Ordinary language is all right.
One could divide humanity into two classes:
those who master a metaphor, and those who hold by a formula.
Those with a bent for both are too few, they do not comprise a class.
(In §83, the philosopher stands apart from the group at play, claiming to know more than Wittgenstein has just said to be the case about them. As in §82 the possibilities attractive for, or vexing to, the philosopher are the first and third, where he distances himself from the other or must take the other at no more than his word.)
Does what Wittgenstein's interlocutor imagines in §84a—a sort of complete game, with a system of rules that exclude all doubt—really do something about the doubt he seems to think it does? In §84b Wittgenstein responds assertively to the interlocutor (who had asked, 'well can't we imagine…?'), pointing out that 'das sagt nicht, daß wir zweifeln, weil wir uns einen Zweifel denken können'. By way of illustration, he says—not that he can imagine a doubt, exactly, but—that he can imagine someone who doubts in a certain case, without for that reason himself doubting in the same case. What's the significance of this reference to the similarity of the cases? And what's the significance of his asserting this point by imagining someone else, who doubts, rather than simply imagining the doubt, say as one he might face?
Wittgenstein's doubter, let's call him, is in the case of standing before the closed door to his house, and being unsure whether an abyss has opened up on the other side of the door. He doubts whether his case is one in which he can leave safely (without checking) or one in which he will fall into an abyss, should he pass through the door without checking what's on the other side: solid ground or a hole. So he what he does is to make sure, before he goes through, so that he doesn't fall in a hole.
Wittgenstein doesn't say why the doubter has this uncertainty. He also doesn't say why the doubter takes it seriously, but perhaps that doesn't need any further explanation: he does note that the doubter makes sure of what's on the other side of the door before he passes through, which certainly seems like the sensible thing to do for someone who really does have that doubt. Here Wittgenstein's parenthetical concession, that it could sometimes prove to be the case that the doubter was right to doubt—because an abyss has opened up—seems to reflect his not ruling the doubt completely out of bounds, beyond what's imaginable. For he imagines that such a doubter may be proven right, i.e., that this is a doubt which we can also imagine being confirmed.
Does Wittgenstein need to say why the doubter has this uncertainty? Does he need to say why he doesn't? For he does say that in the same case, he does not doubt. On a certain conception of reasoning by cases, he should be able to distinguish his case from the one the doubter finds himself in: otherwise, he too should doubt. (And start worrying about how to put to rest all the doubts he can imagine.) But to expect this of Wittgenstein would be to put too much emphasis on his saying 'the same case', to his calling the cases the same, as if they were identical, indistinguishable. Because they are the same, in this respect: in one, Wittgenstein stands before the door to his house, about to leave. In the other, the doubter stands before the door to his house, about to leave. But in another, more significant respect, the cases are different. The doubter is in doubt: uncertain about whether an abyss lies in wait for him. Wittgenstein is not uncertain. Before his door, he does not have that doubt. How do we know he doesn't? He says he doesn't. And how does he know he doesn't? Well, why does the doubter doubt? Wittgenstein doesn't say, in either case.
The difference between the cases could be put more simply: Wittgenstein and the doubter are not the same. He can imagine someone who doubts in this case, but when he does, he imagines someone else. He does not doubt. His case is different: at the very least, because he is different. It is, we could say, the usual one, in which that is something he never doubts.
This is all supposed to illustrate Wittgenstein's point in response to §84a: 'Aber das sagt nicht, daß wir zweifeln, weil wir uns einen Zweifel denken können'. As a response to the interlocutor's questions about being able to imagine a game whose system of rules would put every doubt to rest, this is pretty oblique. And anyway, wasn't the possibility of every doubt being taken care of by the imagined game, with its system of rules, the point? If so, then what would it matter whether the doubts were imagined or not?
