The theory underlying these derivations relies on the distinction between conditional probabilities, as in 
  
    
      
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    {\displaystyle P(cancer|smoking)}
  , and interventional probabilities, as in 
  
    
      
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    {\displaystyle P(cancer|do(smoking))}
  .
Some philosophers of history such as Arthur Danto have claimed that "explanations in history and elsewhere" describe "not simply an event—something that happens—but a change". Like many practicing historians, they treat causes as intersecting actions and sets of actions which bring about "larger changes", in Dantos words: to decide "what are the elements which persist through a change" is "rather simple" when treating an individuals "shift in attitude", but "it is considerably more complex and metaphysically challenging when we are interested in such a change as, say, the break-up of feudalism or the emergence of nationalism".Much of the historical debate about causes has focused on the relationship between communicative and other actions, between singular and repeated ones, and between actions, structures of action or group and institutional contexts and wider sets of conditions. John Gaddis has distinguished between exceptional and general causes (following Marc Bloch) and between "routine" and "distinctive links" in causal relationships: "in accounting for what happened at Hiroshima on August 6, 1945, we attach greater importance to the fact that President Truman ordered the dropping of an atomic bomb than to the decision of the Army Air Force to carry out his orders." He has also pointed to the difference between immediate, intermediate and distant causes.