kripkenstein's quaddition - exposition

oh kripke... or kripkenstein.. or whatever...

so here's the real deal. i have not read wittgenstein's philosophical investigations so take this entire post with a grain of salt--or a heap of it.

anyway the argument as it struck kripke goes somewhat like this:

suppose you've never performed the mathematical function "plus" with integers greater than 50. A is a teacher and YOU are B.

A: "17 plus 23 is..."
B: "40"
A: "yes! you got it! now, 58 plus 67 is..."
B [takes a bit longer. B computes in his head] "125."
A: "uh... i'm sorry. i don't think you understand. try again."
B [computes again]: "no i did it again in my head and.. well i was right. it's 125."
A: "uh... i think someone didn't teach you this right. 58 plus 67 is 5."
B: [baffled] "whaatt??"

so here's the trick. when you heard the word "plus" you thought that was a function where you combine numbers , such that

'plus (a,b)' = addition (a,b) --> 'a + b' when {x| -∞, ∞}

however, it is not logically inconsistent that "plus" really referred to the function of quaddition such that

'plus* (a,b)' = quaddition (a,b) ---> 'a+ b' when {x| -∞, 50} and '5' when {x| 50, ∞}

now, it's important to note that this skeptic who is proposing this skeptical scenario is not being a skeptic about the concept of addition. he's not saying that the concept of addition is vague in any way. he's just saying that it's not logically inconsistent to propose that it may be the case that whenever we use the word "addition" or the mathematical symbol of "+" we might be talking about quaddition instead of addition.

this skepticism, however, is not just an epistemological skepticism about whether we know we're adding or quadding, but it extends to a metaphysical skepticism about our own use of concepts. we can think we know what concept we're using but we could be mistaken.

i'm interested to see how or if kripke attempts to solve this...