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• 3 Likes

  AudaciousRed Alum Member

  June 2019 2689 karma

  Contrapositives mean the exact same thing. It's just reversed. Negations are when you make the statement mean something entirely opposite.

  Contrapositive:
  "All non-water breathing mammals have limbs." Contra: "If it doesn't have limbs, it is not a non-water breathing mammal."
  If they all have limbs, and a thing in question doesn't have limbs, it can't be one of them, right? It just says the same statement, in a different order.

  Negation:
  "All non-water breathing mammals have limbs" becomes "It is NOT the case that All non-water breathing mammals have limbs." So... NOT ALL do. But could some? Sure. Could none? Sure. Just as long as not ALL do. There are some (1+) who do not.
  And what do those not do? Have limbs, right? So, there is at least one thing that is a non-water breathing mammal who does NOT have limbs. Dolphins have fins and tails and don't breathe water, so maybe they count since they're not "limbs." Maybe there is a mammal version of a serpent. Who knows. But the opposite of "all do" is "some do not". Even if it's just one, it negates the statement.
  It's like looking out the window when someone tells you "All of the dogs have been fed!" and you see two that have no food. "Some of the dogs have not been fed," you say, based on this evidence. You are contradicting him and saying he's wrong based on the new info that two dogs have no food in heir bowls. It severely hurts his argument that he fed all the dogs if some of them weren't fed. And there lies the purpose, I think, of negations. It pokes big holes and undermines arguments.
• 1 Like

  GodsPlan Member

  June 2019 176 karma

  I'm not too sure how to reply to people on here but thanks, this clears up alot. I was getting the concepts confused.