09 February 2011

Notes on Wittgenstein’s “On Certainty”, Part 2

Part 1 Part 2 Part 3 Part 4 Part 5 Part 6 Part 7

Wittgenstein has so far shown that Moore’s response to scepticism is inadequate, or simply mistaken. He now proceeds to diagnose scepticism from his own point of view.

35. But can’t it be imagined that there should be no physical objects? I don’t know. And yet “there are physical objects” is nonsense. Is it supposed to be an empirical proposition?—And is this an empirical proposition: “There seem to be physical objects”?

36. “A is a physical object” is a piece of instruction which we give only to someone who doesn’t yet understand either what “A” means, or what “physical object” means. Thus it is instruction about the use of words, and “physical object” is a logical concept. (Like colour, quantity, …) And that is why no such proposition as: “There are physical objects” can be formulated. Yet we encounter such unsuccessful shots at every turn.

I think this is a crucial juncture, which the previous sections have been leading up to. Wittgenstein has so far been circling around this problem: why, exactly, is it nonsense to say things such as “there are physical objects”? Sceptical doubt takes our intuitions as empirical propositions, so we end up with “there are physical objects” as a hypothesis, with a counter-hypothesis, “there are no physical objects”. But if “there are physical objects” is nonsense, so is its negation. This is seen even more clearly with “there seem to be physical objects”, whose negation is unintelligible. Wittgenstein is saying in §36 that “physical object” is not available as an empirical category. Rather, it takes part in statements such as “A is a physical object”, which is similar to saying something such as, “we call A a 'physical object’”. Thus, it takes part in grammatical or logical statements, rather than empirical ones. I will try to explain this in what follows.

Moore infers from “here is a hand” that “there are physical objects”, but this is just what cannot be done. We cannot infer from “A is a physical object” that “there are physical objects”. Why not, exactly?

Well, way back in §2 Wittgenstein says “what we can ask is whether it makes sense to doubt it,” and this is the key. Is its negation unintelligible, as is “there do not seem to be physical objects”? I think so, because if we are to understand it as an empirical propositions we should be able to identify criteria for its truth. But what would they be? Nothing can stand as evidence for the non-existence of physical objects, because the sceptical doubt asks that we allow a different possible reality as explaining the world we experience, e.g., the malicious demon or the brain-in-a-vat hypothesis. But nothing would appear to be different if these were true, so it is impossible to accept them as empirical at all. Indeed, we cannot distinguish between the two cases, therefore we cannot make sense of them, because they present themselves as empirical propositions that have no criteria that can be attached to them, and thus provide not the faintest possibility of justification. Incidentally, this also indicates why we cannot say “I know there are physical objects,” because what is not justified is not knowledge.

But a thought occurs to me here. Isn’t this exactly the target of scepticism, that we have no justification for many of our basic beliefs? In which case, is Wittgenstein simply attempting to shrug it off, saying that yes, scepticism is right: we cannot know these basic beliefs. Crucially, though, he questions whether the question is philosophically significant, or can even be stated. Well, which is it? Explicitly, he claims that sceptical hypotheses are nonsense, but I am not completely convinced by this, and perhaps there is room here for the sceptic to say “Yes! That’s exactly what I’m saying! You cannot know that there are physical objects. In fact, you have no justification for the belief at all!”

The next section almost suggests that Wittgenstein anticipated these thoughts.

37. But is it an adequate answer to the scepticism of the idealist, or the assurances of the realist, to say that “There are no physical objects” is nonsense? For them after all it is not nonsense. It would, however, be an answer to say: this assertion, or its opposite is a misfiring attempt to express what can’t be expressed like that. And that it does misfire can be shewn; but that isn’t the end of the matter. We need to realize that what presents itself to us as the first expression of a difficulty, or of its solution, may as yet not be correctly expressed at all. Just as one who has a just censure of a picture to make will often at first offer the censure where it does not belong, and an investigation is needed in order to find the right point of attack for the critic.

