Commentary on passages from Wittgenstein on Rules and Private Language, pp. ix-14

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• It deserves emphasis that I do not in this piece of writing attempt to speak for myself, or, except in occasional and minor asides, to say anything about my own views on the substantive issues. The primary purpose of this work is the presentation of a problem and an argument, not its critical evaluation. Primarily I can be read, except in a few obvious asides, as almost like an attorney presenting a major philosophical argument as it struck me. (K, p. ix).
  

  COMMENTARY: The import of this passage from the preface struck me recently with the force of a revelation, for I often find Kripke acting like a lawyer trying to make his very weak case appear to be much stronger than it is, by using rather slippery techniques. I see this passage as Kripke's warning to us that he is going to try every trick in the book to make us think that all of this makes sense or is legitimate. Be on the lookout for red herrings in particular, for this is what lawyers specialize in.
  

• In §201 Wittgenstein says, "this was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule." In this section of the present essay, in my own way I will attempt to develop the 'paradox' in question. The 'paradox' is perhaps the central problem of Philosophical Investigations. . . . It may be regarded as a new form of philosophical scepticism. (K, p. 7)
  
  COMMENTARY: This passage contains three key points, first, that Kripke purports to be developing a paradox he finds in Wittgenstein, that the paradox is the "central problem" of PI, and that Wittgenstein gives us a new form of philosophical scepticism. All three points have been challenged by commentators. The paradox Kripke offers us is not to be found in Wittgenstein, it is often claimed. A fortiori, the paradox Kripke offers us is not the central problem of PI. Nor, it is claimed, is Wittgenstein offering us any sort of philosophical scepticism, let alone a new form. Wittgenstein is not, it is often claimed, a sceptic. Indeed, he is generally thought to be opposed to scepticism. Baker and Hacker in their Scepticism, Rules and Language, are Kripke's main challengers on all of these points.
  
  
• Following Wittgenstein, I will develop the problem initially with respect to a mathematical example, though the relevant sceptical problem applies to all meaningful uses of language. I, like almost all English speakers, use the word 'plus' and the symbol '+' to denote a well-known mathematical function, addition. . . . Let me suppose . . . that '68 + 57' is a computation that I have never performed before. . . . I perform the computation, obtaining, of course, the answer '125'. . . . Now suppose I encounter a bizarre sceptic. This sceptic . . . suggests [that] . . . in the past I used 'plus' and '+' to denote a function which I will call 'quus' . . . . . . . It is defined by:
  
  x quus y = x + y, if x, y < 57
  = 5 otherwise. (K, pp. 7-9).

   

  COMMENTARY: This provides the basics of the sceptical challenge. I provide it here mainly for the sake of completeness.
  

• The sceptic claims (or feigns to claim) that I am now misinterpreting my own previous usage. By 'plus', he says, I always meant quus; now, under the influence of some insane frenzy, or a bout of LSD, I have come to misinterpret my own previous usage. Ridiculous and fantastic though it is, the sceptic's hypothesis is not logically impossible. . . . Now if the sceptic proposes his hypotheses sincerely, he is crazy; such a bizarre hypothesis as the proposal that I always meant quus is absolutely wild. Wild it indubitably is, no doubt it is false; but if it is false, there must be some fact about my past usage that can be cited to refute it. For although the hypothesis is wild, it does not seem to be a priori impossible. (K, p. 9).
  
