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# Using Mathematical Logic To Expose a Forged Painting

Introduction
On the PBS show The History Detectives, a Frederick, Maryland family claims to have an authentic Gilbert Stewart portrait of George Washington, the first president of the United States. If it is authentic, it could be worth as much as \$50,000. Is it authentic? The History Detectives use logic to find the answer to this question.

Facts of the Investigation as Given on The History Detectives

• The portrait is signed Gilbert Stewart whereas Gilbert Stewart always signed his portraits G. Stewart.
• The likeness is a drawing, and Gilbert Stewart was not known to have produced drawings after 1780.
• The portrait shown shows George Washington as President in a uniform, but George Washington would not have been wearing a uniform in 1795 as President.*

The Logic Involved
Let
P = "The signature is authentic."
Q = "This drawing is typical of Gilbert Stewart's work of the time period."
R= "The drawing represents George Washington in the time period of the painting."
S = "The drawing is an authentic Gilbert Stewart portrait of George Washington.

Thus, we have the statement, (P and Q and R) if and only if S.  This statement is only true if both parts (P and Q and R) and S are true or if both parts (P and Q and R) and S are false. The part (P and Q and R) is false if any of the parts P, Q, or R are false. In this case, all 3 parts are false.  This implies that S must also be false.

Conclusion
The drawing is a forgery.  In fact, the art historian working on this case established this as the work of convicted forger Ferdinand Danton.

*Although not explicitly stated in The History Detectives article, I made the assumption that the portrait shows George Washington in a presidential setting, based on the context of comments made.