I think a common reading here goes like Baker and Hacker's, emphasizing the contrast between imaginable doubt, and the absence of doubt for his own, usual case, which Wittgenstein asserts: given some obvious difference between the two, there's no need to concern ourselves with dispelling every possible, every imaginable, doubt. The philosopher, say a certain kind of skeptic, is on this reading just silly, foolish—blinded by an ideal, something of that sort.
Perhaps this reading trades on the obvious exaggeration attaching to Wittgenstein's illustration of his point. For this makes it seem as if no imaginable doubt leads naturally to being in doubt, so that asserting that it is not just because we can imagine a doubt, that we doubt, is an assertion that imagined doubt and 'real doubt' somehow do not even make contact. Or imagining is not enough: something else, something from reality, is required to get us all the way to doubt. Thus Wittgenstein's illustration appears as a way of emphasizing how unrealistic, bordering on bonkers, it would be to let mere imagination determine that one doubts.
But, as I suggested, it appears as if the interlocutor's intention to exclude all doubt in his imagined game makes this sort of reading of Wittgenstein's response seize upon a false issue. Certainly it would not be a response which would satisfy a more fully developed skepticism (or traditional philosophical response to skepticism, say via the elaboration of a system of rules), which though imagining doubt would presumably imagine it realistically, reasonably.
So how is what Wittgenstein says a response? What is it responding to? What it is that he denies follows from, or is meant by, or is said on the basis of, what the interlocutor imagined concerning a complete game, is 'that we are in doubt because it is possible for us to imagine a doubt'. The 'because' there is slim, but suppose it relates mainly to whatever would make us doubt. As I said earlier, Wittgenstein says nothing about what would make his doubter doubt. Nor about what makes him, Wittgenstein, not doubt. What we could call the criteria for doubting, for what we would ordinarily call 'doubt', are only distantly under consideration. And, as I've said, while imagining his complete game, the interlocutor is imagining doubts. So perhaps what Wittgenstein is denying, is that this imagination of doubt is why the interlocutor doubts. In imagining his complete game, which he supposes will take care of every possible doubt, the interlocutor has, Wittgenstein is implying, not yet taken care of his doubt. For isn't the interlocutor, at least, someone who is in doubt?
Suppose so, for now. Why say, beyond that, that Wittgenstein's response says effectively that what the interlocutor imagines has not taken care of the doubt he has, because imagining a doubt is not the same as doubting?
I said that in illustrating his point, Wittgenstein distinguished between himself and the doubter; his own case and the doubter's case, or rather, what he does in that case, as against what the doubter does. Wittgenstein is not the doubter: put that otherwise as, Wittgenstein knows who he is—he knows himself. He knows what his doubts are; he knows, at least this much, where the case of standing before the door is concerned: that he does not doubt. He does not doubt what is the case—what is obviously the case.
Does the interlocutor? Express his difficulty in these terms: of identifying his doubts, of knowing what it is that he doubts, knowing why he doubts. If imagining his complete game would take care, along the way, of imagining all the doubts that could arise concerning the application of its rules, would that necessarily entail identifying the doubts which are his among those that are ruled out? Would imagining this game allow him to know himself in that respect?
('For the most part, we are not where we are, but in a false position. Through an infirmity of our natures, we suppose a case, and put ourselves into it, and hence are in two cases at the same time, and it is doubly difficult to get out. In sane moments we regard only the facts, the case that is.')
Why §81 §82 §83 §84 §85 as they are, in sequence, in the Investigations?
What does the doubt first mentioned in §84, in connection with the idea of games (like the application/utilization of a word) being 'überall von Regeln begrenzt' or not, have to do with §§82–83's relationship to §81?
§§82–83 would seem to imply that our uses of words are in general 'not everywhere bounded by rules'. (The reference back to an earlier point at which Wittgenstein said that 'the application of a word' was not so bounded is back to the final paragraph of §68, where in response to a question about the word 'game', or perhaps 'number', not having a regulated application or not being part of some regulated play, Wittgenstein's response is 'it is not everywhere bounded by rules; but there are no rules in tennis for…'.) And this, specifically, because of our having examined the ways in which we would ordinarily be able to say that our uses of words proceed according to rules—not because of some other subtleties about boundaries or such.
