Re: Nonfirstorderizability


George Dance wrote:
> In that light, I was wondering: when you have time (ie, when the real
> discussion is over), would you mind explaining to a simple lay person
> why the Geach-Kaplan sentence cannot be 'firstorderized' as:
>
> ExEyAz((Cx & Cy) & (Axy & Ayx) & (Axz -> z=y) & (Ayz -> z=x))
> (Ca =df. a is a critic; Aab =df. a admires b)?
>
> Or refer me to a weblink, if that's easier.

I take that sentence to imply the Geach-Kaplan sentence but not the
converse. That there are at most two critics who admire only each other
(and not themselves) implies that there are some critics (provided
those critics are not the same since we using the plural--'critics')
who admire only each other. But that there are some critics who admire
only each other does not imply that there are at most two critics who
admire only each other--there could be three, four, etc.

.

Relevant Pages

  • Re: Nonfirstorderizability
    ... > The Geach-Kaplan sentence refers implicitly to a domain D ... > including critics and other individuals they may admire, ... > as far as first-order sentences are concerned, ...
    (sci.logic)
  • Re: Nonfirstorderizability
    ... The Geach-Kaplan sentence refers implicitly to a domain D ... including critics and other individuals they may admire, ... as far as first-order sentences are concerned, ...
    (sci.logic)
  • Re: Nonfirstorderizability
    ... > I take that sentence to imply the Geach-Kaplan sentence but not the ... That there are at most two critics who admire only each other ... predicate, let me see what happens when that predicate is removed: ...
    (sci.logic)
  • Re: Nonfirstorderizability
    ... > Not a simplification, I'm afraid, but a better translation of "Some ... > critics admire only each other". ...
    (sci.logic)
  • Re: Nonfirstorderizability
    ... This formalizes "There are two critics who ... reasonable reading of the odd statement "Some critics admire only ...
    (sci.logic)