  
  COMMENTARY: There are many things to say about this passage. First, why is the hypothesis ridiculous, fantastic, crazy, bizarre, or "no doubt false"? Surely there is nothing wild or crazy about affirming an hypothesis that is confirmed by all the facts that we have at our disposal, as the quus hypothesis is designed and alleged to be. But just as surely we have some reason for seeing the sceptic's hypothesis as wild or crazy. Perhaps we find it odd to claim that someone could mean a function s/he never heard of, prior to encountering the sceptic. Kripke no where addresses, let alone answers, the question of how we could mean a function we've never heard of before. (I would also contend that it's a fact about us that we have not heard of quus, nor any other of the bent terms which the sceptic appeals to, before encountering the sceptic). So if this is our reason for denying the sceptic's claim, viz., it's absurd to suppose that I could mean a function I've never heard of, Kripke simply has no answer for us. Another way the hypothesis could be deemed to be wild is by appreciating that it is committed to our saying that 68 + 57 = 5, which, I must confess, seems enough to justify rejecting it, in the same way that Goodman's grue hypothesis is to be rejected because it commits us to saying that the next emerald we examine will be blue. (For the record, Goodman does not regard the grue hypothesis to be a viable one. He created it to cast doubt on various conceptions of confirmation). Of course, even if we went on to say, 68 + 57 = 125, the sceptic might claim that we still meant/mean quus but that we've made an error in quussing. Still, at some point, such contentions by the sceptic would be and should be recognized as the desperate pleadings of a lunatic. There are only so many times that we can act contrary to the sceptic's hypothesis and still see that hypothesis as legitimate. (Of course, some might defend the lunatic here; see, e.g., R. M. Hare's notion of a blik, which he uses to distinguish people who see whatever the world may bring as being compatible with things being run by an all-good, all-powerful god, from those who don't. Perhaps our belief that we meant plus by '+' is a blik!).
  Although I agree with Putnam that the hypothesis that I mean quus can be empirically refuted by my continually giving answers to computations that are incompatible with meaning quus, it can be wondered whether or how this bears on the sceptic's hypothesis that I meant quus in the past. After all, (as I note below), our past meaning doesn't constrain our present meaning. So I could have meant quus in the past and simply decided to mean plus from this point on. That I now mean plus, or, better, that I now do not mean quus, does not show that I didn't mean quus in the past.
  Ultimately, I think, what we wish to say is that the reason we find the hypothesis wild and fantastic is that we know full well that we are not guilty of presently misinterpreting our past usage, or equivalently, we know full well that we did not mean quus in the past. The difficulty is whether there is a way of convincing the sceptic of this. Notice, too, that Kripke also allows that it's pretty obvious that we did not mean quus in the past
  One move is to ask the sceptic what he takes as evidence of misinterpretation, or, to put it another way, to ask what the sceptic takes as evidence that we meant such and so in the past. Although there is no explicit answer to this in the text, implicitly, the answer to it is that the only evidence we have to go on in determining what we meant is our past behavior, broadly conceived. However, the past behavior of someone who was a quusser is alleged to be identical to that of someone who was a plusser. Hence our difficulty. We will see later on that the claim that the past behavior of a quusser is identical to that of a plusser is not without its hedges and qualifications. Nor is the claim without its critics. (In particular, see Simon Blackburn's, "The Individual Strikes Back". Blackburn contends that it's a mistake to suppose that "nothing about [a "bent" rule follower] is different until the occasion of bent application applies").
  Be this as it may, I wonder if it isn't possible for us to bite the bullet and agree with the sceptic that since there is no fact that can refute his hypothesis, that his hypothesis is not false. In short, where is the difficulty in agreeing with the sceptic that no fact refutes his hypothesis and so accepting that it's not false that we meant quus in the past? Let's not suppose that such agreement commits us to saying that it's false that we meant plus in the past. It doesn't. For if we accept the sceptic's story, there is no fact that refutes our "hypothesis" that we meant plus in the past either. So it's not false that we meant plus in the past! What is false, on this view, is that we meant plus rather than quus in the past.
  But why is this a problem? Kripke's answer seems to be that the problem is that of arbitrariness, i.e., our rule followings would be, at best, mere "unjustified leaps in the dark". According to Kripke, if it's false that we meant plus rather than quus, then we either wouldn't know what to say in the case "68 + 57", or our answer to this case would be arbitrary. Frankly, I don't see that either is the case since the sceptic does not and cannot (at least, he cannot do so without rendering his challenge incoherent ) cast doubt on our understanding of either the plus or quus functions. What is arbitrary is our choice of a sign to designate a function but the functions plus and quus are not arbitrary. A fortiori, the responses one must give to certain problems in order to count as following either function are not arbitrary. (More on this below).
  One more thing to say about this passage is that of all the reports on LSD, none suggests that it makes a quusser a plusser, or a plusser a quusser.
  
