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MoeBlee wrote:
> Newberry wrote:
> > >
> > > However, if you ask "what is a higher order logic?" then one reasonable
> > > answer to that might be "a logic in which it is possible to quantify
> > > over sets or functions or predicates (not just over individuals)" and
> > > there are many logical systems in which this can be done but which are
> > > not typed (though they are not normally called higher order logics).
> > > The best known is set theory
> >
> > This is what confuses me. Is set theory a multi-order logic done in a
> > first order logic?
>
> Maybe we can say it is LIKE a multi-order logic that is a first order
> theory. But strictly speaking, first order set theory is a first order
> theory. And it can be a multi-sorted first order theory, but that is
> still a first order theory.
Can we treat
Fx as equivalent to x e F
and if not why not?
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