A New Version of the Private Language Argument?

Ben Gibran
Science and Philosophy
17 min readJul 31, 2020
Photo by Simon Migaj on Unsplash

There’s such a vast literature on Ludwig Wittgenstein’s ‘private language argument’ (PLA for short) — almost 5,000 references in Google Scholar, excluding unpublished theses — that it’s impossible, in any realistic time-frame, to ascertain if the version I’m presenting here is a new one (hence the question mark). Life is short, so I’m just going to riff off the top of my head, and if this was originally someone else’s idea, then it’s their new version of PLA, not mine (in which case, I’m just explaining it in plain English). To quote Wittgenstein’s preface to the Investigations, “If my remarks do not bear a stamp which marks them as mine, — I do not wish to lay any further claim to them as my property”.

I call this a ‘version’ because it’s not an attempt at exegesis, at construing what Wittgenstein ‘really’ meant. It isn’t apparent that the Philosophical Investigations is a finished work and that Wittgenstein always knew what he ‘really’ meant either. After all, he referred to the book as a collection of “sketches”, and much of it takes the form of questions rather than statements. What is offered here is an argument that draws on the Investigations, but stands or falls on its own merits, quite apart from whether it’s a ‘faithful’ construal of Wittgenstein’s thought.

Much of the debate on PLAs revolves around what ‘private’ means. That’s where this PLA differs from many others. In this version, that’s not the main issue. Of course, it’s possible to argue about whether different kinds of private language are possible, depending on which definition of ‘private’ we choose. Some of those arguments are perhaps worth pursuing in their own right, but that won’t be done here.

This PLA focuses on rule-following, that it’s impossible to give oneself rules (I know that sounds counter-intuitive, but bear with me). Therefore, since languages are necessarily rule-based, it’s impossible to invent a language for oneself alone (I don’t mean a language that just ‘piggy-backs’ another language by substituting the entries in, say, an English dictionary with non-English words, while leaving the definitions in English, like what Esperanto does. I mean a speaker inventing a first language for him/herself in which all the definitions are also in that language).

What does ‘rule’ mean here? If someone believes they’re using a language, they also believe there’s something non-arbitrary in virtue of which they call an x an ‘x’ and not a ‘y’ in that language. By ‘non-arbitrary’, I mean it’s not the rule-follower just choosing randomly (by throwing dice, for example) or merely by his/her personal predilection or taste at that moment (like picking a dessert off a menu). I can call a cat a ‘dog’ or ‘shoe’ just because I feel like it, but that wouldn’t be semantically correct. Whatever that non-arbitrariness is that makes it semantically incorrect — or that makes anything non-arbitrary — that’s what ‘rule’ means here. An activity without rules cannot be a language.

Many scholars have made what I believe to be a mistake, in attempting to define ‘rule’ positively in their PLA. For example as some kind of regularity, convention, ‘community agreement’, ‘external criteria’, etc. They then go on to argue for or against the possibility of a private language based on that definition. I think that exercise will always run into either unhelpful vagueness or exceptional cases, because ‘rule’ in this case can only be defined negatively, as something to which choices can be subject, and it’s not merely the rule-follower deciding randomly or on a whim.

The above isn’t a general definition of ‘rule’. It’s a minimal definition for the purpose of this PLA. Perhaps not a sufficiently unpacked definition if you’re asking if a computer can understand language, for example. After all, computer programs are non-arbitrary, but we’d be reluctant to claim that a desktop machine, however powerful, can understand what ‘love’ or ‘friend’ means. That’s a complex question that may require a more sophisticated definition of ‘rule’ (certainly of ‘choice’). After all, there’s no one-size-fits-all definition for ‘game’ or ‘time’. Why should there be for ‘rule’?

On the above definition of ‘rule’, the fact that Robinson Crusoe can put a mark in his diary every time he sees a certain species of bird, etc., is irrelevant to the question of whether he’s following a rule. It doesn’t matter if, as far as other observers can tell, it’s the same mark for the same type of bird. He’s still not following a rule. We can posit all the possible rules that are consistent with his behavior (Wittgenstein discusses this in his remarks on rule-following), but Crusoe isn’t following any of them.

