Notes on Wittgenstein on Certainty, Part Three

66. I make assertions about reality, assertions which have different degrees of assurance. How does the degree of assurance come out? What consequences has it? We may be dealing, for example, with the certainty of memory, or again of perception. I may be sure of something, but still know what test might convince me of error. I am e.g. quite sure of the date of a battle, but if I should find a different date in a recognized work of history, I should alter my opinion, and this would not mean I lost all faith in judging.

In the last installment I was saying that there are different kinds of certainty, and I was digging out the special kind of certainty described by Wittgenstein in §6 (though he doesn’t come out and say what it is he is describing) as a “queer and extremely important mental state.” This certainty is the unquestionable kind that renders doubt inconceivable. Not only do we not doubt it – that’s just what being certain is – but we cannot imagine doubting it (unless we are a certain kind of philosopher, of course), and we reveal it when we misuse the word know in saying such things as “I know there is an external world.” This is the certainty that is embedded in the rules of the game: it is just part of what frames all other concepts and talk in that context, and does not depend on finding evidence or proof. Indeed, we can hardly form a notion of what it does depend on.

Then, in reference to §54, I looked at the discontinuity between the certainty of empirical propositions and the certainty of logical propositions, the latter being the embedded kind just discussed. But in the end I couldn’t decide whether Wittgenstein was talking difference in kind or difference in degree. Here in §66 Wittgenstein seems to illustrate another kind of certainty, one that we can imagine being overturned. With the special indubitable certainty, doubt is impossible without misusing language, as the sceptics and idealists do. But in this case – recalling the date of a battle – we can readily admit the possibility of being wrong. Now, the question I have here is, does this kind of certainty in fact also consist in the “queer and extremely important mental state”? After all, if you can admit the possibility of being wrong then we might question whether you are certain, or have any right to be, meaning that the certainty that one feels is nothing but this mental state, which apparently manifests itself on the basis of beliefs that can be doubted as well as those that can’t.

The compatibility of certainty and the conceivability of being wrong doesn’t seem troublesome in the case of memory, such as with his example of the date of a battle. But he also mentions certainty of perception. He cannot have in mind the sight I have of these hands that I hold in front of me, because I can’t seriously entertain the possibility that I’m not really seeing them. Surely he must mean such perceptions that we are less sure of — but “less sure of” might be alternatively phrased as “less certain of”, so are we talking about grades of certainty rather than different kinds?

Well, yes — he says so right there in §66: “I make assertions about reality, assertions which have different degrees of assurance”. But maybe we can also view these examples in the light of the earlier distinction between empirical and logical propositions. “The Battle of Hastings happened in the year 1066” is an empirical proposition, but “This is a hand” is a logical one. Is the difference between these one of degree or kind? Maybe it doesn’t matter, and maybe it varies. Recalling Wittgenstein’s aversion to definition, it might be that there are no hard and fast divisions here, even though there are definite distinctions to be made: the river and the river bed melt into one another yet remain different in kind.

EDIT (May 30th 2011): Reading §66 again it occurs to me that he might be talking solely about empirical propositions. After all, one does not, outside of philosophy, make assertions such as “there is an external world”; the only assertions we ordinarily make about reality are empirical. Among these propositions there is no confusion: there clearly are degrees of assurance, depending on such things as the strength of evidence. Thus, the discontinuity between logical and empirical is maintained. No doubt this is a rather black-and-white interpretation, but I think it helps.

Leading on to the next sections, I should point out that §66 brings up mistakes. I might have been making a mistake for all these years about the date of the Battle of Hastings.

67. Could we imagine a man who keeps on making mistakes where we regard a mistake as ruled out, and in fact never encounter one? E.g. he says he lives in such and such a place, is so and so old, comes from such and such a city, and he speaks with the same certainty (giving all the tokens of it) as I do, but he is wrong. But what is his relation to this error? What am I to suppose?

68. The question is: what is the logician to say here?

Where a mistake is ruled out, it is logically impossible. Making a mistake is not part of the logical framework of the language-game in such cases. “The logician”, unable to logically demonstrate what is wrong, can say little.

69. I should like to say: “If I am wrong about this, I have no guarantee that anything I say is true.” But others won’t say that about me, nor will I say it about other people.

70. For months I have lived at address A, I have read the name of the street and the number of the house countless times, have received countless letters here and given countless people the address. If I am wrong about it, the mistake is hardly less that if I were (wrongly) to believe I was writing Chinese and not German.

71. If my friend were to imagine one day that he had been living for a long time past in such and such a place, etc.etc., I should not call this a mistake, but rather a mental disturbance, perhaps a transient one.

72. Not every false belief of this sort is a mistake.

I can imagine having my certainty in the date of the Battle of Hastings overturned and thus shown to be a mistake. But, come to think of it, this feels no more legitimate a doubt than to doubt the existence of my hands in front of me. Anyway, though I might come to see my belief in 1066 as a mistake, my belief that I live in Edinburgh, if I do not, could only ever be seen as a sign of mental disturbance. But, to me, there seems little difference here. Perhaps 1066 is a bad example. I have been certain of things in the past and turned out to be wrong.

