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  "body": "\n## Summary\n\nHigher-order logic extends [[first-order logic|086QKPF0A6]] with variables, and quantifiers, for relations on elements, relations on such relations, and so on at every finite level.\nEach variable carries a type that says at which level it lives.\nIt is the logic behind simple type theory and several proof assistants, such as Isabelle/HOL.\n\n## Explanations\n\n### L1 human\n\nFirst-order logic talks about objects.\nSecond-order logic also talks about sets of objects.\nThird-order logic adds sets of sets of objects, and higher-order logic allows every finite level of this hierarchy.\nFor example, \"every collection of sets of numbers has a union\" quantifies over collections of sets, so it is a third-order statement.\n",
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