Many scholars have argued, “So what if we can’t tell which rule Crusoe is following? Maybe he’s following one of them.” In this PLA, he isn’t. Not till some folks land on that island, and Crusoe and them collectively decide which rule he was following. Because he wasn’t following any rule until that happened. He and them can together decide retroactively that he was following a rule.

Until that happens, he was not following a rule. And here’s the kicker. It wouldn’t matter if Crusoe grew up speaking English before he was shipwrecked as an adult, and wrote a ‘rule’ for himself in English, such as “Draw a circle in the diary if you see a seagull.” If he can’t give himself a rule that way, he certainly can’t do it by making up a whole new first language (say, if he was left on the island as a baby).

Why do I say this? Suppose I tell myself, “If going to work, cycle there”. I’ve given myself a rule, right? Wrong. One morning it rains and I decide to drive to work. Have I broken my ‘rule’? I could reasonably claim that when I gave myself the ‘rule’, I didn’t intend to cycle in the rain. So when I gave myself the ‘rule’, what I really meant was ‘If going to work, cycle there [the primary clause], but not when a, b, c, etc [conditions under which the primary clause doesn’t apply]’. This is not to suggest that I had a complete list of conditions in mind when I gave myself the ‘rule’ (such that I could write them down). Rather, when I gave myself the ‘rule’, I assumed 1) there were possible conditions under which the primary clause wouldn’t apply, and 2) I didn’t know what all those conditions were.

Assumptions 1) and 2) underlie all rules (that is, human conventions, not mathematical, logical or scientific laws, except insofar as their interpretations are governed by conventions). 1) and 2) are why law libraries are full of case law and judge-made law, why the tax code gets thicker by the year, and why computers don’t make good judges. Also why there’s a longstanding distinction between the ‘letter of the law’ (the primary clause) and the ‘spirit of the law’ (the underlying principles or considerations behind the law, which justify the exceptions). There are exceptions to (that is, implicit in) every rule, and the folks who made the rule don’t know what all those exceptions are when they made the rule.

Here’s another way to look at it. All rules are ‘nested’ in more fundamental, more general rules, in the sense that the former gets its point from the latter. Take the rule ‘If going to work, cycle there’. This is possibly nested in the broader rule ‘Take the healthiest means of transport’, which is in turn nested in the even broader rule ‘Live as healthily as you can’. If it turns out that cycling is no longer the healthiest way to commute — maybe my office has shifted nearer, and it’s healthier to walk there — then the cycling rule no longer makes sense (as a rule, not as a sentence).

Am I thereby breaking that rule by not cycling to work? Yes and no. I’ve broken the letter of the rule, but kept the spirit of the rule because I obeyed the underlying rationale. The exceptions to the letter of the rule are part of that rationale. Suppose my office moved into the basement of my house, and I insisted on going to work by tumbling down the basement steps on my bicycle. Then my obeying the cycling rule would be irrational (assuming there were no penalties for disobedience).

Now, let’s assume that my office is a nice 15-minute cycle away, but I decide I’m too lazy to cycle today, so I take the bus to work. Have I broken my ‘rule’? Not necessarily. I could always say, “One of the conditions under which the primary clause doesn’t apply is when I’m too lazy to cycle.” We can see how that might make sense, like an occasional ‘cheat’ meal when you’re dieting, perhaps. But wait! How can we tell when I’ve finally broken my rule? That is, when I’ve gone against the original underlying rationale.

After all, can’t I just keep adding exceptions and say they were part of the rationale all along? That’s why you, as an individual, can’t ‘give yourself’ rules. Because then you alone decide, for yourself, at any given moment, which exceptions underlie the rule, and which constitute a breach of the rule (dieters know what I’m talking about, it’s called ‘rationalization’). And that’s as good as not having a rule. It removes the non-arbitrariness that makes a rule.

Now let’s look at what happens when other people make the rule for you. Suppose the cycling rule is a town ordinance. Initially, the published ordinance only states the primary clause, ‘If going to work, cycle there’. Occasionally, someone disobeys that clause, and after hearing their mitigating reasons, the town council adds various exceptions, such as not cycling in the rain. In other words, the town council is still applying the rule, but they’re increasingly articulating and applying the underlying principles and considerations, the spirit of the rule (after all, cycling in the rain is hardly healthy).