  
• In the discussion below the challenge posed by the sceptic takes two forms. First, he questions whether there is any fact that I meant plus, not quus, that will answer his sceptical challenge. Second, he questions whether I have any reason to be so confident that now I should answer '125' rather than '5'. . . . Neither the accuracy of my computation nor of my memory is under dispute. So it ought to be agreed that if I meant plus, then unless I wish to change my usage, I am justified in answering (indeed, compelled to answer) '125', not '5'. An answer to the sceptic must satisfy two conditions. First, it must give an account of what fact it is (about my mental state) that constitutes my meaning plus, not quus. But further, there is a condition that any putative candidate for such a fact must satisfy. It must, in some sense, show how I am justified in giving the answer '125' to '68 + 57'. . . . Otherwise, the sceptic has not been answered when he holds that my present response is arbitrary. (K, p. 11).
  
  
  COMMENTARY: An extremely important passage. Here Kripke has laid out the so-called sceptical challenge. To begin with, notice that the first form of the challenge challenges us to find a fact to answer the sceptic's challenge. This sounds like a piece of double-talk but it can be read so as to make sense. The ultimate sceptical challenge is that of legitimating our meaning-talk. This requires, or so the sceptic seems to suppose, that we be able to refute his hypothesis that we meant quus in the past, rather than plus. In this passage Kripke is challenging us to find a fact that can show that we did not mean quus in the past. Ultimately, Kripke, or Kripke's Wittgenstein, claims that no such fact can be found. One interesting question here is two-fold, one, what does KW count as a "fact" (or "facts) and why are we confined to "facts" in trying to refute the sceptic's hypothesis. A related, albeit anticipatory question is whether KW's own sceptical solution to the sceptical problem purports to refute the sceptic's hypothesis that we meant quus in the past? (For those new to Kripke's book, KW is alleged to give a sceptical solution to the sceptical problem, i.e., a solution that begins by accepting the "unanswerability" of the sceptical challenge, i.e., that begins by accepting the nonexistence of any fact that refutes the sceptic's hypothesis that we meant quus in the past, but which somehow avoids the disastrous conclusion that our meaning-talk is nonsense and our rule followings arbitrary or nonsensical). More particularly, does KW take his sceptical solution as refuting the sceptic's hypothesis albeit without appeal to facts? If so, then the sceptical challenge to the legitimacy of our meaning talk and rule following is based on a mistake, viz., the mistake of supposing that we must refute the sceptic's hypothesis that we meant quus (or show that we meant plus rather than quus), by appeal to meaning facts, in order to save ourselves from semantic nihilism. For if the sceptic's hypothesis that we meant quus can be disconfirmed, albeit without facts, then the lack of facts to refute the sceptic cannot be said to lead to the impossibility of meaning.
  Another worry about the assumption that the sceptical solution refutes or disconfirms the sceptic's hypothesis that we meant quus is more basic, viz., whether and how it is possible to refute or disconfirm an hypothesis, under the assumption that there are no facts that do so. We might be able, e.g., by appeal to simplicity considerations (or similar nonfactual considerations), to justify choosing one hypothesis over another, despite our not having any facts to warrant the choice. And though I wouldn't be inclined to say that the rejected hypothesis in such a case had been refuted or disconfirmed, it might still be allowed that the rejection of the hypothesis had been justified, in some sense, without appeal to meaning facts. However, veterans of Kripke's book know that such an approach is explicitly ruled out by Kripke (see K, pp. 38-9). The bottom line here is that it is quite mysterious how KW could refute the sceptical hypothesis without appeal to facts.
