Kripkenstein! (The Rule Following Paradox)

An explanation of Kripke's Interpretation of Wittgenstein's Rule Following Paradox, as outlined in Wittgenstein on Rules and Private language, known colloquially as Kripkenstein.

Sponsors: João Costa Neto, Dakota Jones, Joe Felix, Prince Otchere, Mike Samuel, Daniel Helland, Mohammad Azmi Banibaker, Dennis Sexton, Yu Saburi, Mauricino Andrade, Will Roberts and √2. Thanks for your support!

[kendogbsc]

It's not Kripkenstein, it's Kripkenstein's *monster!* Kripkenstein is the person who created the monster. How many times do I have to correct people? Geez...

Just kidding!
Hey I really am!

[avatarmage]

Thank you, this was a very clear explanation. Glad I finally found it! Why do so many people have to present philosophy in confusing ways...

[charliesteiner]

Like many problems in epistemology, this makes a lot more sense once you know about a certain formalization of Occam's Razor, called Solomonoff Induction. Long story short, there are good reasons to treat simpler rules as more likely, and so you can arrive at some degree of confidence that someone is following a certain rule (this creates a second skeptical paradox about how one defines simplicity, which one does more or less have to accept at least provisionally).

[bernardquine]

The original experiment was used by Putnam in his «The meaning of ‘meaning’» for explaining that the intentionality component do not determine the meaning of the terms we use, because given two possible worlds in which earth (1) people use “water” in the same way earth (2) people use “water”, the superficial “water” every person knows, but without knowing that water in earth (1) has a different chemistry structure H20 to that of earth (2) called, let's said, XYZ. Ok, good point there. But then after, Putnam himself offers a theory of meaning dealing with the reference in a way that makes compatible the uses of the past, intuitive usage of daily, common people, with the very structures and relations we do know for the external, actual properties of a thing in our world. Basically, the meaning of water must contain the stereotype features, both superficial and deep, says Putnam, and referring them to a conception of a progressive, corrective semantic task open to scientific changes or other kind of changes in our usages, or concepts or whatever alike; given so, though two persons can use the word “gold” to refer different properties, let's say the convention of precious luxury at one hand and the chemical structure at the other, Putnam would simply says that meaning as stereotypical extensionality and common usage of concepts, terms and relations, is compatible with the social division internal to language. One person could use meaningfully the word “gold” with the first socially divided stereotypical extensionality (precious luxury) while maintaining part of the set of total stereotype extensionality the word “gold” has (precious luxury and the chemical structure). It could be accepted the double-content aspect of usage of meaning-rules simply by noting the degrees in the stereotypical extensionality a well community connected speaker is able to access. Note that if you try to set on the skeptical argument on the previous meaning rules used to determine whether a well community connected speaker is using correctly a word, by the community itself or a member of it, it would follows the same solution the Putnam's theory of meaning is offering the same stereotypical extensionality for the meta-language that assign meaning to the object-languange as well to the object-languange in itself.

It seems to me strange why some people use that experiment to show that no meaning is guaranteed, since the very Putnam offered (as I see) a good and humble description of what a usage is and should be in order to apply to different, but similar cases of extensionality and at the same time being open to correct at temporal intervals.

In conclusion, Kripke solution is compatible with a non-skeptical interpretation of semantics if one goes with the Putnam's theory of meaning, which allows both the reference and the equivocation derived from a given stereotypical extensionality (let's say, the alchemist stereotypical extensionality in “gold”).

[mikevsamuel]

By the way, relevant to "is there any way that we can determine if someone is following one rule over another?" There's a sub-field of cryptography called secure multi-party computation which Wikipedia describes as having "the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private." If a rule player were computing a different function, these algorithms bound how many steps might complete before cheating is identified. IIRC, this usually assumes that at least 50% of parties are not cheating.

[mikaelthesleff]

This paradox seems closely related to the general issue of verification of scientific laws. As we know experimental verification of a law in particular instances is not sufficient to establish its validity beyond doubt, but if some falsification criterion could be devised for a particular rule, that should in principle solve the problem at least regarding that rule.

[ZeroG]

You can only test if a rule was broken, not if it was followed. By the way, that's a rule.

[John-lfxf]

That seems pretty easy at 5:12.
We can just have someone copy a machine which provably uses some rule.
Construct a Turing machine which inputs (a, b) and outputs a+b using the standard definition of addition. For a proof system of PA, S, there is a proof that this Turing machine M computes the addition (or as prior stated, we could just define it to be the output of this machine, that is, a+b = m iff M(a, b) = m). There are many algorithms which will do this.

A person can do addition, plug the inputs in, and then sticks with your output if and only if it is equivalent to the algorithms output.

[plasmaballin]

Maybe you can be following multiple rules at once. If you are looking at a case where addition and chaddition are the same, then giving the correct answer would be following both rules.
Or, maybe following rules is based on what goes on inside your head. When I compute 2+3=5, the mental algorithm I use does not include a step of checking whether the problem includes 398, 667, so I am not following the rule of chaddition.

[greggorsag]

Great video.

A metaphorical way to understand this is to consider language as the most addictive intoxicant that we know of. It gives us the incredibly powerful, but hallucinatory, conception that it allows us to refer precisely to an external reality, when it actually only allows us to do things (sometimes very complex things, like science). That’s not to say that there is no such thing as external reality, or that we can’t talk about it meaningfully, but just that we can only do so in vague and philosophically unsatisfying ways. Unless quite drunk (on language).

All one really has to do is read Hume, then the Investigations (many times), after perhaps skimming the Tractatus. Kripke is very smart, and helps as a third step if necessary. But Wittgenstein is written as a DIY manual and it’s more fun that way. But it can be challenging; thus the need for repeat struggles (at least for me!)