But there were cases where they refused to excuse someone. For example, Tom says he was too lazy one day, so he took the bus. The town council says, “No, that’s not a good enough reason. We can’t make an exception for that. You’ve broken the rule.” Here, Tom can’t get away by simply adding an exception clause, because he’s not the town council. But as we’ve seen, if he made the rule ‘for himself’, he could always do so.

Here’s where we might be tempted to draw a wrong conclusion. We might think the non-arbitrariness of the ordinance is grounded in its underlying principles. That there’s something in those principles that doesn’t allow for not cycling to work just because you’re lazy. So Crusoe could give himself a set of principles (in English, because he was shipwrecked as an adult) that would limit his freedom to just add any exceptions he wants. Genuine exceptions have to be consistent with the underlying principles he initially laid down, otherwise he’s breaking his own rules.

For instance, he writes in his diary, ‘Draw a circle every time you see a seagull’. Is that rule explicable? By itself, no (as a rule, not as a sentence). But then he adds an underlying rationale, ‘Record the number of seagulls because if there’re lots, it’s a good time to fish’. And that could be nested in further underlying principles like, ‘Catch as much fish as you can’ and ‘Maximize survivability’, etc.

Not only is the top-most rule now explicable, but Crusoe has apparently set limits to what exceptions he can make to the rule without violating its underlying principles. For example, if he decides to stop counting seagulls for a while just because he’s feeling lazy, isn’t he violating the ‘Catch as much fish as you can’ clause? Sorry, nope. Because he can always — either before or after he stops counting seagulls — add an exception to that clause, such as ‘… unless you’re feeling lazy’ (which he can add to the definition of ‘can’, for example. As in, “I just can’t fish today, I’m too lazy”).

As I said, you can always rationalize any exceptions you make to a rule (and this possibly ties into what Wittgenstein said in §201, that “no course of action could be determined by a rule, because any course of action can be made out to accord with the rule”, that is, with its rationale). But doesn’t that apply to the town council’s rule as well? Can’t they just add any exceptions they like? Yes (subject to votes, of course). That’s why it’s a mistake to try to ground the non-arbitrariness of the rule in its underlying principles, because in that case, the town council’s rule (or indeed, any rule) is just as arbitrary as Crusoe’s.

Another wrong conclusion to draw is, “Well, Crusoe just needs to add a rule that no further exceptions can be added.” That doesn’t work either, because adding exceptions is integral to the elucidation of rules. For example, in the rule ‘If going to work, cycle there’, what counts as ‘work’, ‘going to’, or ‘cycle’? Does volunteering count as ‘work’? If my office is next door, am I ‘going to’ work there (in which case, I’d need to cycle)? Does riding a power-assisted bike count as ‘cycling’? After all, you have to pedal those things. If we add a ‘no further exceptions’ clause to the cycling rule, these questions simply go unanswered.

If Crusoe added the ‘no further exceptions’ clause, he would still be free to interpret his ‘rules’ any way he likes, as long as he doesn’t add any further explicit exceptions to his ‘rule book’. “But strict rules, like board game rules, don’t allow exceptions, right?” Not explicitly. In any rule, many exceptions are ‘bracketed off’, not stated but presumed to be understood. No board game rule book says ‘After rolling the dice, move to the next square, but you can have a tea break first’ or ‘The red token represents such-and-such, but if you lose it, you can use a coin’.

What about ‘arbitrary rules’? An ‘arbitrary rule’ is something like ‘If you see a cat, touch your nose’, just as a random example of a rule. There’s no rationale behind an ‘arbitrary rule’. Many ‘Crusoe rules’ cited by philosophers are in that category. Surely, Crusoe can give himself that kind of rule? Nope, because the same problem arises more acutely. Can Crusoe touch his nose with his forearm or a stick? Can he touch his cheek instead? Where does ‘nose’ end and ‘cheek’ begin? Should he touch his nose if he sees a tiger or an ocelot? After all, they’re ‘big cats’. Are there circumstances in which he shouldn’t touch his nose when he sees a cat (perhaps if he’s fighting off a tiger)?

