Re: higher-order logic
From: H. Enderton (hbe_at_sonia.math.ucla.edu)
Date: 01/30/05
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Date: Sun, 30 Jan 2005 22:42:13 +0000 (UTC)
alex goldman <hello@spamm.er> wrote:
>By the way, is the term "higher-order logic" ever used in a sense different
>from "second-order logic"? Since second-order logic allows quantification
>over relations, would third-, etc. order logics allow quantification over
>quantifiers or something similarly outlandish?
It's simpler than that.
First order: quantify over individuals
Second order: quantify over sets of individuals and relations on individuals.
Third order: quantify over sets of sets of individuals (and relations on
relations on individuals).
Quibble: Church actually used a slightly more refined way of counting
third, fourth, ... order.
> I'm interested in learning more about higher-order logic
> (...)
>I was hoping to find a non-advocacy review of main results in higher-order
>logic (as opposed to first-order logic).
You said (in the original post) no plugs, so I won't say anything
about Chapter 4 of my logic book.
--Herb Enderton
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