Editing Formal system (section)

{{Short description|Mathematical model for deduction or proof systems}}
{{Tertiary sources|date=December 2024}}
A '''formal system''' is an [[abstract structure]] and [[Formalism (philosophy of mathematics)|formalization]] of an [[axiomatic system]] used for [[Deductive reasoning|deducing]], using [[rule of inference|rules of inference]], [[theorem]]s from [[axioms]].{{sfn|Hunter|1996|p=7}}

In 1921, [[David Hilbert]] proposed to use formal systems as the foundation of knowledge in [[mathematics]].<ref name=":0">{{cite book
| title = Hilbert's Program, Stanford Encyclopedia of Philosophy 
| date = 31 July 2003
| chapter-url = https://plato.stanford.edu/archives/spr2016/entries/hilbert-program
| last1 = Zach
| first1 = Richard
| chapter = Hilbert's Program
| publisher = Metaphysics Research Lab, Stanford University
}}</ref>

The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of [[notation]], for example, [[Paul Dirac]]'s [[bra–ket notation]].