  By my lights, KW's sceptical solution to the sceptical challenge is not intended to refute or disconfirm the sceptic's hypothesis, nor provide a way to justify rejecting it. Indeed, it simply turns its back on worries about whether we meant plus rather than quus in favor of trying to show how our usual meaning talk can be rendered legitimate despite our inability to ever show that we meant plus rather than quus. In short, KW's sceptical solution does nothing to show that we didn't mean quus in the past. Rather, it simply ignores this problem, contenting itself with showing how it's possible for a community of speakers to have justification conditions for attributing correct or incorrect rule following to others, where these conditions are not "simply that the subject's own authority is unconditionally to be accepted." (K, p. 89). Simply put, KW's sceptical solution does not show us how to do something with justifications conditions that we couldn't do with truth conditions (viz., show that someone meant plus rather than quus, and thereby avoid semantic nihilism). Rather, KW simply doesn't require of justification conditions that they show whether someone meant plus or quus. Of course, the problem with this is that once it's allowed that we don't have to refute, disconfirm or otherwise justify rejecting the sceptic's quus hypothesis in order to avoid semantic nihilism, it becomes mysterious why we should give up on a fact-based conception of meaning. For if fact-based (or truth-condition based) conceptions of meaning are not, a la justification conditions accounts, asked to show that someone meant plus rather than quus, then they have not been shown to be inadequate, have not been shown to result in semantic nihilism.
  My contention then is that it is a serious mistake to see KW's sceptical solution as even attempting to show, let alone succeeding in showing, that we didn't mean quus or that we meant plus rather than quus. The sceptical solution does nothing to show that the plus hypothesis is any more or less justified than the quus hypothesis. Indeed, KW's sceptical solution is focused exclusively on trying to show how we can justify our claim that someone means plus by '+', given that there are no facts that show this. But it completely ignores the worry that drives the sceptical hypothesis, viz., how can we show that we meant plus rather than quus by '+'.
  Similarly, if it's maintained that there's no justification for our answer to '68 + 57' given that there are no facts to show which of plus or quus we meant, then the same goes for KW's justification conception of meaning. For there are no justification or assertion conditions that show I meant plus rather than quus. Mirroring the argument of the sceptic, there is also no justification for my answer to '68 + 57' on the justification conditions view. Also, this problem seems to be much less serious than KW supposes, in part because my confidence about what plus (or quus) requires, as well as my confidence that I presently mean plus and not quus (or vice-versa), are not at all shaken by the sceptical hypothesis that I am presently misinterpreting my past usage. My past usage in no way binds my future use, my past meaning does not constrain my present meaning, something which all of us are no doubt thankful for (recall here Chomsky's confession about his former understanding of the word, 'livid'). If I am under the mistaken impression that the only justifiable answer to '68 + 57' is the one that accords with the function designated by '+', as I formerly meant it, then the inability to answer the sceptic would, it seems, threaten my ability to justify my answer (on either a fact-based view of language or on his own justification conditions conception). But clearly, the answer '125' can be justified by my meaning plus presently.
  
