categorical logic
Black-and-white deduction
Categorical logic is the branch of formal logic dealing with categorical propositions—statements that assert relationships between classes of things.
These propositions take forms like "All A are B," "No A are B," "Some A are B," and "Some A are not B." The classical syllogism belongs here: All men are mortal; Socrates is a man; therefore Socrates is mortal.
This system, originating with Aristotle, dominated Western logic for two millennia before modern symbolic logic largely supplanted it.
Statement expressing a judgment
- predicateSentence's non-subject portion
- subjectMatter under discussion
- quantifierWord expressing amount
- termFixed period or word
extension · class · membership · inclusion · exclusion · affirmation · negation
Formal deductive argument structure
- premiseFoundation for logical argument
- conclusionEnd or deduction
- middle termLink between syllogism's premises
- universalAffecting all equally
particular · affirmative · negative · square of opposition · contradiction · contrariety · Barbara · validity
Conclusion reached through reasoning
- deductionConclusion from premises
- entailmentLogical necessity from premises
- validityQuality of being sound
- soundnessReliability of structure
proof · antecedent · consequent · implication · hypothetical · disjunctive · conditional · logical consequence
Systematic method of inquiry
- AristotleGreek founder of formal logic
- demonstrationPublic display of opinion
- dialecticLogical argument through opposition
proposition
Statement expressing a judgment
- predicateSentence's non-subject portion
- subjectMatter under discussion
- quantifierWord expressing amount
term · extension · class · membership · inclusion · exclusion · affirmation · negation
syllogism
Formal deductive argument structure
- premiseFoundation for logical argument
- conclusionEnd or deduction
- middle termLink between syllogism's premises
universal · particular · affirmative · negative · square of opposition · contradiction · contrariety · Barbara · validity · figure
inference
Conclusion reached through reasoning
- deductionConclusion from premises
- entailmentLogical necessity from premises
- validityQuality of being sound
soundness · proof · antecedent · consequent · implication · hypothetical · disjunctive · conditional · logical consequence · derivation
Organon
Systematic method of inquiry
- AristotleGreek founder of formal logic
- demonstrationPublic display of opinion
- dialecticLogical argument through opposition
- logicpremise, premises, conclusion, conclusions, inference
- AristotelianismAristotle, Aristotelianism, Lyceum, syllogism, Organon
- logic rulessyllogism, inference, contraposition, double negation, conjunction
- Constructive Logicintuitionism, Heyting algebra, constructivism, double negation, natural deduction
logic, category, categorize, categorical, categorization, categories, categorized, categorically, categorizing