Re: Must higher-order logic be typed?



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?

.

Relevant Pages

  • Re: Must higher-order logic be typed?
    ... not typed (though they are not normally called higher order logics). ... The best known is set theory ... the infamous "Russell's Paradox". ...
    (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 ... the infamous "Russell's Paradox". ...
    (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)
  • 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)
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