# Talk:Higher-order logic

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Another definition is that functions can not be passed as arguments in lower-order logic.

Sure they can. \P\Q\x(R(P) ^ Q(x)). I guess that's actually lambda calc, but it's certainly not HOL. 24.95.48.112 01:53, 7 March 2007 (UTC)

- This sentence is vague to the point of comical "in first-order logic, roughly speaking, it is forbidden to quantify over predicates." Are we 'roughly speaking' or are we speaking of 'logic'?...we can't have both. i.e. Either 'first order logic' supports quantification over predicates, or it doesn't. Which is it? —Preceding unsigned comment added by 203.169.23.13 (talk) 22:10, 23 May 2008 (UTC)

- I, think it would be more intuitive to compare higher order logic to second order logic instead of first order logic. —Preceding unsigned comment added by 195.72.96.179 (talk) 13:08, 29 September 2008 (UTC)

## Set of all statements

Can we consider set of all HOL statements as set of ALL statements? I know it may be not set in traditional sense, possibly rather class of statements, but I think you know what I mean 83.23.16.6 (talk) 19:53, 6 May 2012 (UTC)

What do you think will be the cardinality of this set? Poshida (talk) 06:54, 17 September 2015 (UTC)

## ruin

you people are ruining true mathematics, coming up with rules to satisfy sociology 24.177.200.27 (talk) 10:05, 28 October 2013 (UTC)

## some basics needed

This article gets too quickly to talk of type theory and related results. It needs a basic introduction/definitions to why type are needed in HOL. And hand-in-hand with that it should explain the two constructions of classical HOL: one with comprehension axioms and the other with lambda-abstractions. For the latter I can suggest the introductory pages to Melvin Fitting's book Types, Tableaux, and Gödel's God; although the book is mostly about modal HOL, it does have a good intro to classical HOL. 86.127.138.67 (talk) 23:50, 15 April 2015 (UTC)