Negation Trouble!
  • TheMadFool
    13.8k
    Hi there, fellow forum members. I would like to run something by you all that I'm having a hard time wrapping my head around. It's got to do with the notion of logical negation.

    As far as I can tell, the logical negation of a proposition is the denial of that proposition. So, if proposition P = I'm a robot, then the negation of P, written in logic as ~P = I'm not a robot. In layman's terms it's basically a retraction of a statement or thereabouts.

    That out of the way, I'd like you all to consider the statement N = This statement can be negated..

    If we assume N to be true i.e. if N is negatable, then ~N follows but ~N = This statement can't be negated. In other words, if N can be negated then N can't be negated. A contradiction. Therefore, N can't be negated.

    Thus, N = This statement can be negated, can't be negated.

    :chin:
    TheMadFool Options
  • Outlander
    2.2k
    I thought ~ was a symbol for approximation/estimate/or "around". I have ~5 dollars, meaning I have more or less somewhere around five dollars.

    When it comes to these kinds of paradoxes I'd say it's more than likely one or the other is factually incorrect/untrue/incoherent.
    Outlander Options
  • TheMadFool
    13.8k
    The mathematical symbol for approximation consists of two "~" stacked on top of each other.
    TheMadFool Options
  • tim wood
    9.3k
    ↪TheMadFool
    Sure it can. You did it. But it's a contradiction, as you note. Condensed a little bit you've written N=~N. But what can you do with it? What's it good for?
    tim wood Options
  • TheMadFool
    13.8k
    Sure it can. You did it. But it's a contradiction, as you note. Condensed a little bit you've written N=~N. But what can you do with it? What's it good for? — tim wood

    delete. Thanks.
    TheMadFool Options
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