Comment on Is "If A then B" equal to "B if and only if A"?

• Boinkage@lemmy.world ⁨10⁩ ⁨months⁩ ago

  Substitute common sense terms. If I say “if it is an apple, it is a fruit”, does it then follow that a thing is a fruit if and only if it is an apple? No.

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  • Rhynoplaz@lemmy.world ⁨10⁩ ⁨months⁩ ago

    Better read that one again.

    “If B then A” … “B if and only if A”?

    If Apple then fruit. Is Apple ONLY if it’s a fruit.

    This one actually checks out.

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    • Boinkage@lemmy.world ⁨10⁩ ⁨months⁩ ago

      If and only if is a biconditional. “b if and only if a” means “if b then a” AND “b only if a”. B only if A here means “It is an apple only if is a fruit”, in other words, “if it is a fruit, it could only be an apple.” Which ain’t right.

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      • Rhynoplaz@lemmy.world ⁨10⁩ ⁨months⁩ ago

        Gotcha. I was reading it aloud: “It’s an Apple if and only if it’s a fruit.” which isn’t wrong, but I guess the technical definition of “If and only if” assumes more than the words imply.

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