Let’s see. One can obviously be certain and turn out to be wrong, in ordinary familiar ways — and this is the character of mistakes. But where we cannot make a mistake — or rather, where going wrong would be termed as a “mental disturbance” rather than a mistake — have we simply been more certain?

This seems to be what Wittgenstein is asking next:

73. But what is the difference between mistake and mental disturbance? Or what is the difference between my treating it as a mistake and my treating it as mental disturbance?

74. Can we say: a mistake doesn’t only have a cause, it also has a ground? I.e., roughly: when someone makes a mistake, this can be fitted into what he knows aright.

75. Would this be correct: If I merely believed wrongly that there is a table here in front of me, this might still be a mistake; but if I believe wrongly that I have seen this table, or one like it, every day for several months past, and have regularly used it, that isn’t a mistake?

This seems like a good answer. The circumstances that would lead me to see that I had made a mistake about the location of the pub (the Battle of Hastings example seems like a borderline case so I won’t use that one again) are easily enough incorporated into my worldview, but discovering I had been wrong about living in Edinburgh: what could that mean? My imagination struggles with it, and this, surely, shows the belief to be part of the framework. And yet, “I live in Edinburgh” is perhaps not so close to the framework as “there is a city called Edinburgh”. In any case, “I live in Edinburgh” has no ground, (it itself forms part of the ground) whereas “The pub is on Hanover Street” has a firm ground that, in the circumstance of being wrong about it, does not shift. I can be wrong about it while little or nothing else that I believe is threatened.

76. Naturally, my aim must be to give the statements that one would like to make here, but cannot make significantly.

What does he mean? I don’t quite see its importance in context, but surely he must be referring to what we sense in our logical insight: the “crypto-propositions” or “hinge propositions” that might describe or somehow express the indubitable framework or bedrock, but which are really not propositions at all — they cannot be stated as such. But we strive for them when we say things such as “I know that here is a hand.”

77. Perhaps I shall do a multiplication twice to make sure, or perhaps get someone else to work it over. But shall I work it over again twenty times, or get twenty people to go over it? And is that some sort of negligence? Would the certainty really be greater for being checked twenty times?

Recalling my own experiences it is notable that I can be certain — as certain as I can be — of having carried out a procedure correctly, and yet in the end force myself to check it or do it again, just to make sure. In these situations, the certainty is deep and intuitive, whereas the doubt is intellectual, summoned very deliberately; I am doubting my own certainty. Of course, you might then say I was not actually certain at all. I would agree, but I also think it might reveal that certainty is complex.

But here in §77 Wittgenstein wonders if certainty, which, as we have seen, can be greater or lesser, can be strengthened in certain situations by checking a procedure. It seems to me that it can. This just seems like common sense. It is carrying out, or having carried out, the procedure that is the origin of the proposition and certainty combined, but we know that mistakes are sometimes possible. Where mistakes do seem to be possible, repeating or checking a procedure does make our belief more secure. In terms of what I was saying in the previous paragraph, my executive is satisfied when it has compelled the carrying out once more of the procedure.

But it does also seem to be the case that repetition’s efficacy levels off after a while, which is why we can answer Wittgenstein’s question, “Would the certainty really be greater for being checked twenty times?” The answer is, “it probably wouldn’t be greater than it was after the nineteenth check, but it may well be greater than after the first or second check.”

78. And can I give a reason why it isn’t?

Perhaps because in any such situation there is a scale of possible certainty. The utmost certainty might not be as certain as other certainties, but it cannot be surpassed with the only procedure we are familiar with for establishing what is in question. And this utmost can be reached fairly quickly. Is this because we naturally jump to conclusions? We cannot think and act without belief in induction and causality, and I’m not any more certain that the sun will rise again than I was yesterday. Does certainty, or certain kinds of it, come down to our attunement to probabilities?

I think the lesson here is that sometimes there are degrees of certainty, and sometimes there are not, primarily relative to the language-games we’re in — but also, I would say, variable within the language game depending on, for example, whether we have checked our procedure.

But there’s more. Wittgenstein emphasizes reason in §78, and this is important. Let’s say we cannot give a reason why twenty checks will not make me any more certain than one. This is saying that our certainty has no ground, indicating that it lies at the bottom of the language-game, that it is a basic certainty. But the basic certainty for which we cannot give reasons is not the mathematical solution itself as the rule whereby we do not need to check it more than once. If asked the question, “why are you going to stop checking the calculation now?” all we can say is “because I have brought myself to certainty,” and if we are then asked, “but why was your single checking procedure enough? Why did you not have to go on checking several more times?” then we would struggle to answer. The practice has to speak for itself: there is no rule to be extracted here to apply to all cases, i.e., there is no “why”.

79. That I am a man and not a woman can be verified, but if I were to say I was a woman, and then tried to explain the error by saying I hadn’t checked the statement, the explanation would not be accepted.

