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Some logicians, such as [[Paul Grice]], have used [[conversational implicature]] to argue that, despite apparent difficulties, the material conditional is just fine as a translation for the natural language 'if...then...'. Others still have turned to [[relevance logic]] to supply a connection between the antecedent and consequent of provable conditionals.
== More about problems evoked in the preceding paragraph. Nothing is solved by defining strict implication as material implication acted upon by necessity L ==
If one uses the Polish notation where the square, symbol of necessity, is replaced by the symbol L, if one adopts the initial definition given by this article of wikipedia and consequently describes the strict implication of q by p as material implication p → q acted upon by necessity L , one may represent the said strict implication of q by p thus: L (p → q) or ~M (p & ~q).Conformably to De Morgan's laws, p → q says the same thing as ~(p & ~q). To say that p materially implies q is to say that p is incompatible with not-q. Therefore to say that necessarily p implies q is to say that necessarily p is incompatible with not-q.
L (p → q) is tantamount to L ~(p & ~q). If, of necessity, one excludes the conjunction p & ~q, another way to express the fact is to say that the conjunction p & ~q is im-possible. Hence the equivanent expression ~M (p & ~q) ''It is impossible to have the conjunction of p and not-q''
Now, let us suppose that one has necessarily not-p : L~p or in other terms that p is im-possible: ~Mp, it is obvious that the conjunctions p & q and p & ~q are both impossible. If one has ~Mp, if p is im-possible, one can write ~M (p & ~q) as well as ~M (p & q) . Let us conclude: L (p → q), that is to say, ~M (p & ~q) does not represent the strict implication of q by p because ~M (p & ~q) may come from the fact that p is im-possible and not at all from the fact that p entails q.
==See also==
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