Re: Must higher-order logic be typed?


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?

.

Relevant Pages

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    (sci.logic)
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  • Re: Must higher-order logic be typed?
    ... not typed (though they are not normally called higher order logics). ... The best known is set theory ... Maybe we can say it is LIKE a multi-order logic that is a first order ...
    (sci.logic)
  • Re: Must higher-order logic be typed?
    ... not typed (though they are not normally called higher order logics). ... The best known is set theory ... Maybe we can say it is LIKE a multi-order logic that is a first order ...
    (sci.logic)