axiom
Assumed starting point
An axiom is a statement accepted as true without proof, serving as a starting point for reasoning.
In mathematics and logic, axioms are foundational assumptions from which other truths are derived: Euclid's axioms form the basis of plane geometry.
More loosely, an axiom is any self-evident truth or established principle: It's an axiom of politics that all campaigns need money.
Held principle or doctrine
- principleFundamental truth or standard
- preceptRule governing behavior
- canonAccepted authoritative works
- dictumAuthoritative formal statement
maxim · dogma · creed · belief · doctrine · conviction · article of faith · rule
Brief moral principle
- adageTraditional pithy truth
- truismStatement needing no proof
- sayingShort, wise expression
- proverbTraditional saying expressing truth
aphorism · epigram · motto · dictum · platitude · bromide · commonplace · received wisdom
Statement expressing a judgment
- theoremDemonstrated logical conclusion
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
- syllogismFormal deductive argument structure
deduction · logic · epistemology · metaphysics · ontology · rationalism · empiricism · a priori
Assumed starting point
- premiseFoundation for logical argument
- assumptionUnverified belief accepted as true
- givenAccepted as fact
- starting pointPlace of commencement
basis · cornerstone · bedrock · foundation · groundwork · underpinning · first principle · fundamental
Requiring no demonstration
- incontrovertibleImpossible to deny
- irrefutableImpossible to disprove
- undeniableImpossible to contradict
- unquestionableCannot be challenged
indisputable · absolute · universal · immutable · given · accepted · established · unassailable
tenet
Held principle or doctrine
- principleFundamental truth or standard
- preceptRule governing behavior
- canonAccepted authoritative works
dictum · maxim · dogma · creed · belief · doctrine · conviction · article of faith · rule · law
maxim
Brief moral principle
proverb · aphorism · epigram · motto · dictum · platitude · bromide · commonplace · received wisdom · conventional wisdom
proposition
Statement expressing a judgment
- theoremDemonstrated logical conclusion
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
syllogism · deduction · logic · epistemology · metaphysics · ontology · rationalism · empiricism · a priori · self-evident
postulate
Assumed starting point
- premiseFoundation for logical argument
- assumptionUnverified belief accepted as true
- givenAccepted as fact
starting point · basis · cornerstone · bedrock · foundation · groundwork · underpinning · first principle · fundamental · elementary
self-evident
Requiring no demonstration
- incontrovertibleImpossible to deny
- irrefutableImpossible to disprove
- undeniableImpossible to contradict
unquestionable · indisputable · absolute · universal · immutable · given · accepted · established · unassailable · necessary
- philosophy termstruth, reason, knowledge, wisdom, logic
- abstract algebraalgebra, group, isomorphism, Boolean algebra, commutator
- mathematicsalgebra, arithmetic, calculus, geometry, number
- math conceptsangle, numbers, algebra, circle, equations
- math termsnumbers, plus or minus, linear growth, square, operand
- proverbsproverbs, sayings, maxims, adages, aphorisms
axiomtheorem
Demonstrated logical conclusion
corollary · conjecture · lemma · hypothesis · inference
axiomcontradiction
Opposing claims, incompatible together
absurdity · nonsense · paradox · fallacy · self-contradiction
axiomcontroversy
Prolonged public disagreement
disputed claim · matter of opinion · ambiguity · speculation · heresy
- axis of evilNamed hostile state grouping
- rotational axisCenter of revolution
- horizontal axisFlat orientation line
- Axis forcesWWII's fascist military coalition
- off axis
- axis of symmetryLine dividing congruent halves