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684Quantifying over functions in first-order logic

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  • cedricstjl
    Jun 8, 2006
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      I have some difficulty seeing the difference in expressiveness between
      first-order logic and higher-order logics. Wikipedia (as well as AIMA,
      AFAICT) says that F-O logic cannot quantify over functions. But
      couldn't it be achieved equivalently by reifying functions and
      predicates? I.e.:

      x = fun(var)


      x = call_function(fun, var)

      and then one can express reflexivity:

      for all fun, a, b: reflexive(fun) <=> call_function(fun, a, b) =
      call_function(fun, b, a)

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