Arguments Regarding The Semantic Truth of Vacuously True Logical Statements
This is a complex question and, for simplicity of exposition, we will here consider only vacuous truth as concerns logical implication, i.e., the case when has the form, and is false. This case strikes many people as odd, and it is not immediately obvious whether all such statements are true, all such statements are false, or some are true while others are false.
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“When I am convinced of any principle, it is only an idea which strikes more strongly upon me. When I give the preference to one set of arguments above another, I do nothing but decide from my feeling concerning the superiority of their influence.”
—David Hume (1711–1776)
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“We know truth when we see it, from opinion, as we know when we are awake that we are awake.”
—Ralph Waldo Emerson (1803–1882)
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—Friedrich Nietzsche (1844–1900)
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—T.S. (Thomas Stearns)