postulates
Takes as given
Postulates are foundational assumptions accepted as true without proof, serving as starting points for reasoning or argument.
In geometry, Euclid's postulates underpin the entire system.
In science, postulates are baseline propositions from which theories develop.
The verb postulate means to assume or claim something as a basis for reasoning: The theory postulates that language shapes thought.
Property with buildings
- presuppositionsImplicit prior beliefs
- suppositionsUnverified beliefs or guesses
- presumptionsBeliefs accepted without evidence
- givensAccepted starting truths
axioms · starting points · preconditions · stipulations · ground rules · first principles · antecedents · preliminaries
Accepted starting principles
- corollariesPropositions following from others
- lemmasProven statements aiding proofs
- proofsDemonstrations of truth
- EuclidFather of geometry
geometry · Pythagorean · non-Euclidean · deduction · self-evident truths
Unverified assumptions or theories
- theoriesExplanations based on evidence
- propositionsStatements asserted for consideration
- speculationsUnverified theories or guesses
Basic truths underlying reasoning
- KantGerman Enlightenment thinker
- synthetic a prioriNecessary truths that expand knowledge
- rationalismReason as knowledge source
- DescartesCogito ergo sum's author
premises
Property with buildings
- presuppositionsImplicit prior beliefs
- suppositionsUnverified beliefs or guesses
- presumptionsBeliefs accepted without evidence
givens · axioms · starting points · preconditions · stipulations · ground rules · first principles · antecedents · preliminaries
axioms
Accepted starting principles
- corollariesPropositions following from others
- lemmasProven statements aiding proofs
- proofsDemonstrations of truth
Euclid · geometry · Pythagorean · non-Euclidean · deduction · self-evident truths
conjectures
Unverified assumptions or theories
- theoriesExplanations based on evidence
- propositionsStatements asserted for consideration
- speculationsUnverified theories or guesses
first principles
Basic truths underlying reasoning
- KantGerman Enlightenment thinker
- synthetic a prioriNecessary truths that expand knowledge
- rationalismReason as knowledge source
- ancient mathalgebra, arithmetic, geometry, fractions, addition
- Greek mathematicsEuclid, Archimedes, Pythagoras, geometry, theorem
- formal systemsformal logic, axioms, derivation, proofs, theorems
- Swiss politicsdirect democracy, cantons, referendums, initiatives, popular vote
- geometryangles, circles, angle, shapes, lines
- math conceptsangle, numbers, algebra, circle, equations
postulatesconclusions
Judgments reached through reasoning
deductions · proofs · theorems · results · findings
postulatesmeasures
Quantifies or evaluates
observations · empirical data · measurements · experiments · evidence
postulatesquestions
Requests for information
hypotheses · conjectures · doubts · challenges · refutations
- Koch's postulatesCriteria linking pathogen to disease
postulate, postulation, postulated, postulating, postulations