Kripke poses the challenge:
Who is to say that this [quus] is not the function previously meant by '+'? (9)
The answer is simple: the rules of arithmetic. We either follow them correctly or we do not. — Fooloso4
I wrote a simple program for my computer, following the rules of arithmetic originating with the principle of succession from set theory. When I ask the program to add two numbers it follows the rule I have instilled. — jgill
Show some fact about your previous usage of "plus" that demonstrates that it wasn't "quus." — frank
Yes, but in the thought experiment, you've never done that. The idea is that in real life there's a number you've never added up to before. For the sake of presenting the challenge, we just pick 57. — frank
The challenge is to point to some fact — frank
...our ability to follow rules correctly and consistently is not dependent upon the application of a privately held conceptual understanding of the rule (the justified mental fact), — Fooloso4
...there was no rule following. If you disagree, he's asking you to prove it. — frank
You chose 57, but 59 would have been better because the number after 59 is in fact 1:00. — Hanover
If we're dealing in synthetic truths, we see the same thing. The rules governing planetary travel show a predictable course and the coordinates can be predicted so that it would appear which number would follow next, until something interferes with the travel. Would we then say we're not following the word game because the next in sequence wasn't predictable from the last in that one instance? — Hanover
Kripke's skepticism is based on his assumption that there must be some fact independent of and other than the fact of the practice of addition. — Fooloso4
if I'm disregarding the obvious silliness of the whole thing — flannel jesus
Quaddition doesn't generally solve the sorts of problems I've thus far been using addition to solve, so no, I haven't been doing that. — flannel jesus
seems like you're just ignoring the whole section where I argue that addition generally solves the sorts of problems I use it to solve, even for numbers > 57. — flannel jesus
If someone is going to tell me what's in my mind - and telling me I've been using quaddition instead of addition is doing just that - then they should have a good reason for believing that. — flannel jesus
He's asking for a fact that shows you've actually adhered to this practice as opposed to the practice of quaddition. — frank
As long as we are dealing with quantities less than this imaginary number that has not been dealt with before, then there are a multitude of rules we might invent that we could say are being adhered to. It is only when we encounter this number that we can say say that what follows is or is not arithmetic, for the rules of arithmetic do not allow that two positive integers added together will be less than either one. — Fooloso4
So if up until we get to this number, which as far as we know no one has ever encountered, there is no discernible difference between plus and quus and puus. The practice is the same. What then is the skeptical objection? — Fooloso4
In the challenge, addition and quaddition produce the same results up to 57, and that's as far as you've ever gone. — frank
That there is no fact about which rule you were following. — frank
This challenge comes from Saul Kripke’s Wittgenstein on Rules and Private Language (1982). Note that Kripke advises against taking it as an attempt to correctly interpret Wittgenstein (which is a convoluted statement considering the nature of the challenge), but rather it's a problem that occurred to him while reading Wittgenstein. This post is the challenge in my words:
We start with noting that there is a number so large, you've never dealt with it before, but in our challenge, we'll just pick 57. You've never dealt with anything over that. You and I are sitting with a skeptic.
I ask you to add 68+57.
You confidently say "125."
The skeptic asks, "How did you get that answer?"
You say "I used the rules of addition as I have so often before, and I am consistent in my rule following."
The skeptic says, "But wait. You haven't been doing addition. It was quaddition. When you said plus, you meant quus, and: x quus y = x+y for sums less than 57, but over that, the answer is always 5. So you haven't been consistent. If you were consistent, you would have said "5.""
Of course you conclude that the skeptic is high and you berate him. He, in turn, asks you to prove him wrong. Show some fact about your previous usage of "plus" that demonstrates that it wasn't "quus." — frank
First, it must give an account of what fact it is
(about my mental state) that constitutes my meaning plus, not
quus. — frank
If our ability to follow rules correctly and consistently is not dependent upon the application of a privately held conceptual understanding of the rule (the justified mental fact), but can be explained in terms of training and conformity to standard practice, then what remains of the skeptical problem? — Fooloso4
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