Why is it that in formal logic, the phrase “If Bob drinks, then everyone drinks” is true if Bob doesn’t drink ?

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in other words, why are statements of the form “If A then B” always true if A is false?

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Anonymous 0 Comments

Because phrases like that are silent on not(A). Effectively, If not(A) then <anything can happen>. There is no conflict in a system which has one “If A” statement and another “If not(A)” statement, in fact this is the sort of construction you’d expect.If you leave off the “If not(A)”, then the default is <anything can happen> which is always true.

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