Crusoe can’t answer those questions, because they’re about the rationale for the rule, and arbitrary ‘rules’ don’t have rationales. So he’s free to act on his own ‘rule’ any way he likes. Which raises the question, why would anyone make an ‘arbitrary rule’ anyway, except as an example of an ‘arbitrary rule’? A ‘rule’ without a rationale, i.e. an ‘arbitrary rule’, is not a rule. A further problem, with particular reference to PLAs, is you can’t construct a language with only arbitrary rules, because semantic meanings can’t be arbitrary. Languages are used to perform non-arbitrary tasks like writing instruction manuals, or making contracts, etc, so the rules of the language can’t be entirely arbitrary.

The non-arbitrariness of the town ordinance lies simply in the fact that those who are subject to it can’t add any exceptions they like (apart from the few town councilors, and only by majority vote in council). But if one is making ‘rules’ for oneself, then one is one’s own lawgiver and as such, the accountability to someone else is missing; and with it, the non-arbitrariness. You can always rationalize any apparent breach of your own ‘rule’. In a nutshell, that’s why Crusoe can’t give himself rules.

It doesn’t matter if the ‘rules’ are in a natural language such as English, or a first language he made up for himself. That distinction is irrelevant in this PLA. However, given that rules are essential to semantic meaning, and Crusoe can’t give himself rules, it follows that he can’t make a language for himself. Unless he’s accountable to someone else in how he does so. The reason why we think we (or Crusoe) can ‘give oneself’ rules is because virtually all the time, we are so accountable.

Another reason we think one can ‘give oneself’ rules is because we tend to confuse a purported statement of a rule, such as an ‘arbitrary rule’, with a rule (because in practice, an apparent statement of a rule often expresses a rule). Remember how I defined ‘rule’, as a non-arbitrary factor that can govern choice. Merely saying to yourself “If going to work, cycle there” is not tantamount to placing yourself under a non-arbitrary consideration, because you haven’t spelled out all the mitigating circumstances in which you would not cycle if going to work, i.e. what counts as obeying/breaking the rule.

Nor can you list all those considerations, because you don’t know them all. This isn’t an epistemic problem. Rules naturally come with an open-ended set of exceptions. For every exception listed, you could always ask, “And what about the exceptions to that?” Which is perhaps why Wittgenstein says, “any interpretation still hangs in the air with what it interprets, and cannot give it any support” (§198a).

But if the rule was given to you by someone else, they don’t have to list all the exceptions for it to be non-arbitrary, for you. For example, if it’s a town ordinance, you have a non-arbitrary consideration that governs your choice to cycle or not to cycle to work, namely the town council’s consent. That is — non-arbitrary for you, even if the town council doesn’t know all the possible exceptions either. You can’t just give yourself any excuse to not cycle to work. If the town council disagrees with your excuse, in advance or retroactively, you’ve broken the rule.

Now, some may reply, “Hold on! Aren’t you just passing the buck to the town council? If they don’t know all the exceptions, then the rule’s arbitrary, period.” The reason someone might say this is because they have a positive definition of ‘rule’ in mind, as some kind of regularity. Remember, my definition of rule doesn’t say it must be a regularity; a rule just has to be non-arbitrary in the sense of the rule-follower not choosing to act merely randomly (for example, by tossing coins) or capriciously (on a whim, or by taste).

In this PLA, it wouldn’t matter if the law-giver was choosing at random or capriciously. For example, if all the town council’s exceptions came out of a random word generator (minus the gobbledygook), or if the town council was replaced with an absolute monarch who can make any exceptions he/she likes. The non-arbitrariness lies in the inability of the rule-follower to make any exceptions he/she likes. Even if the town council’s output is random, the rule-follower is still subject to the council’s decisions.

Some folks might want to double down, though. “That’s not good enough! A rule must have some regularity.” Okay. For the sake of argument, let’s concede that. After all, I’m sympathetic to that view myself. Nevertheless, it isn’t relevant to this PLA, for the purpose of showing that Crusoe can or can’t give himself rules. As I mentioned at the start, even if we can discern an apparent regularity in Crusoe’s behavior, Crusoe still isn’t following a rule. So regularity isn’t going to settle that question. Remember, I’ve not given a general definition of ‘rule’ here, just one that has the minimum criteria to show Crusoe can’t make up his own first language. So the question of whether regularity is necessary to rules in general is a separate issue.