There is, then, a “difficulty” here, regarding knowledge and certainty. It is almost as if Wittgenstein might say to the sceptic, “yes, you’re right, but you can’t say it like that. It’s true, we cannot find the certainty you’re looking for, but it’s a mistake to look for it.” Back in §26 he stated that there was no end to the possibility of error, and this points to the “difficulty”, and must surely invite the sceptic’s hyperbolical doubts.

A reminder:

Radical scepticism: our grounds for belief do not justify them at all

Perhaps, then, Wittgenstein would fall foul of Crispin Wright’s criticism of the response to scepticism that he calls the “Russellian Retreat”, which is the admission that we cannot prove, say, the existence of the external world. But this only looks like a retreat if you are willing to indulge the sceptic by playing him at his own game, which is exactly what Wright does, only to arrive at somewhere like the same position: the sceptic cannot legitimately argue for his hypotheses, and we must finally depend on Wittgenstein’s hinge propositions.

38. Knowledge in mathematics: Here one has to keep on reminding oneself of the unimportance of the ‘inner process’ or ‘state’ and ask “Why should it be important?” What does it matter to me? What is interesting is how we use mathematical propositions.

39. This is how calculation is done, in such circumstances a calculation is treated as absolutely reliable, as certainly correct.

40. Upon “I know that here is my hand” there may follow the question “How do you know?” and the answer to that presupposes that this can be known in that way. So, instead of “I know that here is my hand”, one might say “Here is my hand”, and then add how one knows.

If a calculation — which is a series of steps carried out to produce a result — is accepted as the right one for the job, then it is “treated as absolutely reliable,” and this is why, in a situation where we all agree that the calculation has been carried out correctly, any doubt about the result is illegitimate. Doubt in this case makes no sense, because it is the correct completion of the calculation that certainty here consists in. Our knowledge shows itself in our actions.

Upon “this is the solution to the equation” there may follow the question “How do you know?” The answer is the act of calculating, or pointing to the evidence of having carried out the calculation. Remember section 5, “Whether a proposition can turn out false after all depends on what I make count as determinants for that proposition.” The determinants for “this is the solution to the equation” may include the evidence of calculation, and likewise the determinants for “here is a hand” may include the fact that you can see it and feel it—which would be an answer to the question “how do you know?”

41 “I know where I am feeling pain”, “I know that I feel it here“ is as wrong as “I know that I am in pain”. But “I know where you touched my arm” is right.

I could retort with something like “but I know where I am feeling pain”, just to emphasize my obvious certainty in reply to an outrageously suspicious interrogator — and here I think we meet again the “queer and extremely important mental state” from §6, in which we are tempted to misuse the word “know” — but otherwise it is wrong to say I know something that I cannot doubt. But can others doubt it? Maybe they think I am pretending to be in pain. In that case, is it then correct to say “I know” to assuage their doubts? No, because only my honesty is being questioned, not my ability to correctly judge that I am in pain. Such a doubt would be senseless, thus rendering positive knowledge equally so—which takes us back to the tempting misuse. But my knowledge of where my arm was touched can be doubted, which is why I can say “I know where you touched my arm.”

42. One can say “He believes it, but it isn’t so”, but not “He knows it, but it isn’t so”. Does this stem from the difference between the mental states of belief and knowledge? No.—One may for example call “mental state” what is expressed by tone of voice in speaking, by gestures etc. It would thus be possible to speak of a mental state of conviction, and that may be the same whether it is knowledge or false belief. To think that different states must correspond to the words “believe” and “know” would be as if one believed that different people had to correspond to the word “I” and the name “Ludwig”, because the concepts are different.

Fairly obviously, what is known must be true, but what is believed need not be—and the mental state may be the same in each case. Why is this important to Wittgenstein at this point? To be sure, it means that one’s certainty is not necessarily a guarantee, to others, that one is not wrong. When we indulge in the tempting misuse, e.g., “What are you talking about? I bloody well know I’m in pain!” we convey certainty, but not, solely in the use of “I know”, knowledge. Is the point of this just to emphasize that this common misuse, which does communicate certainty, i.e., a mental state, should not be taken seriously as communicating an instance of knowledge?