80. The truth of my statements is the test of my understanding of these statements.

81. That is to say: if I make certain false statements, it becomes uncertain whether I understand them.

82. What counts as an adequate test of a statement belongs to logic. It belongs to the description of the language-game.

83. The truth of certain empirical propositions belongs to our frame of reference.

This all looks quite familiar —

5. Whether a proposition can turn out false after all depends on what I make count as determinants for that proposition.

First of all in §79 Wittgenstein establishes the kind of statements that he goes on to refer to in the sections that follow, namely those statements such as “I am a woman”, or “here is a hand”; logical statements, which are about the language-game rather than about the world (§82). They are the statements that can completely preclude doubt, because such doubt would lack any ground in which doubt could gain sense. §83 refers to what I have variously called the framework or bedrock, and makes the point that this “frame of reference” presupposes, or consists in, certain true statements — statements whose truth frames whatever language-game they lie within. But we should be careful here. Surely it is not the statements themselves that form the frame of reference. Wittgenstein says that it is the truth of these statements that forms part of the bedrock, hence the statements perhaps only reach down to these basic truths, which in turn are manifest in our actions before any statements can been made. It’s tempting here to bring in Heidegger’s truth as disclosedness, which as I understand it is just the way the world reveals itself to us prior to propositional truth.

So if we look again at §5, we see that if the determinants determine a logical proposition, it cannot turn out to be false, and if we deny it we must have misunderstood it. What are the determinants here? Well, the determinants for “Here is a hand” are just such things as that I always see a hand when I look at my hand, I have always had a hand, and have never had a reason to think that my hand has dropped off — determinants that provide the frame of reference for other, less secure, talk about my hands, i.e., empirical propositions. If, on the other hand, the determinants are what provide evidence for an empirical proposition, such as “You touched my hand near the base of the thumb”, then it can turn out to be false after all — at least, we can properly doubt it, because those determinants have a ground, which in this case is a logical framework that is described or delimited by the network of logical or grammatical rules that we touch on when we say “Here is a hand.”

84. Moore says he knows that the earth existed long before his birth. And put like that it seems to be a personal statement about him, even if it is in addition a statement about the physical world. Now it is philosophically uninteresting whether Moore knows this or that, but it is interesting that, and how, it can be known. If Moore had informed us that he knew the distance separating certain stars, we might conclude from that that he had made some special investigations, and we shall want to know what these were. But Moore chooses precisely a case in which we all seem to know the same as he, and without being able to say how. I believe e.g. that I know as much about this matter (the existence of the earth) as Moore does, and if he knows that it is as he says, then I know it too. For it isn’t, either, as if he had arrived at this proposition by pursuing some line of thought which, while it is open to me, I have not in fact pursued.

85. And what goes into someone’s knowing this? Knowledge of history, say? He must know what it means to say: the earth has already existed for such and such a length of time. For not any intelligent adult must know that. We see men building and demolishing houses, and are led to ask:“How long has this house been here?” But how does one come on the idea of asking this about a mountain, for example? And have all men the notion of the earth as a body, which may come into being and pass away? Why shouldn’t I think of the earth as flat, but extending without end in every direction (including depth)? But in that case one might still say “I know that this mountain existed long before my birth.” – But suppose I met a man who didn’t believe that?

86. Suppose I replaced Moore’s “I know” by “I am of the unshakeable conviction”?

87. Can’t an assertoric sentence, which was capable of functioning as an hypothesis, also be used as a foundation for research and action? I.e. can’t it simply be isolated from doubt, though not according to any explicit rule? It simply gets assumed as a truism, never called in question, perhaps not even ever formulated.

88. It may be for example that all enquiry on our part is set so as to exempt certain propositions from doubt, if they were ever formulated. They lie apart from the route travelled by enquiry.

89. One would like to say: “Everything speaks for, and nothing against the earth’s having existed long before…” Yet might I not believe the contrary after all? But the question is: What would the practical effects of this belief be? – Perhaps someone says: “That’s not the point. A belief is what it is whether it has any practical effects or not.” One thinks: It is the same adjustment of the human mind anyway.

Again I think Wittgenstein’s relativism crops up here. He is suggesting that what was once an empirical proposition, which had a grounding in the language-game, can now become a part of that grounding — can become part of the frame of reference. The way he describes it, when or where this happens is arbitrary and unpredictable, and this seems to me to create a kind of contradiction. If certainty is a matter of local, pragmatic and contingent rules, dependent only on particular language-games, then how can it be any kind of certainty worthy of the name?

But this is precisely where he would admonish me, telling me to “forget this transcendent certainty”. (§47) It is important to remember what Wittgenstein is doing here: he is describing how we talk, and what we mean when we say “I know” and “I am certain”, and how philosophers depart from this ordinary usage. He is not concerned, as Descartes and his heirs have been, with how to establish knowledge or certainty.

Next part

Wittgenstein, L., ed. G. E. M. Anscombe, G. H. von Wright, 1969: On Certainty, Harper & Row

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