If the null hypothesis that 
  
    
      
        
          a
          
            j
          
        
        =
        0
      
    
    {\displaystyle a_{j}=0}
   is rejected, then the alternative hypothesis that 
  
    
      
        
          a
          
            j
          
        
        ≠
        0
      
    
    {\displaystyle a_{j}\neq 0}
   and equivalently that 
  
    
      
        
          x
          
            j
          
        
      
    
    {\displaystyle x_{j}}
   causes y cannot be rejected.
In this case, the "cause" is the explanans for the explanandum, and failure to recognize that different kinds of "cause" are being considered can lead to futile debate. Of Aristotles four explanatory modes, the one nearest to the concerns of the present article is the "efficient" one. David Hume, as part of his opposition to rationalism, argued that pure reason alone cannot prove the reality of efficient causality; instead, he appealed to custom and mental habit, observing that all human knowledge derives solely from experience. The topic of causality remains a staple in contemporary philosophy. Concept
Metaphysics
The nature of cause and effect is a concern of the subject known as metaphysics. Kant thought that time and space were notions prior to human understanding of the progress or evolution of the world, and he also recognized the priority of causality. But he did not have the understanding that came with knowledge of Minkowski geometry and the special theory of relativity, that the notion of causality can be used as a prior foundation from which to construct notions of time and space. Ontology
A general metaphysical question about cause and effect is what kind of entity can be a cause, and what kind of entity can be an effect. One viewpoint on this question is that cause and effect are of one and the same kind of entity, with causality an asymmetric relation between them.