Using Mathematical Logic To Expose a Forged Painting
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
P = "The signature is authentic."
Q = "This drawing is typical of Gilbert Stewart's work of the
R= "The drawing represents George Washington in the time period
of the painting."
S = "The drawing is an authentic Gilbert Stewart portrait of
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.
The drawing is a forgery. In fact, the art historian working on
this case established this as the work of convicted forger
*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.