Material conditional

<p>The material conditional (also known as material implication) is a <a href="/facts/Binary_operation/CYtow0bz">binary operation</a> commonly used in <a href="/facts/Mathematical_logic/SaI7Y3wN">logic</a>. When the conditional symbol 
  
    
      
        →
      
    
    {\displaystyle \rightarrow }
  
 is <a href="/facts/Interpretation_(logic)/goPmjjQG">interpreted</a> as material implication, a formula 
  
    
      
        P
        →
        Q
      
    
    {\displaystyle P\rightarrow Q}
  
 is true unless 
  
    
      
        P
      
    
    {\displaystyle P}
  
 is true and 
  
    
      
        Q
      
    
    {\displaystyle Q}
  
 is false.
</p><p>Material implication is used in all the basic systems of <a href="/facts/Classical_logic/ls62MAms">classical logic</a> as well as some <a href="/facts/Nonclassical_logic/caR36T5n">nonclassical logics</a>. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many <a href="/facts/Programming_language/cWTYbgWa">programming languages</a>. However, many logics replace material implication with other operators such as the <a href="/facts/Strict_conditional/HEgeQBHq">strict conditional</a> and the <a href="/facts/Variably_strict_conditional/GdfYSv1k">variably strict conditional</a>. Due to the <a href="/facts/Paradoxes_of_material_implication/kIBSEESa">paradoxes of material implication</a> and related problems, material implication is not generally considered a viable analysis of <a href="/facts/Conditional_sentence/qJvIK5y4">conditional sentences</a> in <a href="/facts/Natural_language/B4gLS7Kd">natural language</a>.
</p>

Material conditional open-in-new

Material conditional