logical proof
Rigorous deductive argument
A logical proof is a sequence of statements that establishes a conclusion through valid reasoning from accepted premises.
In formal logic and mathematics, each step follows necessarily from previous steps or axioms: The theorem requires a logical proof, not just intuition.
Distinguished from empirical evidence, a logical proof demonstrates truth through structure rather than observation.
- syllogismFormal deductive argument structure
- deductionConclusion from premises
- lemmaBase form, or helper theorem
- QEDProof-concluding abbreviation
- inferenceConclusion reached through reasoning
premise · soundness · theorem · truth table · corollary · if and only if · axiom · first principles · tautology · certitude · rebuttal · validity · conclusion · hypothesis · postulate · rigorous · step-by-step · demonstration
- logicpremise, premises, conclusion, conclusions, inference
- logic termsif, then, valid, premises, and
- Proof Theorytheorem, axiom, lemma, corollary, natural deduction
- research methodsexperiment, hypothesis, deduction, experiments, induction
- theorytheory, hypothesis, theorem, axiom, postulate
- pure reasonpure reason, a priori, synthetic a priori, self-evident truth, first principles
logical proofintuition
Instinctive immediate understanding
guesswork · gut feeling · hunch · instinct · faith
logical proofhearsay
Unverified secondhand information
rumor · opinion · assumption · presumption · conjecture
logical prooffallacy
Error in reasoning
logical fallacy · faulty reasoning · non sequitur · circular reasoning · sophistry