So, what are the implications of this PLA? The same implications that follow from some other versions (hopefully without the weaknesses of those versions). For example, for the problem of egoism (Christine Korsgaard has written much on this, particularly in the chapter ‘The Origin of Value and the Scope of Obligation’ in her book The Sources of Normativity. The following is taken mainly from my own article, ‘Egoism and the Private Language Argument’ in The Philosopher, Volume LXXXXV №2, 2007. My thanks to Michael Bavidge for permission to re-use it elsewhere).

Egoism is the view that other people don’t matter, except as a means to my own ends. A familiar argument for egoism is as follows. “My sensation of pain is, in itself, the only reason for me to end pain, so I have no reason to end pain I don’t feel (i.e., someone else’s pain).” This ‘experiential’ argument makes egoism a default position for those who believe the argument, in the absence of a countervailing rationale for altruism (the view that other people matter, to some extent, as ends in themselves). Egoism prescribes doing as much as I can to avoid my own suffering, even at the expense of others. This attitude can, of course, give rise to cooperative behavior for egoistic ends, but egoistic cooperation tends to break down under the strain of free-riding and non-compliance, and generally excludes the weak.

Is the experiential argument valid? According to this PLA, it isn’t, because one’s sensation of pain is not itself a reason to do anything. Reasons have the same non-arbitrariness requirement as rules. An ‘arbitrary reason’ is no reason at all. In the case of egoism, the ‘reason’ offered serves as a justification for action. According to the experiential argument, the reason for my ending the pain is the sensation itself, not something extraneous which would call for a separate justification. The sensation itself is, of course, ‘private’, in the sense that it can only be apprehended by the subject. Since the sensation is private, the subject’s not accountable to anyone else for how the subject chooses to respond to that sensation, since no one else can be cognizant of that sensation.

In which case, the private sensation cannot be a reason, though it (or its neuro-physiological correlate) may elicit an instinctive or reflex response from, or even a preference to act a certain way in, the subject. If the private sensation was the subject’s sole consideration in deciding how to respond, then his/her decision lacks accountability to someone else, and therefore lacks the non-arbitrariness that is necessary to valid reasons.

The considerations which justify my privileging my suffering above someone else’s have to be assessible by others, i.e. be ‘public’, in order to be reasons (even for me, if I want to be rational). Such public considerations include first-person reports in the first instance, along with pain behavior and other correlates such as signs of injury, etc. Of course, sensations play a part, as what we identify (albeit indirectly and imperfectly in someone else’s case, based on one’s own) with those correlates.

Go down the list of publicly defensible reasons, and none justify egoism. So the experiential argument is invalid. But, surely, doesn’t my pain compel me to end it? Yes it does, but a compulsion isn’t a reason. A strong wind compels me to fly off a cliff, but it isn’t a reason to either go along or resist. If the subjective feeling of pain isn’t a reason to end it, then not feeling someone else’s pain is not a reason to ignore theirs. Correspondingly, it’s not someone else’s first-person experience of pain that gives us a reason to stop it, it’s their public reaction to that pain, which we identify with how we would react to something equally unpleasant that we’re feeling.

Some argue that egoism doesn’t rest on the experiential argument, but on the ‘ownership’ of suffering. “The fact that the suffering is ‘mine’ makes a difference to me in a way that someone else’s suffering doesn’t.” On this PLA, whether something is ‘mine’ depends on public criteria (such as the fact that it has my name on it, or is attached to my body); and the private ‘I’ of bare first-person consciousness can’t offer a reason to act, any more than a private sensation can. In trying to find a sense of ‘ownership’ that justifies egoism, we find ourselves resorting either to public criteria which won’t do the job, or a private use of ‘my’ which cannot justify action.

What are the implications for egoism? We can’t appeal to skepticism about other minds, or privileged access to our own, to justify egoism. Even if egoism isn’t otherwise rationally defensible, egoistic behavior is understandable — the pain reflex probably conditions us through negative reinforcement to behave egoistically. This possibly explains why anti-egoist arguments have little effect on egoistic attitudes, though pro-egoist arguments (valid or otherwise) can exacerbate such attitudes, if only by offering an intellectual excuse to ignore moral inhibitions. Behaviorally, we are all egoists to some extent, so even though a purely egoistic ethics would be a nightmare, an ethics which doesn’t take egoistic attitudes and behavior into account is unlikely to be practicable.

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Ben Gibran
Science and Philosophy

Ben writes on the theory and social science of communication, and anything else that comes to mind