Asked • 04/15/19

Is there a way to understand material implication without truth-tables?

I understand how, given the truth-functional definition of the conditional, any sentence of the form


If P then Q


is truth-functionally equivalent to


Either not-P or Q


Or, to put it symbolically:  P → Q is truth-functionally equivalent to ~P v Q.


The reason why this is so is because, given the truth-tables for conditionals (P → Q), disjunctions (P v Q), and negations (~P), any sentence of the form P → Q will have the same truth-value as any sentence of the form ~P v Q.


However, suppose someone is unsure or skeptical of the truth-functional definition of the conditional. Is there some other way of showing that, for any sentence P, Q, the conditional P → Q is true if and only if the disjunction ~P v Q is true?

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