"Brouer's" (Brouwer's?) Theorem

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MindWalk

"Brouer's" (Brouwer's?) Theorem

Post by MindWalk » Mon Dec 03, 2012 7:06 pm

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.

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Metacrock
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Re: "Brouer's" (Brouwer's?) Theorem

Post by Metacrock » Wed Dec 05, 2012 4:59 pm

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.
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met
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Re: "Brouer's" (Brouwer's?) Theorem

Post by met » Tue Jun 10, 2014 11:12 pm

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

Same thing as PNp.--> p.

Aka "Rule of B"

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The “One” is the space of the “world” of the tick, but also the “pinch” of the lobster, or that rendezvous in person to confirm online pictures (with a new lover or an old God). This is the machinery operative...as “onto-theology."
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