Definition:Formalism
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Definition
Formalism is the philosophical position that mathematics can be considered as manipulation of symbols independently of their meaning or interpretation.
Hence, to a formalist, the truth value of a statement in mathematics does not depend upon whether or how it describes an independent reality.
Instead, it is a game played according to a set of rules that allow the construction of sequences of symbols from other sequences of symbols.
Hence the concern of a formalist is to provide proofs of consistency that prevent contradictions from being made.
Similarly to intuitionists, formalist do not accept proofs that require an infinite number of steps.
Also see
- Results about formalism can be found here.
Historical Note
Formalism is often associated with David Hilbert.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): formalism
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): formalism