Wittgenstein On Rules and Private Language - The "straight" Solution

The "straight" Solution

In contrast to the kind of solution offered by Kripke (above) and Crispin Wright (elsewhere), John McDowell interprets Wittgenstein as correctly (by McDowell's lights) offering a "straight solution". McDowell argues that Wittgenstein does present the paradox (as Kripke argues), but he argues further that Wittgenstein rejects the paradox on the grounds that it assimilates understanding and interpretation. Meaning that in order to understand something, we must have an interpretation. That is, to understand what is meant by "plus," we must first have an interpretation of what "plus" means. This leads one to either skepticism - how do you know your interpretation is the correct interpretation?- or relativity whereby our understandings, and thus interpretations, are only so determined in so far as we have used them. In this latter view, endorsed by Wittgenstein in Wright's readings, there are no facts about numerical addition that man has so far not discovered,so when we come upon such situations, we can flesh out our interpretations further. Both of these alternatives are quite unsatisfying; the latter because we want to say that the objects of our understandings are independent from us in some way: that there are facts about numbers, that have not yet been added.

McDowell writes further, in his interpretation of Wittgenstein, that to understand rule-following we should understand it as resulting from inculcation into a custom or practice. Thus, to understand addition, is simply to have been inculcated into a practice of adding.