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

The challenge is to point to some fact that shows which rule you were following in the past. Remember, the challenge is not about epistemology. It's not about how we know what rule you were following. It's conclusion, and the one Kripke doesn't see Wittgenstein ever ruling out is this: there was no rule following. If you disagree, he's asking you to prove it.

This is not an exegesis of Wittgenstein. It's not an attempt to correctly capture what he thought out of the elusive text he wrote. This thread is about considering a Kripkean challenge.

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.

New rule: replace an a with an i.

All the talk of rules seems overdone. This just comes down to counting, as I showed in my last post. It pays to remember that arithmetic used to be done on an abacus. Some animals can apparently do rudimentary counting; should we think they are following rules?

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

That's wonderful. There's probably a calculator program already on there, though. See if you can find it. :cheer:

Show some fact about your previous usage of "plus" that demonstrates that it wasn't "quus." — frank

These analytic truths are arbitrary, so there is no correct usage outside your agreed upon rules.

You chose 57, but 59 would have been better because the number after 59 is in fact 1:00.

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?

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

Ah right. Well, in that case, if I'm disregarding the obvious silliness of the whole thing, then I would think about the sorts of problems I was trying to solve with addition, and think about it those sorts of problems would be solvable by quaddition.

Perhaps I used addition once to count how many apples me and my brother picked together. I picked 5 and he picked 10, so together we picked 15. I'd then think, would quaddition give me the correct answer? In this case, yes, but in the case where one of us picked 57 or more? No, clearly not.

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.

https://as.nyu.edu/content/dam/nyu-as/philosophy/documents/faculty-documents/boghossian/Boghossian_Rule-Following-Considerations.pdf

A summary and survey of the literature.

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

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.

You chose 57, but 59 would have been better because the number after 59 is in fact 1:00. — Hanover

:lol:

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

For Kripke's challenge, we want a fact that shows intentional rule following. This entails justification and correctness. We usually wouldn't look for that kind of rule following in a planet because we imagine they just blindly do what they're going to do and we identify a structure in it. We then use that historic structure to predict where it's headed (which is what technical analysis of a market is, btw.)

An example of a fact that might work is dispositionality: which says it's a fact about the world that you have a predisposition to answer "125" instead of "5". That kind of thing.

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

He grants that there's such a thing as the practice of addition. He's asking for a fact that shows you've actually adhered to this practice as opposed to the practice of quaddition.

if I'm disregarding the obvious silliness of the whole thing — flannel jesus

I'm finding it to be pretty mind blowing, but I can see how it would seem silly to some.

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

In the challenge, addition and quaddition produce the same results up to 57, and that's as far as you've ever gone. If there is no fact about which one you were doing all this time, then it shows that if meaning arises from rule following, there is no meaning. That's the crazy part.

There is more than one sense in which we say someone is following a rule. If I if I ask a child what the rule of counting is more than likely she cannot state a rule but will simply demonstrate how it is done by counting.

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. Addition is an operation that generally solves all such problems, regardless of if they're above or below 57.

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. I have a good argument for why I've been using addition. What's the counter ?

Addition is a specific algorithm. Quaddition is another specific algorithm. If someone's telling me that I'm wrong about what algorithm I'm using inside my head, and the algorithm they think I'm using is some arbitrarily complicated thing I've never even heard of before, they better have a good argument.

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

In the challenge, you've never dealt with numbers above 57. Addition and quaddition give the same answers up to that point. The question is: what fact would show us that you were adding and not quadding?

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

If I could give you a fact about which rule you were following, then the challenge would fail. I think I need to flesh out the criteria a proposed fact has to meet in order to crash the challenge. I've just been busy lately. Need to collect the army of brain cells.

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.

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

That's correct.

It does occur to me to say that I'm relying a lot on the SEP article as I read along. It gives a broader context than I would have on my own. A deeper look at the PLA is also a good idea.

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?

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

That there is no fact about which rule you were following.

In the challenge, addition and quaddition produce the same results up to 57, and that's as far as you've ever gone. — frank

Do they? What about 68 + 1? I mean 68 is the outcome of, say, 30 + 38. I need to do addition to be able to do quaddition; I don't need to be able to do quaddition to do addition.

So if I'm asked to "add 68" that wouldn't make sense und quaddition.

True: 68 = 57 + x
False: 68 = 57 quus x (that's always 5)

So how does addition flow into quaddition? What's the rule here? Which of the following is correct:

1 quus 68 = 5
1 quus 68 = 6

I can argue for both, but I don't know enough about quaddition to decide on my own. I'm way more familiar with addition. This may be the result of an unnoticed stroke, though. Who knows?

That there is no fact about which rule you were following. — frank

If what is being done is in accord with addition then it does not matter which rule one thinks they are following.

The fact that Kripke is able to make a distinction between addition and quaddition means that there is in fact a discernible difference. No arbitrary rule imposed under conditions that do not occur should lead to skeptical confusion.

It goes like this:

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

:up:

On page 11, Kripke talks about the criteria the wanted "meaning fact" would have to meet:


"In the discussion below the challenge posed by the sceptic
takes two forms. First, he questions whether there is any fact
that I meant plus, not quus, that will answer his sceptical
challenge. Second, he questions whether I have any reason to
be so confident that now I should answer '125' rather than '5'.
The two forms of the challenge are related. I am confident that
I should answer '125' because I am confident that this answer
also accords with what I meant. Neither the accuracy of my
computation nor of my memory is under dispute. So it ought
to be agreed that ifl meant plus, then unless I wish to change
my usage, I am justified in answering (indeed compelled to
answer) '125', not '5'. An answer to the sceptic must satisfy
two conditions. First, it must give an account of what fact it is
(about my mental state) that constitutes my meaning plus, not
quus. But further, there is a condition that any putative
candidate for such a fact must satisfy. It must, in some sense,
show how I am justified in giving the answer '125' to '68+57'.
The 'directions' mentioned in the previous paragraph, that
determine what I should do in each instance, must somehow
be 'contained' in any candidate for the fact as to what I meant.
Otherwise, the sceptic has not been answered when he holds
that my present response is arbitrary. Exactly how this
condition operates will become much clearer below, after we
discuss Wittgenstein's paradox on an intuitive level, when we
consider various philosophical theories as to what the fact that
I meant plus might consist in. There will be many specific
objections to these theories."

So

1. We need a fact that explains why I'm compelled to answer 125.

2. We need a fact that contains the "directions."

It is reassuring to know that we have saved addition from Kripke's skeptic ... at least for the time being.

First, it must give an account of what fact it is
(about my mental state) that constitutes my meaning plus, not
quus. — frank

Here I think he is simply wrong. My mental state and whatever my meaning might be has no bearing on how to properly add numbers.

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

It goes like this: — frank

Yeah, I've read this. I guess I shouldn't have posted. (I'm still confused about the meaningfulness of "68" from a quus-centric world-view, but that might just be marginally on topic.)

The answer is 42, I guess.

It is reassuring to know that we have saved addition from Kripke's skeptic ... at least for the time being. — Fooloso4

Ha ha! Yea. Except it wasn't addition that was in danger. :wink:

The answer is 42, I guess. — Dawnstorm

As always. :razz:

There are two subjects I'm going to branch off into, one is the reductive theory of meaning, and the other is normativity of meaning. So this thread is probably at an end for now. :yikes: