What's the core argument in Kripke’s “Wittgenstein on Rules and Private Language”?

Question

I’ve had a first light read of Kripkenstein and want to work through identifying what the key claims are.

The text is relatively short, and appears to be structured as:

1. Introduction. A warm-up.
2. The Problem: justifying why the central paradox is actually substantial and not trivial.
3. The solution.
4. An epilogue chapter further reflecting on the implications of the idea for “the problem of other minds”.

The “problem” appears to be based around a passage of the Philosophical Investigations in which Wittgenstein talks about a possible circularity in how we often conceive of “rule-following”, including in a mathematical sense.

Kripke’s central choice of example is considering asking someone to “do something” regarding two numbers: for 3 and 7, they return 10; for 6 and 15, they return 21. When someone sees this data, they may naturally assume the “rule” is addition. But Kripke adds in that after this assumption, it may be the case that as we consider more numbers, it turns out that for 111 and 115, the correct number to be returned is 5.

I think Kripke himself says in the introduction that there is something about the claim that “a pattern can not determined by data points” that can seem naive or trivial, and not like much of a deep philosophical observation; and yet he went from thinking that about Wittgenstein, to thinking about it on a deeper level and feeling like there was actually a significant, and non-trivial, argument to be made, here; maybe this claim is vindicated in the book.

Some initial ways to deal with the inability to ever distinguish between a plus-operation and some quus-operation seem to me to be:

1. Arguing that the plus-operation is not determined by an arbitrary collection of values; but that each value is generated by a procedure; so there is an inherent distinction between plus and quus;
2. But perhaps Kripke might be saying that even if that were true, we still would not be able to figure out if we were looking at the data of plus or quus when presented with some values.

So far, it seems like one can ask if this “aporia” is meant to be seen as inherent to any definition of “plus” at all, as in, that it is inherently impossible to even define addition in such a way that it is determined what 257 + 389 is, without just being given a listing out of all the values; or if the skepticism is something more on the linguistic level, or a matter of drawing inductive inferences based on observations; in that there is such a thing as addition, but no way to communicate or distinguish that that is the rule uniquely being followed, for some data. The latter might be seen to be more a mathematical statement about there being an infinitude of unique sequences containing any giving subsequence, for example.

I noticed there is a nice section where Kripke addresses the idea that addition is something determined by a rule that generates all the values, like a computer program; he seems to say that this “does not solve the problem”, because even then, when observing some data, you still have to postulate which algorithm is generating that data.

His solution to the paradox goes in a surprising direction - it comes to be a question not so much about “functions generating patterns”, but much more about the philosophy of mind and our ability to communicate intentions through language. There is an interesting section in which he explores some very Wittgensteinian ideas that it is actually incoherent or paradoxical to think that we can transfer our knowledge of one’s first-person experiences to imagined ‘others’; for example, the sensation of pain we feel, imagined as occurring in the conscious experience of another human; because - relating to Hume’s view - the “self” is not a clearly identifiable element in consciousness; instead of saying “I feel pain”, one could say “it pains”, like a verb without a subject; and so without that self-other distinction, there is nowhere coherent to transfer the phenomenal existence of “pain” to (or roughly this is the argument).

Thus, the key problem in the paradox seems to be that we could never impute a state of mind corresponding to “following this rule” vs. “following that rule” to an ‘other’; and so the reason the philosophical argument appears to be weighty, to Kripke, is not that it leads to a simplistic kind of universal skepticism, like, “We don’t ever truly know if any mathematical functions have consistent behavior”, but actually because it tells us something about the ideas of private language, consciousness and the problem of other minds.

But I don’t understand it clearly enough yet, so I would welcome some more exact discussion. Thanks.

Reference: https://iep.utm.edu/kripkes-wittgenstein/

Answer 1

Well your question here is completely rambly, there is a huge literature on this and it is in my view a centrally important topic of all philosophy. But what is your actual question?

I myself think both Kripke and Wittgenstein are deeply and fundamentally wrong in their view. But that should not stop me or you from understanding that view. For instance when you write,

“Thus, the key problem in the paradox seems to be that we could never impute a state of mind corresponding to “following this rule” vs. “following that rule” to an ‘other’; and so the reason the philosophical argument appears to be weighty,”

You must have realised the whole discussion in Kripke and Wittgenstein 130 to 300 is about whether you can justify yourself in following plus or quus.In my own opinion in a naturalistic theory of language we would not even need the justification condition. And such a theory would not also include mathematical practice.