Re: Nonfirstorderizability

Keith Ramsay wrote:
> George Dance wrote:
> |george wrote:
> |> > > Some relative of each villager and some relative
> |> > > of each townsman hate each other.
> |>
> |> How about
> |> Axy[ Vx&Ty -> Euv[ Rxu & Ryv & Huv & Hvu ] ]
> |
> |How does that differ from what you snipped:
> | AxAyEzEu((Vx -> Rzx) & (Ty -> Ruy) & (Hzu & Huz))
> |?
>
> Suppose there are no villagers or townsmen. Then the
> first version is true, while the second version still
> requires that (if there is anyone) there exists either
> one person z=u who hates himself or two people z<>u
> who hate each other.

I was hoping that george would answer the question, but...

That is a difference: On george's 'boolean' interpretation, "Some
relative of each villager and some relative of each townsman hate each
other" does not imply that "Some people hate each other": it would be
illogical to infer, from someone's asserting the first statement, that
he is also asserting the second.

.

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