43. What sort of proposition is this: “We cannot have miscalculated in 12×12=144”? It must surely be a proposition of logic.—But now, is it not the same, or doesn’t it come to the same, as the statement 12×12=144?

Although it might be wrong—because a claim to knowledge is not a guarantee of it—the former amounts to the same than the latter. Or if it means something more, all it can add is a self-conscious assertion of certainty, expressed in the same way as “I know I have two hands”. And as we have learned, it is in this kind of case that we cannot say “I know…”, as in “I know that 12×12=144”. It is akin to the difference—or lack of it—between “ '12×12=144’ is true” and “12×12=144”.

44. If you demand a rule from which it follows that there can’t have been a miscalculation here, the answer is that we did not learn this through a rule, but by learning to calculate.

45. We got to know the nature of calculating by learning to calculate.

46. But then can’t it be described how we satisfy ourselves of the reliability of a calculation? O yes! Yet no rule emerges when we do so.—But the most important thing is: The rule is not needed. Nothing is lacking. We do calculate according to a rule, and that is enough.

47. This is how one calculates. Calculating is this. What we learn at school, for example. Forget this transcendent certainty, which is connected with your concept of spirit.

Just as in §26 etc., we see that there is no rule that can guarantee freedom from error. What is taken as guaranteeing it is the act of doing it. Is this then a kind of relativism? Wittgenstein always seems to be driving at the (correlationist) notion that while there may be some questions about how we relate to the world, about how we fit in, they are not something we can ever talk about because we cannot see ourselves from the outside. So it is tempting to think that Wittgenstein’s main target is not only scepticism or idealism, but any talk at all about an independent world, realism coming in for criticism here too. There is thus a tension between, on the one hand, what seems to be an improvement upon Moore’s common sense realism, and on the other hand a strong correlationism that goes further than Kant in that it denies the legitimacy of any talk of things-in-themselves.

But this is not quite relativism. However, there is a deep relativism here as well, in that our bedrock beliefs, those intuitions that we must rely on and which cannot be doubted, exist within particular language games, presumably in different social contexts and times in history. One such language game, for example, is that of calculating a mathematical problem. Whether the calculation can turn out false depends on what, in this context, one takes as determinants (§5) for the proposition (the proposition being, e.g., “12×12=144”). Certainty and knowledge are relative to our language games, to what we make count as such.

But surely that leaves us with the question, what is the general character of that which we make count? This is probably what Wittgenstein is saying we should not ask, partly because in asking it we are looking for an essence, —forgetting about family-resemblances—and partly because we cannot get out of individual language games to do it. We cannot talk of a transcendent reality, because all—certainly all we can talk of—is correlation.

Noticing how easily I slipped in that last paragraph from relativism back to correlationism, it becomes apparent to me that Wittgenstein’s correlationism consists in his relativism.

All of this creates a disconcertingly wide latitude for interpretations—but that’s par for the course with Wittgenstein.

I think it’s worth upsetting the flow a little bit here by comparing some sections.

26. But can’t it be seen from a rule what circumstances logically exclude a mistake in the employment of rules of calculation? What use is a rule to us here? Mightn’t we (in turn) go wrong in applying it?

27. If, however, one wanted to give something like a rule here, then it would contain the expression “in normal circumstances”. And we recognize normal circumstances but cannot precisely describe them. At most, we can describe a range of abnormal ones.

28. What is 'learning a rule’? This. What is “making a mistake in applying it”? This. And what is pointed to here is something indeterminate.

29. Practice in the use of the rule also shews what is a mistake in its employment.

46. But then can’t it be described how we satisfy ourselves of the reliability of a calculation? O yes! Yet no rule emerges when we do so.-But the most important thing is: The rule is not needed. Nothing is lacking. We do calculate according to a rule, and that is enough.

47. This is how one calculates. Calculating is this. ...

96. It might be imagined that some propositions, of the form of empirical propositions, were hardened and functioned as channels for such empirical propositions as were not hardened but fluid; and that this relation altered with time, in that fluid propositions hardened, and hard ones became fluid.

