Definitely a repost, but it fits the season

  • NeatNit@discuss.tchncs.de
    5·
    2 个月前

    Yup, that’s my interpretation too. It just doesn’t sit well with all the other operators.

    All the others are phrased as direct questions about the values of A and B:

    • A AND B = “Are A and B both true?”
    • A OR B = “Are either A or B true, or both?”
    • A NAND B = “Is (A AND B) not true?”
    • A IMPLIES B = “Is it possible, hypothetically speaking, for it to be the case that A implies B, given the current actual values of A and B?”

    You see the issue?

    Edit: looking online, some people see it as: “If A is true, take the value of B.” A implies that you should take the value of B. But if A is false, you shouldn’t take the value of B, instead you should use the default value which is inexplicably defined to be true for this operation.

    This is slightly more satisfying but I still don’t like it. The implication (ha) that true is the default value for a boolean doesn’t sit right with me. I don’t even feel comfortable with a boolean having a default value, let alone it being true instead of false which would be more natural.

    Edit 2: fixed a brain fart for A NAND B

    • Klear@quokk.auEnglish
      6·
      2 个月前

      Consider the implication to be some claim, for example, “When it’s raining (A), it’s wet (B)”. The value of the implication tells us whether we should call the claimant a liar or. So in case it’s raining (A = true) and is is not wet (B = false) the claim turns out to be false, so the value of the implication is false.

      Now, supposing it is not raining (A = false). It doesn’t matter whether it’s wet or not, we can’t call the claim false because there just isn’t enough information.

      It’s about falsifiability (or lack thereof, in case A is never true).

      • NeatNit@discuss.tchncs.de
        2·
        2 个月前

        The comment you replied to is my response to this. It’s the only boolean operation that works this way. All the others are straightforward.

        • Klear@quokk.auEnglish
          2·
          2 个月前

          I think the problem is that you’re thinking in terms of boolean algebra, while implication being implication comes from propositional logic.

          • NeatNit@discuss.tchncs.de
            3·
            2 个月前

            That’s interesting. I’ll have to read up on that. You’re right, I am thinking about boolean algebra.

            In the mean time though, I’ll note that Boolean algebra on Wikipedia also refers to this operation, so I’m not alone:

            Material conditional

            The first operation, x → y, or Cxy, is called material implication. If x is true, then the result of expression x → y is taken to be that of y (e.g. if x is true and y is false, then x → y is also false). But if x is false, then the value of y can be ignored; however, the operation must return some Boolean value and there are only two choices. So by definition, x → y is true when x is false (relevance logic rejects this definition, by viewing an implication with a false premise as something other than either true or false).

            It also uses the second interpretation that I mentioned in my earlier comment (4 above this one), with true being default, rather than the one we’ve been discussing.