On Rules

Do we need to know a rule in order to follow it?

Everyone can perform simple addition. We would all agree that in base 10 numbers 2+2=4 and 1+1=2. We can also agree that there are numbers which we, and for that matter all human beings, have never added.

For the sake of argument let us state that 57 is the largest number a human has ever added. Assuming this to be true then what would 57+68 equal? That’s simple enough. Even though we have never added numbers larger than 57 we can use our past experiences to determine that 57+68=125.

What if I told you that 57+68 is actually equal to 5? Saul Kripke argues that we may actually be doing quaddition instead of addition. The rules for quaddition are quite simple:

  • x quus y = x plus y for all x, y < 57
  • x quus y = 5 for all x, y > 57

Kripke argues that as we have never added numbers greater than 57 before, we may have inadvertently been following quaddition our entire life. There is great overlap between quaddition and addition. For all numbers less than 57 quaddition and addition are equivalent.

The simplest way to attempt and defeat this argument is to state that you were indeed adding and not quadding 57 and 68. We can even break addition down to its simplest form, counting.

When adding these two numbers we are actually counting 57, counting 68, combining the two, and counting the total. 57 plus 68 is equal to 125 because when 57 items are combined with 68 items and counted, we find we have 125 items.

Kripke’s response to this is that we do not even know if we are counting the objects. In fact, while we thought we were counting 125 we were actually quonting the objects. What is quonting? It is similar to quadding. When quonting objects we need to follow one specific rule:

n = number of objects being quonted
If n > 57 then n = 5
Else n = n

When quonting our objects we once again find that 57+68=5.

I am going to stop with Kripke’s argument at this point and once again ask my question: Do we need to know a rule in order to follow it?

In a court of law it is understood that even if one does not know a law one can break it. I can be found guilty of libel without understanding the logistics of libel law. Does the same fall true outside a court of law?

Can I perform quaddition without understanding the rules behind it? Can I quont numbers without understanding what quonting is? Do we need to know a rule in order to follow it?

22 thoughts on “On Rules

  1. There are days that I worry I think about about things a little too much and then I read one of Etan’s submissions and I feel pretty much normal again. wink

    Honestly, I think the answer to this question is self-evident. Being that rules are constructs of human society that restrict or promote behaviors depending on the perceived value they hold it’s certainly possible for someone to act in a way that is in compliance with a rule they have no knowledge of.

    As an example, I have a tendency to say “Howdy” when greeting people. If I were to visit Texas I’d probably greet most folks there with a smile and a “Howdy” just as I do everywhere else, but suppose Texas were to pass a law that makes “Howdy” into the only legally approved greeting you’re allowed to use in the state and I somehow missed this idiotic bit of legislation before my next visit. If I stay true to form then I’m likely to continue to greet people with a friendly “Howdy” regardless of the law and my compliance with that rule would be independent of my awareness of it.

    Rules have no intrinsic value of their own and how likely we are to follow a particular rule is entirely dependent in how much value we see in it. This is why a solid reasoning for the rules we opt to encode in our legal system must be part of the process if we are to convince others of the value of following that rule.

  2. I just want to add an addendium and state that I have cut Kripke’s wonderful skeptical argument short. I only say this because the thread of comments on my personal site has begun to take a route which attacks Kripke’s argument and I find this to be slightly unfair as it is not his full argument.

    I intended for this to be fodder for a discussion on following rules. If people are interested I will try and continue Kripke’s argument at a later date (when it isn’t 7:30 AM smirk ) or you can purchase a copy of Wittgenstein on Rules and Private Language and read it yourself.

  3. Yes, you need to know the rule in order to follow it.  You do not need to understand the reasoning behind the rule but you need to know it to follow it.

    If you do what the rule states without knowing about the rule then you are not following the rule but something else – inadvertently following that rule would not, in this case be a causal relationship because you would be following some other rule.

  4. Do we need to know a rule in order to follow it?

    No, because we may follow a rule by coincidence. On the other hand, to follow a rule consistently requires at least an intuitive, perhaps even subconscious understanding of the rule.

    Kripke’s argument seems pretty weak, but I’m not awake enough to have a go at it.

  5. Surely if quaddition and addition are the same for values up to 57 (and we’ve never gone higher than that) then up until now we have been performing both quaddition and addition.

    Now the time has come for us to choose a system and we may either use quaddition or addition, but not both.  You cannot say “perhaps you have been using quaddition when you thought you were using addition” because they’re identical.

    To contrive a system in order to make a point about rules seems bizarre, especially when addition isn’t a rule it’s a definition.

  6. Les wrote:

    > it’s certainly possible for someone to
    > act in a way that is in compliance with
    > a rule they have no knowledge of.

