Wikipedia is wrong.
This recent revelation has come as quite a shock to me. Obviously hundreds of people deride Wikipedia for its bias and its inaccuracies which, when uncorrected, can grow exponentially. But I’ve always relied on Wikipedia nonetheless: it’s my default place to go to for information; I have a search bar that links to it in the corner of my Firefox window; I trusted it.
Yesterday I discovered that it is completely and utterly wrong about the Sheffer stroke. The Sheffer stroke is a piece of logical notation which Blogger won't allow me to show you because it doesn't have the font set (I'll use the forward slash instead: /). It is used in logical formulae such as the kind in Wittgenstein’s Tractatus where, in 5.1311, Wittgenstein claims that all the other logical constants can be defined from it. The Sheffer stroke means ‘neither _ nor _’ which is expressed in computer science as a NOR function. Therefore (p v q)(p or q) can be defined as ((p/q) /(p/q))(Not (not p or q) or (not p or q).
Wikipedia claims that the Sheffer stroke means NAND ie. ‘not _ and _’ where the not operator has scope over the whole formula not the first variable.
Logicians beware: common usage and Wikipedia has transformed the Sheffer stroke into a NAND operator. It is not to be confused with the Pierce arrow. Here is a discussion regarding this widespread logical misuse and here (for those with access to JSTOR) is the original Sheffer article with the catchy title “A Set of Five Independent Postulates for Boolean Algebras, with Application to Logical Constants”. On page 487, he clearly defines his stroke as ‘neither nor’.
Both the NAND and the NOR interpretations are fine as long the notation makes it clear how it is being used: it appears that the language of logic, just like ordinary languages, is constantly fluctuating and evolving based upon the dictates of custom. However the traditionalist NOR interpretation is technically the correct one based on what Sheffer wrote.