Use of Prenex Form
Some proof calculi will only deal with a theory whose formulae are written in prenex normal form. The concept is essential for developing the arithmetical hierarchy and the analytical hierarchy.
Gödel's proof of his completeness theorem for first-order logic presupposes that all formulae have been recast in prenex normal form.
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“Upon the whole, necessity is something, that exists in the mind, not in objects; nor is it possible for us ever to form the most distant idea of it, consider’d as a quality in bodies. Either we have no idea of necessity, or necessity is nothing but that determination of thought to pass from cause to effects and effects to causes, according to their experienc’d union.”
—David Hume (1711–1776)