This is as opposed to non-formalists, within that field, who hold that there are some things inherently true, and are not, necessarily, dependent on the symbols within mathematics so much as a greater truth.
To formalism's rival, legal realism, this criticism is incoherent, because legal realism assumes that, at least in difficult cases, all applications of the law will require that a judge refer to external (i.e. non-legal) sources, such as the judge's conception of justice, or commercial norms.
In general in the study of the arts and literature, formalism refers to the style of criticism that focuses on artistic or literary techniques in themselves, in separation from the work's social and historical context.
The context for the work, including the reason for its creation, the historical background, and the life of the artist, is not considered to be significant.
[citation needed] Formalism can be applied to a set of notations and rules for manipulating them which yield results in agreement with experiment or other techniques of calculation.
Formalism also more precisely refers to a certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems, specifically associated with David Hilbert.
In the philosophy of mathematics, therefore, a formalist is a person who belongs to the school of formalism, which is a certain mathematical-philosophical doctrine descending from Hilbert.