axioms
Proofs start here
Axioms are statements or principles accepted as true without requiring proof, serving as starting points for reasoning or argument.
In mathematics and logic, axioms form the foundation from which theorems are derived: Euclid's axioms underpin classical geometry.
More broadly, an axiom is any self-evident truth or established principle that people take for granted: It's an axiom of politics that all campaigns promise more than they deliver.
Assumed starting point
- theoremDemonstrated logical conclusion
- proofDemonstration of truth
- lemmaBase form, or helper theorem
- corollaryLogical natural consequence
Euclid · geometry · algebra · logic · deduction · inference · conjecture · rigor
Held principle or doctrine
- doctrineEstablished body of teachings
- preceptRule governing behavior
- maximBrief moral principle
- principleFundamental truth or standard
truth · certainty · a priori · self-evident · Aristotle · Descartes · Spinoza · Kant
Easily perceived, unmistakable
- undeniableImpossible to contradict
- intuitiveKnown without reasoning
- incontrovertibleImpossible to deny
- indubitableImpossible to doubt
manifest · apparent · unquestionable · taken for granted · assumed · presupposed · unproven · irreducible
Solid stone underground
- cornerstoneFoundational building block
- basisUnderlying support or principle
- underpinningFoundational support beneath
- fundamentalForming the base
groundwork · framework · premise · foundation · starting point · first principle · given · assumption
Formal deductive argument structure
- validityQuality of being sound
- soundnessReliability of structure
- tautologyRedundant or circular statement
- contradictionOpposing claims, incompatible together
consistency · completeness · independence · decidability · propositional · truth table · syntax · semantics
Enforceable societal rules
- hypothesisTestable proposed explanation
- theoryExplanatory set of principles
- modelRepresentation or paradigm
- NewtonFamous scientific surname
thermodynamics · conservation · symmetry · invariance · empirical · falsifiable · paradigm · framework
postulate
Assumed starting point
corollary · Euclid · geometry · algebra · logic · deduction · inference · conjecture · rigor · formalism
tenet
Held principle or doctrine
principle · truth · certainty · a priori · self-evident · Aristotle · Descartes · Spinoza · Kant · epistemology
obvious
Easily perceived, unmistakable
- undeniableImpossible to contradict
- intuitiveKnown without reasoning
- incontrovertibleImpossible to deny
indubitable · manifest · apparent · unquestionable · taken for granted · assumed · presupposed · unproven · irreducible · basic
bedrock
Solid stone underground
- cornerstoneFoundational building block
- basisUnderlying support or principle
- underpinningFoundational support beneath
fundamental · groundwork · framework · premise · foundation · starting point · first principle · given · assumption · presupposition
syllogism
Formal deductive argument structure
- validityQuality of being sound
- soundnessReliability of structure
- tautologyRedundant or circular statement
contradiction · consistency · completeness · independence · decidability · propositional · truth table · syntax · semantics
laws
Enforceable societal rules
- hypothesisTestable proposed explanation
- theoryExplanatory set of principles
- modelRepresentation or paradigm
Newton · thermodynamics · conservation · symmetry · invariance · empirical · falsifiable · paradigm · framework · principles
- mathaddition, subtraction, multiplication, division, algebra
- mathematicsalgebra, arithmetic, calculus, geometry, number
- math conceptsangle, numbers, algebra, circle, equations
- proverbsproverbs, sayings, maxims, adages, aphorisms
- beliefsbelief, beliefs, creed, creeds, faith
- expressionsexpression, I love you, phrase, idioms, thank you
axiomstheorems
Proven mathematical statements
corollaries · proofs · derivations · conclusions · deductions
axiomsparadoxes
Seemingly self-refuting statements
contradictions · antinomies · absurdities · inconsistencies · fallacies
axiomsconjectures
Unverified assumptions or theories
hypotheses · speculations · suppositions · opinions · theories