> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/100-fundamentals/terms/higher-order.md).

# Higher-order

**Higher-order functions** are functions that can treat functions (function as language construct) like any other value, e.g. they can accept functions as arguments and return functions.

**Higher-order logics**

* quantifying over *individuals*
* quantifying over *sets of individuals*
* quantifying over *sets of predicates*

*n-order logics*, ZOL » FOL » SOL » HOL

* Zeroth-order logics, n = 0
* First-order  logics, n = 1
* Second-order logics, n = 2
* Higher-order logics, n > 2

FOL,SOL are not higher-order logics.

To achieve **higher-order** you need to start have variables that range over "higher" concepts.

Orders: a theoretic language with variables that range over objects is a higher-order language (right?)