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Formalism (philosophy of mathematics)
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<p>In the <a href="/facts/Philosophy_of_mathematics/z7xBcdWA">philosophy of mathematics</a>, formalism is the view that holds that statements of <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Logic/8JnpJLtt">logic</a> can be considered to be statements about the consequences of the manipulation of <a href="/facts/String_(computer_science)/4ChJu5WS">strings</a> (alphanumeric sequences of symbols, usually as equations) using established <a href="/facts/Rule_of_inference/QV5NklQ9">manipulation rules</a>. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an <a href="/facts/Ontology/QJKTsEIJ">ontology</a> of objects or properties than <a href="/facts/Ludo_(board_game)/hIKxwD1B">ludo</a> or <a href="/facts/Chess/47ykvkHF">chess</a>." According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they are not "about" anything at all. Rather, mathematical statements are <a href="/facts/Syntax_(logic)/WrLeuvgp">syntactic</a> forms whose shapes and locations have no meaning unless they are given an <a href="/facts/Interpretation_(logic)/goPmjjQG">interpretation</a> (or <a href="/facts/Semantics/1L4WwLAP">semantics</a>). In contrast to <a href="/facts/Mathematical_realism/z7xBcdWA">mathematical realism</a>, <a href="/facts/Logicism/YvHs6X3E">logicism</a>, or <a href="/facts/Intuitionism/1gTeosv9">intuitionism</a>, formalism's contours are less defined due to broad approaches that can be categorized as formalist. </p><p>Along with realism and intuitionism, formalism is one of the main theories in the philosophy of mathematics that developed in the late nineteenth and early twentieth century. Among formalists, <a href="/facts/David_Hilbert/1vhlHn4b">David Hilbert</a> was the most prominent advocate. </p>