97. The mythology may change back into a state of flux, the river-bed of thoughts may shift. But I distinguish between the movement of the waters on the river-bed and the shift of the bed itself; though there is not a sharp division of the one from the other.

I sense a connection between the idea (§26-29 and §46-47) that we can never set down a rule to guarantee our correctness; and the idea (§96-97) — which I looked at briefly in my recent post on intuitions — that we cannot delimit the field of propositions that could never be overturned. Are they two ways of saying the same thing? They are certainly closely connected, and we can see this especially in the phrase from §28, “what is pointed to here is something indeterminate.” The rules are indeterminate — they can never be set down with precision — and this is why the intuitions on which our activities are based, or which are demonstrated in those activities, are themselves also indeterminate in their extent, because the utility of the rule is in pinpointing, in our activity, which beliefs we can rely on. There is more to be said here, no doubt.

Getting back on track, from §47:

Forget this transcendent certainty, which is connected with your concept of spirit.

What does this mean? First of all, it is ruling out the possibility of metaphysical certainty, a justification from beyond our human world. The sceptic is therefore on to something, or has at least spotted that justification eventually comes to an end. If you really don’t mind affecting a hyperbolical doubt, then you won’t find anything standing in your way. Our knowledge depends on context, and it cannot establish itself from without. We cannot be more certain than we ordinarily are in those specific situations we find ourselves in — or, more accurately, in specific language games — where doubt does not enter our mind and is revealed, upon further examination, to be nonsense. It is a mistake to ask that we can reach to some deeper certainty: there is no such thing.

But what does Wittgenstein mean by saying that transcendent certainty is connected with the concept of spirit? Does he mean the concept of transcendent certainty? I must suppose so. And does this stand for metaphysical concerns in general? Or, which seems more likely, is it the transcendent soul, whose home is supposedly the reality above and beyond mundane human life? This makes sense, because it is when we are attached to the idea of a transcendent self that we expect to find transcendent certainty. Perhaps at this point it would help to keep in mind the historical context in which Wittgenstein is writing, and against whom his remarks are directed.

He is seeking to attack Moore’s enemies, after first exposing Moore’s own tactic as wrongheaded. Who were they? I have been referring to “the sceptic” all the way through these notes, and will probably continue to do so, but really Moore was more interested in specifically defending common sense against the idealism of Bradley. I’m not familiar with him, but from what little I’ve read he seems to have been the shining star amongst the group that was dominant in British philosophy until the analytic philosophy of Russell et al really took over. Their philosophy was a form of idealism owing much to Kant and Hegel, taking the metaphysical orientation from the latter. In fact, they came to be known as “neo-Hegelians”, a label probably applied by Russell and his cohorts. This could well explain Wittgenstein’s use of “spirit” (Geist), central to Hegel’s philosophy.

48. However, out of a host of calculations certain ones might be designated as reliable once for all, others as not yet fixed. And now, is this a logical distinction?

49. But remember: even when the calculation is something fixed for me, this is only a decision for a practical purpose.

50. When does one say, I know that … x … = ....? When one has checked the calculation.

Aside from his question, “is this a logical distinction?”, these sections seem to re-iterate earlier ones. But what is this question getting at? Let’s look at the next sections first.

51. What sort of proposition is: “What could a mistake here be like!” ? It would have to be a logical proposition. But it is a logic that is not used, because what it tells us is not learned through propositions.—It is a logical proposition; for it does describe the conceptual (linguistic) situation.

52. This situation is thus not the same for a proposition like “At this distance from the sun there is a planet” and “Here is a hand” (namely my own hand). The second can’t be called a hypothesis. But there isn’t a sharp boundary line between them.

Here is how I understand this. A logical proposition is about the language game, or about the concepts we are using. In contrast, there are other propositions that are about the world. But while there may be a logic to our rules and to our certainty, it is, like the rules, not explicitly used, because it is subsumed by our activities, which have not been learned “through propositions”. The logic is not ordinarily set out in the form of propositions, just as the rules are not set out explicitly.

