I just got to this paragraph in the first chapter of The Principia Mathematica:
"Definition and real variables. When the defiens contains one or more real variables, the definiendum must also contain them. For in this case we have a function of the real variables, and the definiendum must have the same meaning as the defiens for all values of these variables, which requires that the symbol which is the defiendum should contain the letters representing the real variables. This rule is not always observed by mathematicians, and its infringement has sometimes caused important confusions of thought, notably in geometry and the philosophy of space."
Anyone have any idea about what Russell and Whitehead might be talking about in that last sentence?