Re: Nonfirstorderizability

Torkel Franzen wrote:
> "George Dance" <georgedance04@xxxxxxxx> writes:
>
> > ExEyAz((x/=y) & (Cx & Cy) & (Axy & Ayx) & (Axz -> (Cz & Azx)) & (Ayz ->
> > (Cz & Azy))).
> >
> > Not a simplification, I'm afraid, but a better translation of "Some
> > critics admire only each other". ("There are at least two critics who
> > admire each other, both or all of whom admire only critics who admire
> > them."
>
> I guess this too is a possible interpretation of "Some critics
> admire only each other". Those who write about branching quantifiers
> use some odd examples, such as Hintikka's
>
> Some relative of each villager and some relative
> of each townsman hate each other.

My first approximation to formalizing that would be:
AxAyEzEu((Vx -> Rzx) & (Ty -> Ruy) & (Hzu & Huz))

I've been looking for other such sentences on the web, BTW, and I've
found one that looks harder: "The men formed a circle around the
building."

.

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