  
• The ground rules of our formulation of the problem should be made clear. For the sceptic to converse with me at all, we must have a common language. So I am supposing that the sceptic, provisionally, is not questioning my present use of the word 'plus'; he agrees that, according to my present usage, '68 plus 57' denotes 125. . . . I put the problem in this way so as to avoid confusing questions about whether the discussion is taking place 'both inside and outside language' in some illegitimate sense. If we are querying the meaning of the word 'plus', how can we use it (and variants, like 'quus') at the same time? So I suppose that the sceptic assumes that he and I agree in our present uses of the word 'plus': we both use it to denote addition. He does not -- at least initially -- deny or doubt that addition is a genuine function, defined on all pairs of integers, nor does he deny that we can speak of it. Rather he asks why I now believe that by 'plus' in the past, I meant addition rather than quaddition. (K, pp. 11-12).
  
  COMMENTARY: This passage (and a relative of it on p. 21) contains a confusion that leads Kripke to claim that the sceptic's conclusion is much more radical than it can be, i.e., more radical than his argument allows. First, there is simply no need for the sceptic and I to agree on our present uses of 'plus'. In particular, there is no reason that the sceptic and I must agree to presently use 'plus' to denote addition. For not only is there no need to refer to present uses at all in raising the sceptical challenge (since the challenge concerns what I meant, not what I mean), but if I use 'plus' to refer to addition, and 'quus' to refer to quaddition, and the sceptic uses each term in the opposite way, the sceptical challenge can still be raised. All that is needed is that he and I share the word/sign, 'plus', as well as an understanding of the nature of various mathematical notions and functions. It should be obvious that two people can have a proper understanding of two different functions and yet use different names for each function.
  Simply put, Kripke seems to identify, (i) querying the meaning of 'plus', with (ii) querying the meaning of plus. That is, Kripke seems to suppose that one cannot speak of the plus function while one is querying the meaning of 'plus'. This is a very serious mistake on his part, for the very simple reason that there is no such thing as "querying the meaning of plus".
  Plus is a function, not a word. You can query the meaning of words but you cannot query the meaning of functions. Plus and quus are functions; 'plus' and 'quus' are words/signs. Plus and quus are not words/signs, they're functions. "Plus ' and 'quus' are words/signs, not functions. Functions don't have meanings, they have domains and extensions. Words have meanings. One can certainly query the meaning of words/signs without agreeing on the nature of the things allegedly meant by the signs. Our alleged inability, by the sceptic's lights, to mean some function rather than another ought not be taken (as Kripke seems to take it in the passage above) to threaten the existence or nature of functions. Nor ought it be supposed to threaten our knowledge of differences between functions and words/signs.
  Relatedly, it's easy to overlook the import of an obvious feature of the sceptical challenge, viz., the fact that it asks us for a fact that shows we meant plus rather than some function which is identical to plus on all of the cases we've explicitly considered or answered in our past history. Many (including Kripke here in this passage) fail to appreciate that our past history serves to refute any sceptic who would ask for a fact that shows we meant plus by '+' rather than, e.g., minus, or times, not to mention table, chair, Santa Claus or lillibulero. The fact that we have said or thought, 2 + 2 = 4, 2 + 3 = 5, . . ., 41 + 30 = 71, . . ., 56 + 56 =112, prevents the sceptic from legitimately claiming that there's no fact that shows that we didn't mean minus or times, etc., by '+', in the past. For our answers to computation problems are facts that scotch the hypothesis that I meant minus by '+'. The point here is that not any old set of answers to computation problems involving '+' is compatible with meaning plus by '+'. Similarly, not any old set of answers to computation problems involving '+' is compatible with meaning quus by '+'. It needs to be appreciated that neither before, during, nor after the sceptical challenge have we been given a reason to doubt that plus is a "genuine function" (nor any reason to doubt that quus is a "genuine function" either). Nor have we been given a reason to doubt our understanding of the plus function (or the quus function). At best, we've been given reasons to doubt that there are any facts that distinguish between my meaning plus rather than quus by 'plus' or '+'. But let's not suppose that this lack of "meaning facts" translates into a lack of "function facts", i.e., facts about the domain and extensions, and so identity, of various functions. The plus function by any other name would still require 68 + 57 to be 125. And the quus function by any other name would still be identical to the plus function (by any other name) on all the cases involving numbers less than 57. The moral of all of this is, of course, Chuang tzu's, viz., give me the functions and you can have the names, just as Chuang Tzu's fisherman asks for the fish and leaves the trap.
  So, what the sceptic's argument shows is, at best, that there is no fact about whether I meant plus rather than quus by 'plus', either in the past or in the present. But let's not suppose that the sceptic has shown that there is no fact about whether I mean plus. There are lots of facts about me that warrant claiming that I meant/mean plus by 'plus'. These same facts warrant saying that I meant/mean plus rather than minus or times or lillibulero by 'plus'. Of course, they also warrant saying that I meant/mean quus. Therein, allegedly, is our problem. Still, the distinction between there being no facts about what I mean (which is, in the only sense relevant to the discussion, wildly false, e.g., the answers I have given to computation problems are facts that show I don't mean minus or times, by 'plus') and there being no fact warranting a choice between my meaning plus or my meaning quus, (which, I would allow, is true) must be kept in mind. For it is crucial to keep the sceptic within the bounds of sense. Otherwise, we come away thinking (and I think Kripke very much wants us to come away thinking) that the sceptic has undermined our game of telling whether someone means plus rather than minus, or times or whatever. In fact, the sceptic shows, at best, that there are no facts warranting a choice between what I call "meaning competitors", i.e., functions like plus and quus.
  
  
• Of course, ultimately, if the sceptic is right, the concepts of meaning and of intending one function rather than another will make no sense. For the sceptic holds that no fact about my past history -- nothing that was ever in my mind, or in my external behavior -- establishes that I meant plus rather than quus. . . . But if this is correct, there can of course be no fact about which function I meant, and if there can be no fact about which particular function I meant in the past, there can be none in the present either. (K, p. 13).
  
