KnowraMaterial conditionalLinked fromLinked fromThe 21 pages that link to Material conditional, each with the reason it gives.All 21Broader topic 4Related 12Compared with 5Natural deductionRelated: Conditional introduction models proof from a temporary antecedent assumption.Logical consequenceCompared with: A true material conditional does not by itself establish a consequence relation.Paraconsistent logicCompared with: Its classical behavior combines with contradiction to validate explosion.Modus ponensRelated: This interpretation of “if P then Q” makes the rule’s truth-preserving character explicit.Logical connectiveBroader topic: Its truth table defines the standard truth-functional conditional.Truth valueBroader topic: Its truth table illustrates how a connective assigns values to compound statements.Logical implicationBroader topic: It gives the truth-functional reading of implication stated in the definition.Modus tollensRelated: Its truth conditions make the inference from a false consequent to a false antecedent valid.DisjunctionRelated: Classically, an implication can be expressed as a disjunction with a negated antecedent.Relevant logicCompared with: Its truth conditions allow conditionals that relevant implication rejects.Exclusive orCompared with: Implication is asymmetric and has a different truth condition from exclusive or.Conditional proofRelated: It is one common interpretation of the conditional established by the proof method.Logical validityCompared with: Its truth condition resembles validity but applies to a conditional, not an argument.Disjunctive syllogismRelated: The inference can be derived from the equivalence between P or Q and not P implies Q.Affirming the consequentRelated: Its truth conditions reveal why P → Q and Q can both hold while P is false.Peirce's lawRelated: The law's nested implications are interpreted classically using this connective.Biconditional introductionRelated: In classical logic, each direction used by the rule can be represented with this connective.Constructive dilemmaRelated: Under this standard interpretation, the conditional premises make the rule truth-preserving.Sheffer strokeRelated: NAND can define implication, showing its reach beyond negation and conjunction.Consequentia mirabilisBroader topic: The principle is commonly expressed as the implication from not-P to P entailing P.If and only ifRelated: The biconditional combines implications in both directions.
KnowraMaterial conditionalLinked fromLinked fromThe 21 pages that link to Material conditional, each with the reason it gives.All 21Broader topic 4Related 12Compared with 5Natural deductionRelated: Conditional introduction models proof from a temporary antecedent assumption.Logical consequenceCompared with: A true material conditional does not by itself establish a consequence relation.Paraconsistent logicCompared with: Its classical behavior combines with contradiction to validate explosion.Modus ponensRelated: This interpretation of “if P then Q” makes the rule’s truth-preserving character explicit.Logical connectiveBroader topic: Its truth table defines the standard truth-functional conditional.Truth valueBroader topic: Its truth table illustrates how a connective assigns values to compound statements.Logical implicationBroader topic: It gives the truth-functional reading of implication stated in the definition.Modus tollensRelated: Its truth conditions make the inference from a false consequent to a false antecedent valid.DisjunctionRelated: Classically, an implication can be expressed as a disjunction with a negated antecedent.Relevant logicCompared with: Its truth conditions allow conditionals that relevant implication rejects.Exclusive orCompared with: Implication is asymmetric and has a different truth condition from exclusive or.Conditional proofRelated: It is one common interpretation of the conditional established by the proof method.Logical validityCompared with: Its truth condition resembles validity but applies to a conditional, not an argument.Disjunctive syllogismRelated: The inference can be derived from the equivalence between P or Q and not P implies Q.Affirming the consequentRelated: Its truth conditions reveal why P → Q and Q can both hold while P is false.Peirce's lawRelated: The law's nested implications are interpreted classically using this connective.Biconditional introductionRelated: In classical logic, each direction used by the rule can be represented with this connective.Constructive dilemmaRelated: Under this standard interpretation, the conditional premises make the rule truth-preserving.Sheffer strokeRelated: NAND can define implication, showing its reach beyond negation and conjunction.Consequentia mirabilisBroader topic: The principle is commonly expressed as the implication from not-P to P entailing P.If and only ifRelated: The biconditional combines implications in both directions.