axiomatic
Assumed without proof
Axiomatic describes something taken as self-evidently true, requiring no proof: It's axiomatic that politicians want to get reelected.
In logic and mathematics, axioms are foundational propositions from which other truths are derived.
More loosely, axiomatic means obvious or beyond question: The need for clean water is axiomatic.
Easily perceived, unmistakable
- self-evidentRequiring no demonstration
- incontrovertibleImpossible to deny
- irrefutableImpossible to disprove
- undeniableImpossible to contradict
indisputable · unquestionable · manifest · apparent · evident · patent · clear · indubitable
Forming the base
- bedrockSolid stone underground
- cornerstoneFoundational building block
- foundationUnderlying support structure
- basisUnderlying support or principle
underpinning · groundwork · core · basic · essential · primary · elementary · premise
Demonstrated logical conclusion
- proofDemonstration of truth
- postulateAssumed starting point
- corollaryLogical natural consequence
- lemmaBase form, or helper theorem
Euclid · geometry · non-Euclidean · consistency · completeness · arithmetic
Deriving specifics from generals
- syllogisticUsing formal deductive reasoning
- propositionalOf logical statements
- validityQuality of being sound
- tautologyRedundant or circular statement
inference · antecedent · consequent · reasoning · argument · categorical · truth-value · entailment
obvious
Easily perceived, unmistakable
- self-evidentRequiring no demonstration
- incontrovertibleImpossible to deny
- irrefutableImpossible to disprove
undeniable · indisputable · unquestionable · manifest · apparent · evident · patent · clear · indubitable · unassailable
fundamental
Forming the base
- bedrockSolid stone underground
- cornerstoneFoundational building block
- foundationUnderlying support structure
basis · underpinning · groundwork · core · basic · essential · primary · elementary · premise · given
theorem
Demonstrated logical conclusion
lemma · Euclid · geometry · non-Euclidean · consistency · completeness · arithmetic
deductive
Deriving specifics from generals
- syllogisticUsing formal deductive reasoning
- propositionalOf logical statements
- validityQuality of being sound
tautology · inference · antecedent · consequent · reasoning · argument · categorical · truth-value · entailment · derivation
axiomaticquestionable
Of uncertain validity
debatable · disputable · dubious · doubtful · contestable
axiomaticunobvious
Not readily apparent
derived · inferential · demonstrable · provable · empirical