Hume, Nabokov, and Rule-Following

For those of you who don’t know me, my name is Daniel Moerner, and I’m a freshman studying philosophy and computer science at Pomona College. I first got into philosophy as a Lincoln-Douglas debater in high school. It’s probably fitting that my first post is a continuation of the debate about rule-following.

Recall Kripke’s attack on the dispositionalist defense of rule-following. According to the dispositionalist, the fact that we are predisposed to follow addition, rather than quaddition, is enough to establish that we are in fact using addition in this application. Kripke makes two answers to this: First, that dispositions are descriptive accounts of mental states, which can’t justify a normative statement as to why we ought to apply this rule rather than any other in this case. Second, dispositions are finite, whereas rules are infinite. I want to focus on this second point. Paul Boghossian summarizes it fairly well:

“Why are facts about how a speaker is disposed to use an expression held to be insufficient to determine its meaning? Kripke develops two sorts of consideration. First, the idea of meaning something by a word is an idea with an infinitary character—if I mean plus by ‘+’, there there are literally no end of truths about how I ought to apply the term, namely to just the members of this set of triples and not to others, if I am to use it in accord with its meaning. This is not merely an artefact of the arithmetical example; it holds for any concept. If I mean horse by ‘horse’, then there are literally no end of truths about how it would be correct me to apply the term—to horses on Alpha Centauri, to horses in Imperial Armenia, and so on, but not to cows or cats wherever they may be—if I am to use it in accord with its meaning. But, Kripke, argues, the totality of my dispositions is finite, being the dispositions of a finite being that exists for a finite time. And so, facts about dispositions cannot capture what it is for me to mean addition by ‘+’.” (Paul Boghossian, “The Rule-Following Considerations”, p. 509)

For those who are interested, I’ve appended at the end of this post an alternate defense of the finite nature of dispositions that Boghossian himself provides.[1]

Now, read this fragment by David Hume, written more than 200 years before Kripke:

“It may now be ask’d in general, concerning this pain or pleasure, that distinguishes moral good and evil, From what principles is it derived , and whence does it arise in the human mind? To this I reply, first, that `tis absurd to imagine, that in every particular instance, these sentiments are produc’d by an original quality and primary constitution. For as the number of our duties is, in a manner, infinite, `tis impossible that our original instincts should extend to each of them, and from our very first infancy impress on the human mind all that multitude of precepts, which are contain’d in the compleatest system of ethics. Such a method of proceeding is not conformable to the usual maxims, by which nature is conducted, where a few principles produce all that variety we observe in the universe, and every thing is carry’d on in the easiest and most simple manner. `Tis necessary, therefore, to abridge these primary impulses, and find some more general principles, upon which all our notions of morals are founded.” (A Treatise of Human Nature,

Just consider the italicized portion. Notice any similarities between Hume and Boghossian? At first glance, Hume seems to be exactly foreshadowing Kripke’s argument. Our infinite duties—which are defined by rules—cannot be defined by our first instincts (that is to say, our dispositions), because those instincts are of a finite nature. Of course, after this point, the argument diverges. Hume does not pursue (or perhaps realize) the possible radical consequences of this argument. First, he seems to think that applications of deductive logic to laws of the natural world are immune from this problem. For Hume, the problem is constrained to the limited realm of moral principles, which can’t be found as facts anywhere in the world. Second, Hume believes that we can in some way expand upon our impulses and derive general principles for our moral rules.

But notice how strange this last sentence is. If someone told me to “abridge these primary impulses” in favor of more “general principles”, what would I do? I would apply practical reason to the question and try to form some sort of general idea about the content of morality. However, Hume is the same man who wrote that “reason is the slave of the passions”. So what does he mean? If Hume has a way to to save morality from his limited pseudo rule-following line of thought here by generating these more general principles from the passions, without biting into his own argument, and without appeal to practical reason, then he seems to have found one possible solution to the more general rule-following paradox.

Truth be told, I don’t know if he has an answer. I need to read more Hume. However, I think it’s more likely that he does not. I’ve just downloaded a paper by Kieran Setiya [2] which argues that Hume actually defends a limited account of practical reason. According to my brief read of that paper, it seems like this section of the Treatise would be very strong support for Setiya’s belief, since it’s hard to think how Hume can defend these more “general principles” without practical (or, heaven forbid, theoretical) reason. I’m meeting with a professor in two weeks to discuss this; I’ll post here if this leads to any new insight.