    True, but I would argue that the point of rule following rather is not breaking any of the rules that one is aware of. “Following” of a rule without awareness of it is purely accidental and I wouldn’t even use the term following a rule in such a context (hence the quotation marks). On the other hand, it is certainly true – as Etan has pointed out – that one can break rules that one is not aware of.

    Well, maybe I didn’t fully understand Etan’s question/intention in the first place.

  7. Maybe I’m missing something, having not purchased the book and read the full argument, but based on what Etan presented here, Kripke’s reasoning is entertaining but silly.

    Kripke, if I understand correctly, makes a distinction between “actual” addition, addition we have “actually” done, and “quaddition”, addition we have never “actually” done, but have merely (mistakenly) assumed to follow the extrapolated reasoning of “actual” addition.  He then claims that quaddition has different rules than addition, and we have no reason to suppose, following his example, that 57+68 is 125 rather than 5.

    This is funny but just silly.  This is exactly like supposing that we live in a world where the sun comes up in the East every day, until December 9, 2004, when it will come up in the West.  Impossible to logically disprove, but fully unmotivated, and contrary to everything we have learned about the useful extrapolation of logic.

  8. etan queried: Do we need to know a rule in order to follow it?

    I would say that the question is ill-formed.  What do you mean, exactly, by “know”?  Does a non-mathematical outfielder “know” that y=x squared, or is the parabolic trajectory of his throw to second base the result of some other kind of knowledge?  Do we “know” how to digest?  Does hemoglobin “know” how to transport oxygen?  It all depends on what you mean by “know”.

  9. DoF- no, I don’t think Etan is referring to that kind of secret law, although I must confess I’m not sure what Kripke’s point was either.  In any case, your link is chilling, and I was having such a good day… thanks a lot, DoF…

  10. If you are unknowingly following a rule, IMO you are not following it.

    Lets look at it this way.

    I am meandering through New York City streets. A woman in front of me is walking from Macy’s on 34th street and herald square to Grand Central Station on 42nd and Madison.

    I realize that I need to meet Foobar at his office at 42nd and Madison.

    We both walk the exact same route, making the exact same steps and stops; but I am *not* following her. We have the same destination that each seperately came to require without foreknowledge or communication.

    Coincidence is not the same as following the law. To “Follow a Rule or Law” IMO takes a conscious thought and action, otherwise it is just coincidental that you ‘followed’ it.

    I hope the above makes sense… I haven’t had my coffee yet smile

  11. What about the ‘Laws’ of thermodynamics?  Is a closed system aware of these laws, such that it follows them?  The answer, obviously, would be “No.”  The system has no consciousness, therefore no awareness, yet it follows these laws nonetheless.

    The fact is that the ‘Laws’ of thermodynamics are human constructs that explain behavior.  Likewise, any law or rule is a human construct.  It would certainly seem that I could comply with the law without awareness of it.

    For example, a person is raised in an isolated rural community, where he is taught that the Squarkmeth Tome (the holy book of the People) is the only law that applies to man.  This tome contains no restrictions on the ability of the People to kill.  He leaves this isolated community and goes to live amongst the Heb-hebs (what they call outsiders) in Illinois.  Now, so long as he doesn’t kill anyone, he is obeying the law of the US and the State of Illinois, without any awareness of it.  If he kills, he will not break the law of Squarkmeth, but he will be incarcerated in the Illinois correctional system, nonetheless.

    If you can break a law without being aware of it, you can comply with it without awareness just the same.

  12. Addressing Mr. Hoke’s response here:

    We both walk the exact same route, making the exact same steps and stops; but I am *not* following her. We have the same destination that each separately came to require without foreknowledge or communication.

    Is this really analogous to following an unknown rule? I don’t think it matches up all that well.

    For starters the only things proscribing that you both take the same path and end up at the same destination would be the fact that you were in similar starting positions with similar destinations and made similar decisions on the optimal route to take. There isn’t anything in that example in the way of a defined rule saying it was the only route you could take which either of you could have broken due to ignorance. If either one of you happened to decide at some point along the way to suddenly deviate from the other’s path and take a few extra side streets to the destination, well, that’d be OK too because there’s nothing that says you can’t or shouldn’t.

    This is as opposed to the idea that she was taking that route because of an established rule that specifically said it was the only route she should follow whereas you are ignorant of that rule and only followed that route because it seemed like the proper thing to do given your circumstances.

    Coincidence is not the same as following the law. To “Follow a Rule or Law

  13. It’s all in the word follow.

    If you FOLLOW a rule than you most probably are aware of it.

