formal logic
Deductive rule system
Formal logic is the study of valid reasoning through symbolic systems and precise rules, abstracting from the content of arguments to focus on their structure.
Where informal logic examines everyday reasoning, formal logic uses notation like variables and operators to represent relationships: Formal logic can prove that "All A are B" and "All B are C" yields "All A are C".
The field underlies mathematics, computer science, and philosophy.
Conclusion from premises
- inferenceConclusion reached through reasoning
- propositionStatement expressing a judgment
- validityQuality of being sound
- soundnessReliability of structure
completeness · axiom · theorem · proof · argumentation · contradiction · tautology · fallacy
Formal deductive argument structure
- negationDenial or cancellation
- conjunctionWord joining clauses together
- disjunctionState of being apart
- implicationIndirect suggestion or consequence
biconditional · antecedent · consequent · contrapositive · reductio ad absurdum · truth table · De Morgan's laws
Sentence's non-subject portion
- quantifierWord expressing amount
- variableProne to fluctuation
- constantFixed, unvarying quantity
- propositionalOf logical statements
first-order · second-order · modal · notation · symbolization · bound variable
deduction
Conclusion from premises
- inferenceConclusion reached through reasoning
- propositionStatement expressing a judgment
- validityQuality of being sound
soundness · completeness · axiom · theorem · proof · argumentation · contradiction · tautology · fallacy · consistency
syllogism
Formal deductive argument structure
- negationDenial or cancellation
- conjunctionWord joining clauses together
- disjunctionState of being apart
implication · biconditional · antecedent · consequent · contrapositive · reductio ad absurdum · truth table · De Morgan's laws
predicate
Sentence's non-subject portion
- quantifierWord expressing amount
- variableProne to fluctuation
- constantFixed, unvarying quantity
propositional · first-order · second-order · modal · notation · symbolization · bound variable
- exact sciencesmathematics, physics, chemistry, math, algebra
- logicpremise, premises, conclusion, conclusions, inference
- philosophyethics, metaphysics, ontology, epistemology, axiology
- logic termsif, then, valid, premises, and
- philosophy worldethicist, logician, metaphysician, epistemologist, aesthetician
- Analytic PhilosophyBertrand Russell, G.E. Moore, Vienna Circle, linguistic analysis, A.J. Ayer
formal logicintuition
Instinctive immediate understanding
gut feeling · emotional reasoning · magical thinking · superstition · instinct
formal logicsophistry
Deceptive reasoning
illogic · irrationality · hand-waving · circular reasoning · non sequitur
formal, logic, informal, formality, formally, formalize, informality, formalist, formalized