  
  COMMENTARY: Another extremely important passage. Here Kripke has laid out the sceptic's ultimate argument (or ONE of the ulitmate arguments anyway!) for his conclusion that all language is meaningless or nonsensical. (Cf. K, p. 62). To begin with, if we ask what Kripke means here by, "the sceptic is right", it can mean only one thing, viz., that the sceptic is right about the nonexistence of any fact that shows that I mean/meant plus rather than quus. However, Kripke later tells us that his Wittgenstein grants that the sceptic is right about there being no such fact; indeed, this is part and parcel of KW providing us with a sceptical, as opposed to a straight, solution to the sceptical problem. But then it seems that KW, in allowing that the sceptic is right about the nonexistence of meaning facts, is also committed to the nonsensicalness of the concepts of meaning and intending one function rather than another. Of course, KW does not ultimately hold that meaning makes no sense. Indeed, it is the task of KW's sceptical solution to show us how it is possible for to make sense of meaning while yet granting, with the sceptic, that there are no "meaning facts". As such, it is clear that KW does not really accept the if-then statement that begins the passage above. For if he did, he would be committed to the nonsensicalness of meaning, which he isn't so he doesn't; that's logic.
  Being kind, we can say that Kripke has misspoken here and that what he really means to say is that if the sceptic is right about there being no past meaning facts, then so long as we suppose that such facts are required for making sense of meaning, (i.e., insofar as we accept a rather bizarre and unlikely conception of the relationship between past usage and present meaning or the justification of present usage; for now, call such conceptions, truth conditionalisms), meaning and intending one function rather than another makes no sense. Of course, this way of reading Kripke allows us to see that there is room for a sceptical solution to the paradox, for we can defuse the force of granting the nonexistence of meaning facts by rejecting truth conditionalism in favor of something more vaguely defined. Most importantly, it allows us to see that the dreaded consequence of the sceptic's case against past meaning-facts, viz., the nonsensicalness of meaning, doesn't follow without appeal to a rather controversial premise, i.e., one that commits us to a bizarre idea that such past meaning facts are needed for something. (Anticipatory aside: Can we read KW as providing an RAA of conceptions of past meaning facts which see them as necessary for justifying present meaning or present usage? Short Answer to anticipatory aside: Perhaps, but why do we need an RAA of such a bizarre view?).
  
  I also have serious doubts about the legitimacy of KW's argument that because there is no past fact, i.e., no fact about my past history to show which of plus or quus I meant, that there can be no such fact in the present either. The argument seems to me to be guilty of a very obvious fallacy, viz., that of supposing that because we have been unable to find a fact, "in the past", that shows we meant plus rather than quus, that we will be no better off with respect to finding a fact "in the present". It's odd that no major commentator has noticed this problem. (Indeed, Crispin Wright explicitly endorses the move from "no past facts" to "no present facts". See his "Kripke Account of the Argument Against Private Language", p. 763). Perhaps I'm missing something. If so, I welcome enlightenment on this matter. Surely we should be allowed to suppose that the present contains information or linguistic behaviors that were not available in the past. (If not, then 'the past' and 'the present' are being used illegitimately). As such, we could certainly suppose that someone's present linguistic behavior is such as to show that s/he doesn't mean quus (or plus, as the behavior may be). Recall that KW's own sceptical solution leans heavily on our ability to be able to say that someone's responses to computation problems shows that s/he does not mean such-and-so. (See K, pp. 93-5).
  The basic problem with Kripke's argument here is that he's trying to conclude, a la Quine in his indeterminacy thesis, that the plus and quus hypotheses are factually indistinguishable over all of a speaker's linguistic dispositions, when in fact all he's shown is that given a particularly hedged and narrow set of linguistic behaviors (i.e., behaviors involving the use of '+' in computations involving numbers no greater than 56), the plus and quus hypotheses are factually indistinguishable. But in the case of meaning plus rather than quus, as soon as we get someone's answer to a problem (or several problems if we wish to be fussy) which requires different answers for plussers than it does for quussers, we have all the "facts" we need to say that the person does not mean one of the two functions. (In this regard, see Putnam's paper on Wittgenstein's philosophy of mathematics).
  Finally, a clarification of what the sceptic has shown is in order. The opening line of this passage is an overstatement. The sceptic's argument does not warrant saying that for any two functions, the concept of meaning the one rather than the other makes no sense. Rather, the sober description of the sceptic's argument is as follows: The complete inventory of facts (e.g., in the case of 'plus', these facts would at least include our past answers to computation problems, both spoken and unspoken) at our disposal for determining what someone, including oneself, means, leave open the possibility that one means something very different from what one supposes. So stated, it's clear that depending on the functions in question, we can make sense of meaning one function rather than another. As noted in the previous commentary, my previous answers to computation problems shows quite clearly that I meant plus rather than minus, rather than times, not to mention rather than quminus, qutimes, etc. The point here is that there are meaning facts which include, at the least, our past use of 'plus', and these facts do permit us to rule out many, but not all, meaning hypotheses concerning 'plus'. As such, the notion of meaning one thing rather than another has not been rendered completely nonsensical, nor has it been established that there are no facts at all about what someone means. Indeed, if one reflects on what Kripke shows in this book, it's pretty clear that his Wittgenstein shows merely that although certainty about what someone means is impossible, our usual ways of determining meaning, viz., someone's use of a word, are more than adequate. Frankly, this seems a far cry from what Kripke suggests his Wittgenstein offers us.
  