If we suppose that the shift to 'Anwendung' is significant here, then perhaps the idea is that in light of the implication from §§82–83, Wittgenstein is turning to the sense that, at the very least, he has said that the, let's call them, points of application of a word are in some sense bounded. Just not everywhere. So the idea of a rule seems as if it has some grip on the use of a word, despite the contrary implication from §§82–83. Immediately, though, Wittgenstein asks the question which anticipates the line of thought: that in such terms, what we would have to have in mind is 'ein Spiel… das überall von Regeln begrenzt ist'. Perhaps that would be a case in which we could talk, without exception, of the 'rule by which he proceeds'.
But Wittgenstein continues immediately to specify what that might mean, a game everywhere bounded by rules. (Or, circumscribed; limited; defined.) Thus 'whose rules let no doubt to get in; which fill up all gaps'. Apparently the idea of a boundary or limit is generating the form of expression with which doubts are referred to here: it pictures a kind of inside and outside, so doubt is correspondingly pictured as getting in or being prevented from getting in. 'In' is in the play of the game. Doubts are doubts about—as the next remark goes on to suggest—the application of the rules of the game. When they intrude, as it were from outside, play is interrupted, perhaps broken. (I can imagine cases where play could not continue absent some ad hoc agreement as to what to do; and cases where players perhaps could not decide what to do in cases where the rules are silent or contradictory as to some situation which has arisen.)
These questions are met with (in alternating voice) more questions:
'Können wir uns nicht eine Regel denken, die die Anwendung der Regel regelt? Und einen Zweifel, den jene Regel behebt, – und so fort?'
If Wittgenstein is the first speaker, this appears to be an interlocutor asking. So the interlocutor is proposing a way in which there could be a game which was everywhere bounded by rules, which let no doubt get in. The manner in which the interlocutor phrases this suggests that it's not imagined as being particularly problematic—perhaps despite the fact that he is represented as casually appending a 'so forth' to what he says, which might otherwise make us wonder about regress problems. (Perhaps the interlocutor is imagining that such a game would come to a point where an overarching rule would not leave any room for doubt, so no regress would be possible.)
So the manner in which the interlocutor imagines such a game existing is in terms of its being outfitted with rules, specified or ordered so as to take care of doubts of themselves: doubts are themselves the kind of thing which can be remedied by means of rules, so that if we should be faced with a rule which admits of doubt in some case of its application, we simply need more rules—and this will eliminate doubt, prevent it from arising (for someone who understands how to use rules, who has mastered the rules for rules). Rather, prevent it from being consequential; disastrous. Bringing things to a halt. As if the problem with games not so circumscribed is that they lack a complete enough set of rules.
(Think back to the tennis case from §68: if it does not have a rule for how high one is to toss the ball before a serve, then it might seem as if a doubt could arise here: how high am I to throw the ball? Or between two people with different opinions about this, a dispute might arise: are you really allowed to throw the ball that high in the air? What do the rules say? What shall be done when they are silent? The interlocutor here would say: yes, if there were another rule in tennis that specified the way in which one was to follow the rules for serving the ball, etc., then this doubt could not arise: the other rule would prevent this. Or, at the very least, it would tell what to do: so doubt could not 'enter in' and bring play to a standstill. —Is this an example of a 'rule regulating the application of a rule'? One might think elsewhere of a rule about deferring to an umpire: and then his job is, in a sense, to supply judgments where the rules do not, or cannot. Think of the differences between games which customarily do not have 'judges', and those which customarily do (must?).)
Is what the interlocutor is imagining, a case of the exclusion of doubt?
Fog rain snow all from the same gray sky. The sky is indifferent to what transpires.