I would like to know why is universally accepted by mathematicians and logicians that: if P is false and Q true, then P → Q is true.
Why cannot be otherwise? Which are the reasons?
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This issue has been discussed often here. Do a search for "If p then q" to get started. – turkeyhundt Dec 29 '15 at 23:43
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There is a lot that has been written on this in the intersection of philosophy and logic! http://stanford.library.usyd.edu.au/archives/sum2010/entries/logic-conditionals/ – Bernard W Dec 29 '15 at 23:51
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Also see http://math.stackexchange.com/questions/1551320/understanding-vacuously-true-truth-table/1551525#1551525 – Dan Christensen Dec 31 '15 at 02:55