  
• Another important rule of the game is that there are no limitations, in particular, no behaviorist limitations, on the facts that may be cited to answer the sceptic. . . . Wittgenstein's philosophy of mind has often been viewed as behavioristic, but to the extent that Wittgenstein may (or may not) be hostile to the 'inner', no such hostility is to be assumed as a premise; it is to be argued as a conclusion. So whatever 'looking into my mind' may be, the sceptic asserts that even if God were to do it, he still could not determine that I meant addition by 'plus'.
  This feature of Wittgenstein contrasts, for example, with Quine's discussion of the 'indeterminacy of translation'. . . . Quine . . . is more than content to assume that only behavioral evidence is to be admitted into his discussion. (K, p. 14).
  
  COMMENTARY: This passage is a good example of a common problem in Kripke's book, viz., we're often told what the sceptic (or Wittgenstein) allegedly argues without ever really being given the alleged argument. In particular, where does the sceptic argue, let alone establish by argument, that even if God were to look into someone's mind, God still could not determine that the person meant addition by 'plus'? Even granting that the sceptic has shown that there are no meaning facts, there's is an implicit hedge on his argument, viz., it's by human lights that there are no such facts. God, of course, may see things differently. Perhaps it takes God to appreciate that there are infinite objects that inhabit our minds. If so, God may, for all KW's sceptic shows, be able to determine which of plus or quus we meant. In fairness to Kripke, he later backs off of the "not even God could determine" claim, saying that it is merely a "colorful expression" of the sceptic's denial that there are meaning facts. (See K, pp. 40-41). So he too seems to recognize the illegitimacy of taking the sceptic to have established anything about what God can or can't do in this case. For the record, Kripke's claim about what God couldn't do is obviously drawn from Wittgenstein's somewhat similar, but also dissimilar, line about what God can't do, which appears on page 217 of the Investigations.
  The other thing to note about this line is that it is unfair to Quine. I assume that we can all agree that whatever is "in my mind" that is going to be relevant to what I mean, is, or ought to be, capable of being expressed via a public language. As such, Quine sees nothing illegitimate about appeals to the mental per se. What is illegitimate about such appeals is if they are cited as evidence for meaning but yet the introspective "data" is claimed to be inexpressible in a public language. In short, the only legitimate "introspectible" data, for Quine and Wittgenstein, is data that is in principle expressible in a public language. So long as one's introspections are in principle publicly expressible, Quine would see no problem with including them in the data to be used for determining what someone means. The bottom line then is that being offered access to someone's introspections on their meaning is either an offer to enlarge our evidential base to include anything that is "accidentally mental" (i.e., something that has not actually found its way into the public domain but which could be presented publicly; e.g., I might mentally say of somone that s/he is a tremendous bore. Such a mental musing is only "accidentally mental", for I could have said it for all to hear, but didn't), or else it's an offer of nothing at all. Or so Wittgenstein and Quine would allege.
  
  For commentary on pp. 15-37, click here

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