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I think my problem here is that everyone just assumes an extra condition. The question "if Tokyo is in France, then the Eiffel Tower is in Bolivia" is not the s

• fasterik 3y ago
  >"For all x, if x is a marble and x is in the bag, then x is white". The statement is more "For all x in the bag, is x white?" They're the same, just quantifying over different sets. I can quantify over objects in the universe, in which case I need the clause about being in the bag. Or I can quantify over objects in the bag, in which case I'm quantifying over the empty set. all(m=="white" for m in marbles) By De Morgan's laws, this is equivalent to not any(m != "white" for m in marbles) If you want all(m=="white" for m in marbles) to evaluate to False for the empty set, then any(m != "white" for m in marbles) has to evaluate to True for the empty set, or you have to give up on De Morgan's laws. This is how standard first-order logic works. Again, you're welcome to try to make your own system of logic that works differently, but good luck doing that while preserving all of our theorems in set theory and mathematics.