My last thought on dispositions to follow rules right now is a quote from Vladimir Nabokov:

“When commonsense is ejected together with its calculating machine, numbers cease to trouble the mind. Statistics pluck up their skirts and sweep out in a huff. Two and two no longer make four, because it is no longer necessary for them to make four. If they had done so in the artificial logical world which we have left, it had been merely as a matter of habit: two and two used to make four in the same way as guests invited to dinner expect to make an even number. But I invite my numbers to a giddy picnic and then nobody minds whether two and two make five or five minus some quaint fraction. Man at a certain stage of his development invented arithmetic for the purely practical purpose of obtaining some kind of human order in a world which he knew to be ruled by gods whom he could not prevent from playing havoc…Then, as the thousands of centuries trickled by, and the gods retired on a more or less adequate pension, and human calculations grew more and more acrobatic, mathematics transcended their initial condition and became as it were a natural part of the world to which they had been merely applied. Instead of having numbers based on certain phenomena that they happened to fit because we ourselves happened to fit into the pattern we apprehended, the whole world gradually turned out to be based on numbers, and nobody seems to have been surprised at the queer fact of the outer network becoming an inner skeleton” (Vladimir Nabokov, Lectures on Literature, p. 374).

I think it’s no surprise that Rorty is so enamored of Nabokov.

[1] Here is Boghossian’s other denial of infinitary dispositions. I think this is a paradigmatic example of the techniques that Kripkean scholars use to attack defenses of rule following:

“And we are certainly in no position now to show that we do have infinitary dispositions. The trouble is that not every true counterfactual of the form:
If conditions were ideal, then, if C, S would do A
can be used to attribute to S the disposition to do A in C. For example, one can hardly credit a tortoise with the ability to overtake a hare, by pointing out that if conditions were ideal for the tortoise—if, for example, it were much bigger and faster—then it would overtake it. Obviously, only certain idealizations are permissible; and also obviously, we do not now know which idealizations those are. The set of permissible counterfactuals is constrained by criteria of which we currently lack a systematic account. In the absence of such an account, we cannot be completely confident that ascriptions of infinitary dispositions are acceptable, because we cannot be completely confident that the idealized counterfactuals needed to support such ascriptions are licit.”


2 Responses to Hume, Nabokov, and Rule-Following

  1. Brian says:

    Boghossian’s first quote makes me more inclined to agree with Dennett that the deliberations over rule-following are “great labors wasted in trying to break down an unlocked door.” Why should my concept of “horse” apply to horse-like animals in Alpha Centauri? This seems to assume an essentialism that good Darwinians can’t take seriously. My concept of a “horse” is not a perfect representation of an Immutable Natural Kind. Rather, my concept of “horse” is an underdeveloped representation of a loose collection of animals that are similar enough for a useful lumping together under one concept. Once we acknowledge this, it is no longer problematic that the concept of “horse” is often indeterminate in its applications. This dissolution seems more obvious with the example of “horse”, but much harder to apply to mathematics. This may just mean we have to “dethrone” math in some way (although personally, I am intuitively horrified by that prospect – but I recognize that my intuition is not a substantive argument).

    Right now, my questions can be reduced to:
    1. Does math or any branch of knowledge have any “superior” status? Can a pragmatist believe in a spectrum of justification, so that the claim 2 + 2 = 4 is more justified than the claim that horses are mammals? And if such a spectrum exists, what standards should we use to judge a claim’s place on that spectrum?
    -How, psychologically/sociologically (i.e. functionally), is communication in a world of under-determined concepts possible?

  2. Andrew Chesley says:

    Steven Landsburg has something crazy to say in response to your first question:

    “I take my stand with those who believe that ‘two plus two equals four’ is not a truth about stones or about physical objects generally, but a truth about numbers, which existed long before there was anyone around to count with them. The philosopher Paul Benacerraf once proposed a thought experiment [party] that neatly distinguishes the two points of view. Suppose you put two stones on your kitchen table, then two more, then count and discover that there are five stones altogether… over the course of the day, the same thing keeps happening… You climb two flights of stairs from the basement, then another two, and somehow you’re on the fifth floor. Eventually you’re forced to conclude that something has drastically changed. But what? You might say that mathematics has changed–two plus two used to make four, but now it makes five. Or you might say that physics has changed–two plus two make four, just as always, but the physical world no longer seems to care… If, like me, you view the laws of mathematics as necessary truths… instead of throwing out the old math, you’ll want to throw out the old physics. The old physics said that when you put two bunches of objects together, you could predict the total by using addition. Te new physics says you’ve got to use something more complicated than addition. But addition itself has not changed” (Kindle loc. 235-255).

    And the money shot: “I believe then, that arithmetic is both immutable and necessary. Numbers exist, and they exist becaus they must… Mathematical objects–such as the natural numbers and the laws of arithmetic–are real” (Kindle loc. 255-265).

    This seems intuitvely appealing but is obviously lacking in any substance. I’m not sure if I agree with him, but Landsburg seems to be saying that math does have a “superior” status compared to other branches of knowledge. I’m kind of lost in the overall rule following debate, so I won’t make any conclusions based upon his argument. I leave that to those more well informed than I.

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