Implication: Strict or Material?
It is obvious that the notion of implication formalised in classical logic does not comfortably translate into natural language by means of "if… then…", due to a number of problems called the paradoxes of material implication.
The first class of paradoxes involves counterfactuals, such as If the moon is made of green cheese, then 2+2=5, which are puzzling because natural language does not support the principle of explosion. Eliminating this class of paradoxes was the reason for C. I. Lewis's formulation of strict implication, which eventually led to more radically revisionist logics such as relevance logic.
The second class of paradoxes involves redundant premises, falsely suggesting that we know the succedent because of the antecedent: thus "if that man gets elected, granny will die" is materially true since granny is mortal, regardless of the man's election prospects. Such sentences violate the Gricean maxim of relevance, and can be modelled by logics that reject the principle of monotonicity of entailment, such as relevance logic.
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“History creates comprehensibility primarily by arranging facts meaningfully and only in a very limited sense by establishing strict causal connections.”
—Johan Huizinga (18721945)