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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. (There is also second order set theory, but
I don't know much about it, though I want to find out more eventually.)
MoeBlee
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