Doxa

I read the page on ontological arguments and found something called "Brouer's Theorem" (would I be right to assume that that's supposed to be "Brouwer's Theorem"?) cited. Using "N" for the necessity operator and "P" for the possibility operator, it was supposed to be (p->Np)->(Pp->p). But surely there is some mistake. That is logically equivalent to
Pp->p, which is false when p is possible but neither necessary nor actual. (Try plugging in Pp=T, Np=F, p=F to (p->Np)->(Pp->p), and you will find that the "theorem" is false in that case.) This cannot be a theorem. I am wondering, therefore, where you found it, and where it was referred to as a theorem.

MindWalk wrote:I read the page on ontological arguments and found something called "Brouer's Theorem" (would I be right to assume that that's supposed to be "Brouwer's Theorem"?) cited. Using "N" for the necessity operator and "P" for the possibility operator, it was supposed to be (p->Np)->(Pp->p). But surely there is some mistake. That is logically equivalent to
Pp->p, which is false when p is possible but neither necessary nor actual. (Try plugging in Pp=T, Np=F, p=F to (p->Np)->(Pp->p), and you will find that the "theorem" is false in that case.) This cannot be a theorem. I am wondering, therefore, where you found it, and where it was referred to as a theorem.

I don't know anything about that.

It's a theorem of s5 iff p --> Np, just to clarify.

Same thing as PNp.--> p.

Aka "Rule of B"

( I never looked at this forum much before.... )