Negation Trouble!

TheMadFool November 26, 2020 at 13:19 1900 views 4 comments

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:

Comments (4)

Outlander November 26, 2020 at 13:44 #474695 0 likes

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.

TheMadFool November 26, 2020 at 13:50 #474698 0 likes

The mathematical symbol for approximation consists of two "~" stacked on top of each other.

Deleted User November 26, 2020 at 14:05 #474700 0 likes

This user has been deleted and all their posts removed.

TheMadFool November 26, 2020 at 14:17 #474701 0 likes

Quoting tim wood

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?

delete. Thanks.