Our recent discussion with mathematician Russ Lyons on confidence intervals reminded me of a famous logic paradox, in which equality is not as simple as it seems.
The classic example goes as follows: Abraham Lincoln is the 16th president of the United States, but this does not mean that one can substitute the two expressions “Abraham Lincoln” and “the 16th president of the United States” at will. For example, consider the statement, “If things had gone a bit differently in 1860, Stephen Douglas could have become the 16th president of the United States.” This becomes flat-out false if we do the substitution: “If things had gone a bit differently in 1860, Stephen Douglas could have become Abraham Lincoln.”
The classic example goes as follows: Abraham Lincoln is the 16th president of the United States, but this does not mean that one can substitute the two expressions “Abraham Lincoln” and “the 16th president of the United States” at will. For example, consider the statement, “If things had gone a bit differently in 1860, Stephen Douglas could have become the 16th president of the United States.” This becomes flat-out false if we do the substitution: “If things had gone a bit differently in 1860, Stephen Douglas could have become Abraham Lincoln.”
