Getting Around the Plus/Quus Problem

Roughly, the plus/quus problem is that it might be impossible for us to know if, when we use the word 'plus', we are actually referring to the addition function or some other function (call it 'quaddition') that behaves just like addition up to a point, and then does something different. Suppose nobody had ever added any numbers above 1,000,000. Nobody had in fact ever done a problem of the form x + y where either x or y was 1,000,000 or greater. Now suppose also that quaddition is the function that behaves just like addition up to the point that it takes 1,000,000 as one of its arguments, but if either of the arguments x or y is 1,000,000 or greater, the output (or the result of quaddition on those two numbers) is always 5. So 999,900 + 90 = 999,990, but 1,000,000 + 10 = 5, where '+' is interpreted as quus, or referring to quaddition.

So Kripkenstein (Kripke inspired by what Wittgenstein said on this) convinces us there's a problem here. We may actually be referring to quaddition instead of addition, and we may have always been doing so. No way to figure it out.

The Lewisian way (from David Lewis) of getting around this, if I understand it right, relies on the notion of naturalness:

1. Some properties are more natural than others (e.g. being a tiger is more natural than being a tiger-or-electron-or-shoe)
2. Natural properties are reference magnets (i.e., our general terms tend to refer to natural properties in cases where we're not completely specific).
3. Addition is a more natural function than quaddition.
4. So our regular uses of the word 'plus' or 'add' generally refer to addition rather than quaddition.

Lewis spells out this naturalness stuff in On the Plurality of Worlds and "New Work for a Theory of Universals", and Ted Sider discusses it, along with reference magnetism, in "Ontological Realism".