Perhaps it is now clearer what he means in §36, when he says that “physical object” is only a logical concept, not a thing. To say that something is a physical object is not to say what it is but to explain how we can talk about it. Thus in §52, “here is a hand” is a logical proposition, and “At this distance from the sun there is a planet” is empirical. But there is no hard and fast way of telling which is which for all cases. This is rather difficult. Let’s see what we get from the next few sections, where this is elaborated.

54. For it is not true that a mistake merely gets more and more improbable as we pass from the planet to my own hand. No: at some point it has ceased to be conceivable. This is already suggested by the following: if it were not so, it would also be conceivable that we should be wrong in every statement about physical objects; that any we ever make are mistaken.

55. So is the hypothesis possible, that all the things around us don’t exist? Would that not be like the hypothesis of our having miscalculated in all our calculations?

“For it is not true that a mistake merely gets more and more improbable as we pass from the planet to my own hand.”

This emphasizes that it is the impossibility of doubt that renders a proposition logical rather than empirical. In going from the proposition “At this distance from the sun there is a planet” to “here is a hand”, we go from an empirical proposition, i.e., a hypothesis, to a logical one. What does this difference consist in? Not merely that certainty is approached ever closer—no, it must be a stronger distinction than that. It is simply inconceivable that this is not a hand, or that we could have made a mistake in the calculation. There is a discontinuity between these propositions. If there were a sliding scale from less to more certain, doubt would be possible for everything.

It looks, therefore, as if the hypothesis that the things around us don’t exist is not a hypothesis after all, but a logical proposition—that infringes, however, the logic of the language game. Or perhaps it is neither empirical nor logical. It appears in the guise of a hypothesis, but the kind of propositions it can question never appear as hypotheses, indeed never appear as logical propositions, but express the underlying logic that cannot be doubted from within our language—the only place where doubt can take place.

56. When one says: “Perhaps this planet doesn’t exist and the light-phenomenon arises in some other way”, then after all one needs an example of an object which does exist. This doesn’t exist,— as for example does ... Or are we to say that certainty is merely a constructed point to which some things approximate more, some less closely? No. Doubt gradually loses its sense. This language-game just is like that. And everything descriptive of a language-game is part of logic.

I think this simply summarizes his, and my, foregoing remarks, although I wonder about how to interpret “Doubt gradually loses its sense” in the light of the previous sections. Although it suggests a gradualism that I was arguing against with my “discontinuity”, I do think he means us to understand that there comes a point when doubt has completely lost its sense.

But we need to go back to §53.

53. So one might grant that Moore was right, if he is interpreted like this: a proposition saying that here is a physical object may have the same logical status as one saying that here is a red patch.

That Moore was right in saying what, exactly? In saying “I know that here is a hand”, or in inferring “there are physical objects” from “here is a hand”. I’m inclined to go with the latter. But what could it mean to say that this is right if we take “here is a hand” to be logically on a par with “here is a red patch”? This would appear to be emphasizing the logical, that is, grammatical, nature of such propositions. According to Daniele Moyal-Sharrock, these propositions, which Peter Strawson calls crypto-propositions, are the famous hinge propositions.

Masquerading as propositions, they are uncovered as in fact belonging to the framework, the scaffolding of our thoughts.
(Daniele Moyal-Sharrock)

Next, Wittgenstein investigates the “queer and extremely important mental state” from §6.

57. Now might not “I know, I am not just surmising, that here is my hand” be conceived as a proposition of grammar? Hence not temporally.—But in that case isn’t it like this one: “I know, I am not just surmising, that I am seeing red”? And isn’t the consequence “So there are physical objects” like: “So there are colours”?

58. If “I know etc” is conceived as a grammatical proposition, of course the “I” cannot be important. And it properly means “There is no such thing as a doubt in this case” or “The expression 'I do not know’ makes no sense in this case”. And of course it follows from this that “I know” makes no sense either.

59. “I know” is here a logical insight. Only realism can’t be proved by means of it.

