Yeek, that'll teach me to post a complicated problem and then go away for a day.
Nice to see your assertive self again
I think you miss the point too. If your statement is that you rope learn the addition for all single unit numbers and then apply another rule to combine numbers together when they are larger I need only suggest a different 'quus' interpretation. Perhaps perhaps single digit numbers when quused together give a different answer if they are part of a whole number larger than the largest number you've so far added together.
On Using Induction
To clarify, there are two problems here for us:
1. What past fact is there that we have previously meant addition rather than quuaddition?
2. If there is no fact for this on what do we base our confidence for how we should answer a question like "271+12=?" now?
As such induction alone will fail on this point. We cannot infer from past to present that we were using addition because the evidence we have is all equally compatible with both. In that sense this part is a little like a more generalised version of Goodman's Grue Paradox.
Induction + Occams Razor
(after a lot of thinking which turned out to be on the wrong track) is a little trickier but still equally ineffective I think:
It doesn't answer (1) because it doesn't provide a fact about our past that shows we were using addition rather than quuaddition. I can still argue that in the past you meant quuaddition and so far there is no fact you can appeal to to show you didn't.
For (2) the problem will be this: Your belief that addition is the simpler is based on the view that addition more clesly follow the rule you have been using than quuaddition does. But as you have no fact to show you have been using addition in the past you cannot demonstrate that to preceed in an addition like rather than a quuaddition like way is more inkeeping with what you have been doing in the past. Had you been using quuaddition then just continuing as we have been (which I assume is what you mean by the simplest rule) would be to preceed in a quuaddition like manner and answer "5".
Private Language Argument
Is based on this paradox I think. If language cannot be governed by rules Wittgenstein argues it is governed by agreement. I see you doing something that looks like what I'm doing. You get the answers I would have got, so I say to you 'well done, you've learned how to add'. Adding isn't being able to follow a rule but rather getting the same answer everybody else does most of the time. The point then I think is that without other people we have no agreement and thus no language. What I don't see is how this refutes solipsism. Couldn't I have agreement from the mindless zombies I perceive? Why do these zombies need to have minds for me to be able to have an language? Especially condering Wittgenstein has been demonstrating language is about appearing to do something rather than having a rule in mind.