    If you are unaware of a rule but you end up with the same result. Than I say you have used common sense.

    Many rules have been written around common sense.

    There are exceptions to rules everywhere and there are also accidents.

    …crossing the street at the green light…

    A blind man/woman does not see the green light but he can hear the direction of traffic which can tell him when to cross the street…which will in return become a personal rule to cross the street only when he/she hears the cars moving in the same direction as him or her. Even though he or she will be very careful, they can still get hit by a car due to a driver not looking and turning aroung the corner.

    -Not sure if it makes any sense.

  14. Les:

    Is this really analogous to following an unknown rule? I don’t think it matches up all that well.

    You are probably right, but in my undercaffinated haze what I was trying to get across, just because it appears that someone is following something, the fact could be it is a coincidence.

    Unknowingly adhereing to something is different than actively following something

    This makes it into an issue of intent which is actually taken into consideration in many court cases. Indeed, “intent

  15. I’m with John on this one.  I think that our actions may comply with a given set of rules without knowing what the rules were to begin with.  To actually follow a set of rules one must know what the rules are to begin with.

    I’ve worked with companies that are in compliance with SEC rules that had no prior knowledge of some of the rules.

    To oversimplify:  You move into a neighborhood where the housing association has a rule that all homes must be painted either tan, green or blue.  You have not read the bylaws but choose to paint your house green.  You are in compliance with a rule without actually following it.

  16. You either violate a law, or you do not violate a law.  Intent and knowledge are irrelevant.

    Just because you don’t consciously acknowledge the law and say, “today I will not kill, because to kill would be against the law,” does not mean that you are not following the law.  You are not in violation of the law, therefore you must be obeying the law.

    There are laws of action and inaction.  To obey a speed limit, you must make a conscious choice and act, by applying a specific amount of pressure to the accelerator and watching the speedometer.  To obey the law “do not kill” (a simplification for argument’s sake), you simply have to NOT act on your urge/desire/proclivity to kill.

    The argument that will or knowledge is a component seems absurd to me.  In our human, American legal system it may have ramifications for sentencing, etc., but that isn’t the question.

  17. The quaddition example is a poor example because it invalidates many of the mathematical properties of addition:
    – it is not associative: 56 + ( 2 + 1 ) != ( 56 + 2 ) + 1
    – it does not have a true additive inverse: 6 + ( 0 – 6 ) = 0, but 58 + ( 0 – 58 ) = 0 and 58 + ( 53 – 58 ) = 0 and 58 + ( -53 – 58 ) = 0, all depending on when you convert >57 -> 5

    Therefore, quaddition would not form a group, an abelian group, or a ring.  Pretty much any mathematical proof relying on addition would be false if it turned out that we were using quaddition instead of addition.  Bridges would start falling down, buildings would collapse, bad things would happen.

    Luckily, as Chris pointed out, addition is a definition and cannot be broken.  Same goes for scientific laws.  Trying to draw an analogy from this to societal rules is thus invalid, as societal rules can be broken.

  18. Ok, I took the time to read Kripke’s Sceptical Paradox and Solution, and I still don’t see the paradox.  Maybe you have to be an epistemologist, but it seems to me just so much sterile construction of words talking about words, chasing their tails merrily, but with no foundation in the real world- a problem, I must confess, that I have with a great deal of philosophy.

    This, IMHO, is what happens when people speculate about such entities as rules and meanings without considering evolution and engineering- the reason we have rules and meanings at all.  You can’t understand rules and meanings merely on the basis of more rules and meanings- you just run in circles.

  19. What the Greeks, especially Plato, understood about words applies to your comment.  That words are merely a sort of allegory for ideas, so often a discussion which bases itself on words is really a discussion which bases itself on ideas.

    By the way, Philosophy relates to the real world a great deal.  Of course smile , that depends on how we define the “real world.”

                    -:smirk:-Commander Puffin

  20. That words are merely a sort of allegory for ideas, so often a discussion which bases itself on words is really a discussion which bases itself on ideas.

    Scary Squirrel (do you mean like Kathy in “Squirrel Kombat”? Never mind…): I guess I have the same problem with “ideas” in philosophy that I do with “words”- all too often, concepts that are merely logical constructs are manipulated, a logical conclusion is reached, and this conclusion is held to demonstrate something about the real world. A lot of philosophising about free will, for instance, has this character.
    And following, say, Plato’s dictum of “carving Nature at the joints” is fine, as long as one is aware that sometimes there are no joints to carve.  Looking at the world through essentialist glasses filters out a lot of life- it’s not that simple.  That’s the basic problem I have with a lot of philosophy that’s not grounded in natural science.

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