WFF: The Beginner's Game of Modern Logic

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This set of two games taught young children how to combine symbols into grammatically correct logical statements called well-formed formulae (WFFs). The two games in this set are the simplest of the twenty-one “Games of Modern Logic” of WFF ‘N Proof (see MA.335302), which was developed by Layman E. Allen of Yale University Law School under a grant from the Carnegie Corporation for ALL (Accelerated Learning of Logic). Allen applied for a trademark for WFF in August 1963; it was registered the following year but has now expired. The game sold from about 1963.
The set includes twelve wooden cubes, six with lowercase letters and six with uppercase letters, that are used by the players to form WFFs. The lowercase letters represent sentence variables in logic the same way that letters represent number variables in algebra. Uppercase letters represent symbols that allow one to form logical sentences in the same way that the symbols for the four arithmetical operations (addition, subtraction, multiplication, and division) are used to form algebraic expressions.
The set also includes two playing mats, a sheet listing “GAMES for THINKERS” that were available from WFF ‘N PROOF, and a 1968 edition of an instruction manual written by Allen, WFF: The Beginner’s Games of Logic. All these materials are stored in a cardboard box that is marked on the cover: WFF (/) The Beginner’s Game (/) of Modern Logic.
In 1968 Allen moved from Yale to the University of Michigan with a joint appointment in the Law School and the Mental Health Research Institute, where he continued his work on instructional games. Over the years the name and location of the distributor of WFF changed, although the phrase “Games For Thinkers” has been associated with it from before Allen’s move to Ann Arbor. Price lists in the WFF ‘N PROOF Newsletters (part of the documentation in accession 317891) indicate that at first the game was distributed by WFF ‘N PROOF in New Haven, Connecticut, and sold for $1.50, including postage. In 1971 the price was raised to $1.75 and the game was distributed by WFF ‘N PROOF through Maple Packers in Turtle Creek, Pennsylvania. A firm called Learning Games Associates of Ann Arbor later took over distribution of the game and donated this example to the Smithsonian in 1975. The Accelerated Learning Foundation of Fairfield, Iowa, then became the distributor.
Games For Thinkers Website.
Currently not on view
date made
ca 1968
Allen, Layman E.
Learning Games Associates
place made
United States: Michigan, Ann Arbor
Physical Description
plastic (overall material)
wood (overall material)
paper (overall material)
overall: 2.25 cm x 16 cm x 6.25 cm; 7/8 in x 6 5/16 in x 2 15/32 in
ID Number
accession number
catalog number
Credit Line
Gift of Learning Games Associates
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Medicine and Science: Mathematics
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Mathematical Recreations
Data Source
National Museum of American History