
          the floor
     (see Frege 1919). Frege recognizes what is now a commonplace in the logical analysis of natural language. We can attribute more than one logical form to a single sentence. Let us call this the principle of multiple analyses. Frege does not claim that the principle always holds, but as we shall see, modern type theory does claim this.

2. A rule used to choose among solutions to a problem.

3. (sometimes pluralized) Moral rule or aspect.

   I don't doubt your principles.

   You are clearly a person of principle.

   It's the principle of the thing; I won't do business with someone I can't trust.

4. (physics) A rule or law of nature, or the basic idea on how the laws of nature are applied.

   Bernoulli's Principle

   The Pauli Exclusion Principle prevents two fermions from occupying the same state.

   The principle of the internal combustion engine

5. A fundamental essence, particularly one producing a given quality.
   • 1845, William Gregory, Outlines of Chemistry

     Cathartine is the bitter, purgative principle of senna.

6. (obsolete) A beginning.
7. A source, or origin; that from which anything proceeds; fundamental substance or energy; primordial substance; ultimate element, or cause.
   • 1663, John Tillotson, The Wisdom of Being Religious

     The soul of man is an active principle.

8. An original faculty or endowment.
   • 1828, Dugal Stewart, The Philosophy of the Active and Moral Powers of Man

     those active principles whose direct and ultimate object is the communication either of enjoyment or suffering

Usage notes

• Principle ("moral rule"), as a noun, is often confused with principal, which can be an adjective ("most important") or a noun ("school principal"). A memory aid to avoid this confusion is: "The principal alphabetic principle places A before E".

Synonyms

• (moral rule or aspect): tenet

Derived terms

Related terms

• prince
• principal
• principality

Translations

Verb

principle (third-person singular simple present principles, present participle principling, simple past and past participle principled)

1. (transitive) To equip with principles; to establish, or fix, in certain principles; to impress with any tenet or rule of conduct.

   • Let an enthusiast be principled that he or his teacher is inspired.

Further reading

• principle in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• principle in The Century Dictionary, New York, N.Y.: The Century Co., 1911.

English

Etymology

From Middle French axiome in the 15th century, from Latin axi?ma (“axiom; principle”), from Ancient Greek ?????? (axí?ma, “that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ????? (axió?, “to think fit or worthy, to require, to demand”), from ????? (áxios, “fit, worthy”, literally “weighing as much as; of like value”), from ??? (ág?, “I drive”).

Pronunciation

• (Received Pronunciation) IPA^(key): /?aks.?.?m/
• (General American) enPR: ?k's??m, IPA^(key): /?æks.i.?m/
• Hyphenation: ax?i?om

Noun

axiom (plural axioms or axiomata) (the latter is becoming less common and is sometimes considered archaic)

1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
2. (logic, mathematics, proof theory) A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
3. An established principle in some artistic practice or science that is universally received.

Synonyms

• (philosophy, mathematics): axioma (now rare)
• (logic, mathematics): postulate

Hypernyms

• (logic): well-formed formula, wff, WFF

Hyponyms

• (mathematics): axiom of choice, axiom of infinity, axiom of pairing, axiom of power set, axiom of regularity, axiom of union, completeness axiom, parallel axiom

Holonyms

• (logic): formal system

Derived terms

• axiomatic
• axiomatical
• axiomatically
• axiomatise, axiomatize
• axiomatisation, axiomatization

Translations

See also

References

• axiom in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• axiom in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.

Further reading

• axiom on Wikipedia.Wikipedia

Anagrams

• amoxi

Czech

Noun

axiom m

1. axiom

Derived terms

• axiom výb?ru m

Related terms

• axiomatický
• axiomatizovat
• axiomatizace

Swedish

Noun

axiom n

1. axiom

Declension

Related terms

• axiomatisk