Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date" (p. 60).

Further, your past usage of the addition function is susceptible to an infinite number of different quus-like interpretations.

The power of Kripke's example is that in mathematics the rules for the use of expressions appear to be defined clearly for an infinite number of cases.

If we assume for the sake of argument that "plus" refers to the function "+", the skeptical problem simply resurfaces at a higher level.

Skeptical solutions accept the truth of the paradox, but argue that it does not undermine our ordinary beliefs and practices in the way it seems to.

But if there cannot be rules governing the uses of words, as the rule-following paradox apparently shows, this intuitive notion of meaning is utterly undermined.

Kripke holds that other commentators on Philosophical Investigations have believed that the private language argument is presented in sections occurring after §243.

On this latter view, endorsed by Wittgenstein in Wright's readings, there are no facts about numerical addition that we have so far not discovered, so when we come upon such situations, we can flesh out our interpretations further.

This position is often called "anti-antirealism", meaning that he argues that the result of sceptical arguments, like that of the rule-following paradox, is to tempt philosophical theory into realism, thereby making bold metaphysical claims.

Since McDowell offers a straight solution, making the rule-following paradox compatible with realism would be missing Wittgenstein's basic point that the meaning can often be said to be the use.

George M. Wilson argues that there is a way to lay out Kripkenstein as a philosophical position compatible with semantic realism:[6] by differentiating between two sorts of conclusions resulting from the rule-following paradox, illustrated by a speaker S using a term T: BSC (Basic Sceptical Conclusion): There are no facts about S that fix any set of properties as the standard of correctness for S's use of T. RSC (Radical Sceptical Conclusion): No one ever means anything by any term.