As to your question: Does it matter whether we can speak truth about the world? That depends. Do you mean “truth, ” or “quuth”?

(Full disclosure: I got an MA in Philosophy and read Wittgenstein toward the end. Dropped the PhD program and went to law school.)

[ericborsheim]

In the case of math, I think that it works with a simple solution that people do not know the definition but rather have a rough understanding of the concept and an agreement on who to ask if they are unclear about the definition (that is mathematicians who use a formal definition). This applies for math but it does not apply for rules such as H2O is Water.

For a posteriori rules I think that the best thing is to take a position where one sees empirical general propositions as having a characteristic of a fractal domain where every universal proposition has an infinite set of interpretations based on an infinite set of possible domains which are in most cases inconsequential. Only when the distinction becomes meaningful does there become a clear distinction in the rules, and until then there will just be equivocation between the members of the set.

[JackPullen-Paradox]

What about identifying the algorithm; then test them on application of each facet of the algorithm. That doesn't prove the rule, but it would come closer.

[carlosmendes]

Hmm, in more formalized terms (by maths and computer science) this is the Entscheidungsproblem. Alan Turing and Alonzo Church gave the answer: in some instances, yes, it is possible to have a fact (proof) that a rule is being followed correctly. However, it is proven that there is NO UNIVERSAL PROCEDURE to assert that, for any given rule, whether it is being followed correctly.

[veritopian]

I think the answer to this paradox is it contains a fallacy of false premise.
It conflates the concept of "a independent rule", with the concept of "a set of dependent rules".
E.g: The rule of addition (plus) is single, and universal, and independent of quantity. It's a qualitative rule.
But the rule of "quus" is not a rule, it's a set of rules. It contains exceptions. It's a quantitative rule.
So the paradox is invalid because a universal rule is the opposite of a rule with exceptions.

Does that make sense?
Great vid. Thanks.

[mikevsamuel]

"Humans use checklists or written recipes when rules get above a certain complexity" seems to be a fact of the world. "The set of rules that fit within a human's working memory is finite" seems to be another fact of the world. Knowing that and that the human is not using a memory aid would seem to make addition more likely than chaddition and plus more likely than quus. This might be formalizable in terms of a Shannon-coding argument: the average size of minimally-encoded Turing machines that implement addition is smaller than that of those that implement chaddition is a fact of the world. We can accept Quine's argument that no finite number of sentence exchanges will give us complete confidence that the exchangers have the same definition for a term, but we can bound some definitions by reasoning about the kinds of definitions that human minds produce which is theoretically learnable without recourse to sentence exchange.

[otakurocklee]

I have a couple of questions:

1. I have memory of what I did in the past. So I remember that I used plus and not quus. My behaviors may be the same in both situations. But my memories wouldn't, since quus requires checking whether the numbers were greater than 57. So why can't this be evidence for which rule I was following?

2. If the solution amounts to "assertion", then why does it matter if the assertion is done by a "community" or a single person? I don't see the significance of "private vs public" here. We are by fiat declaring the public assertion declares "rule-following"... we can just as easily say assertion by a single individual declares rule-following.

[sethapex]

there is no way to say that someone is ALWAYS using words in the way that they seem to be, but there are situations that are possible in our experience of the world where we can be certain that someone is using their words to mean what they seem to mean. These situations have very precise conditions and might be difficult to set up, but they are possible. One such test is to put someone into an all-white room with a single object and ask them what that object is. This would isolate their experience of the world to the object. If people outside that room give the same or a similar description of that same object, then we know that they are each using their words to mean the same thing.

[dj]

This argument reeks of sophistry and illusion to me, no matter how interesting it may sound at first. In a true Wittgensteinian spirit, we might be inclined to say that the paradox it poses results from a confused attempt to disentangle linguistic from mental meaning, in reference to concepts such as "rule following" and "objective facts" that determine and govern our ruke following practices. Paradoxically, in order to show that it amounts to a pseudoproblem, one cannot simply ignore it, and in order to resolve it we must somehow accept its initial conditions and the way the original argument was formulated in the first place. Krioke sees this, but - as mentioned at the end of the video - it seems that the doubts of a sceptic are still not completely subdued, and I think Wittgenstein was perfectly aware of this when setting up his argument. In my opinion, Wittgenstein succeeded in showing that objective facts cannot determine the correctness conditions that underlie our rule-following practices, but Kripke's solution that brings in the idea of intersubjective agreement doesn't sound convincing to me. Some rules might be such that they are are determined solely by sociocultural norms, but surely not all are (or at least should be for that matter). Why do I believe that I am using the rule of addition when I am adding two numbers together, and not some other rule? Because I was told what the meaning and process of application of that rule was when I was a kid, and that rule hasn't failed me so far in terms of yielding relieble and correct results. Sure, I might mistakenly believe that I am using that instead of an entirely different rule, but I have no reason to suspect this - especially if I take into account that I know all the basic rules of arithmetic that are expected of me to know, and those rules alone can reasonably have any bearing on what I believe correctly or incorrectly follows when applying that rule.

[johnbalfour]

So, does this paradox as applied to addition (or subtraction, multiplication, division) call into question a claim of the consistent logic of mathematics no mater what figures are used?

[castlebravo]

Isn’t it also possible that there are no such things as “rules”? Could it be the case that definitions of things are purely for classification and have no objective basis? Is there any reason why I should classify “addition” as an operator that isn’t purely pragmatic? Could I be justified in defining “shmaddition” as performing 2 + 3 whereas “quaddition” is 5 + 7 and so on? This way there aren’t any rules at all and there’s no paradox. Seems like this type of paradox only reveals the absurdity of classifying things perfectly.