60. It is wrong to say that the 'hypothesis’ that this is a bit of paper would be confirmed or disconfirmed by later experience, and that, in “I know that this is a bit of paper”, the “I know” either relates to such an hypothesis or to a logical determination.

This confirms my suspicions, expressed above in my notes on §54 and §55: when we slip into what I have been calling the “tempting misuse”, we do not manage to state empirical or logical propositions. The propositions appear as hypotheses but actually express an underlying logical insight, but cannot properly act as logical propositions. In §57 Wittgenstein wonders if “I know…” statements can act logically, that is, grammatically, just like “here is a hand”. In §58 he shows some sympathy with the tempting misuse, and it is also this misuse that he is referring to in §59.

This “logical insight” is thus the “queer and extremely important mental state”. A reminder…

6. Now, can one enumerate what one knows (like Moore)? Straight off like that, I believe not. For otherwise the expression “I know” gets misused. And through this misuse a queer and extremely important mental state seems to be revealed.

What does this insight consist of? I think it is when we seek to appeal to the fastness of the framework, the one on which our talk and our concepts hang, and which they depend on for their meaning. This framework — or it might help to think of it as the bedrock — is what supplies certainty, and which itself cannot be justified. When we say “I know that here is a hand”, although it is a misuse, it expresses our strong feeling that the framework is secure, that the bedrock is solid. And the framework is secure, by its own nature.

Someone may repeatedly ask us “but how do you know?”, and when we have exhausted the empirical determinants there is no way to express, in propositions, our most basic certainty, without misusing words.

61. ... A meaning of a word is a kind of employment of it. For it is what we learn when the word is incorporated into our language.

62. That is why there exists a correspondence between the concepts 'rule’ and 'meaning’.

63. If we imagine the facts otherwise than as they are, certain language-games lose some of their importance, while others become important. And in this way there is an alteration—a gradual one—in the use of the vocabulary of a language.

64. Compare the meaning of a word with the 'function’ of an official. And 'different meanings’ with 'different functions’.

65. When language-games change, then there is a change in concepts, and with the concepts the meanings of words change.

Rules and meanings correspond because the meaning of a word is demonstrated by the way it is used, and we are presumably following a rule when we do this. But it is difficult to see quite what the difference is. Perhaps meaning is a special kind of rule? Or meaning bubbles up in a language game owing to the particular intersection of rules that we are following. Now why do I say “bubbles up”? Because if we fix our gaze upon it when analyzing language, we draw it out of its natural home.

Well, the difference is most probably nothing very exotic: we follow ordinary grammar rules, for instance, and meaning takes place in that framework. But two things make Wittgenstein’s concept unique: first, we cannot delimit the language game by making the set of rules explicit—the rules are not so well-defined and static as that—and second, we have not necessarily learned to follow the rules by learning the rules themselves —most of the time we learn them and exhibit them just by following them. Practice makes perfect.

My interpretation of §64 makes things clearer. I understand “function” here as I understand the function of a tool, making words (and not only words but expressions of many kinds) akin to tools. Think of the construction of an Ikea desk. The rules are set down in this case in the instructions, and these determine when and where one should apply the functionality of the Allen key. Thus the rules correspond to the tool’s functions.

I get the feeling I haven’t got to the bottom of this, but that may be owing as much to Wittgenstein’s vagueness as to my own. In any case I haven’t yet read Philosophical Investigations, which has more on rule-following.

Next part


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

Genia Schönbaumsfeld, “‘Objectively there is no truth’ – Wittgenstein and Kierkegaard on Religious Belief”, published in, Ulrich Arnswald (ed), 2009, In Search of Meaning, Ludwig Wittgenstein on Ethics, Mysticism and Religion, Universitätsverlag Karlsruhe

Williams, M, 2004, “Wittgenstein’s Refutation of Idealism”, In Denis McManus (ed.), Wittgenstein and Scepticism, Routledge

Daniele Moyal-Sharrock, 2004, Understanding Wittgenstein’s “On Certainty”, Palgrave Macmillan

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