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BY 4.0 license Open Access Published by De Gruyter March 14, 2022

Certainties and Rule-Following

Andreas Krebs
From the journal Wittgenstein-Studien


This paper argues that Wittgenstein does not assimilate certainties to either linguistic norms or empirical propositions but assigns them to a liminal space between rule and experience. This liminal space is also brought into play in remarks written at the same time as those compiled in On Certainty, but attributed to different bodies of text (Remarks on Colour, Last Writings on the Philosophy of Psychology). The paper maintains that certainties express the agreement and constancy in judgements without which – as Wittgenstein contends in his Philosophical Investigations – rule-following would not be possible. It is shown that this intrinsic relation between rule-following and certainties can explain the liminal status of the latter.

1 Introduction

Most interpretations of On Certainty still treat the text as an independent work, relating its contents mainly to problems of epistemology. This approach tends to neglect cross-references to other topics that occupied Wittgenstein at the same time, such as the logic of colour concepts. Moreover, On Certainty is rarely considered in the context of Wittgenstein's later work as a whole. For philological reasons alone, this way of reading On Certainty is insufficient. As a comparison with the original manuscripts shows, the editors played a significant role in shaping particular sequences of notes into a text suggesting a fair degree of coherence. Even the title “On Certainty” is an invention of the editors. The numbering, also added by them, indicates a well-considered arrangement of remarks, as found in the Philosophical Investigations. In On Certainty, however, the remarks simply appear in the order of the notebook entries. It is no surprise, therefore, that On Certainty also contains contradictory lines of reasoning; in his assessment of some problems, Wittgenstein remains undecided. Additionally, not to be underestimated is the editorial decision to assign the remarks from Wittgenstein’s last notebooks to different bodies of text – besides On Certainty, the Remarks on Colours, the Last Writings on the Philosophy of Psychology, Vol. 2, and Culture and Value. By and large, the editors have based this arrangement on indications given by Wittgenstein: Some remarks are labelled by vertical lines as secondary thoughts – they appear in Culture and Value if they were deemed worthy of publication at all (cf. e. g. MS 174, 5v/CV 1980, 98) – and sometimes changes of topic are clearly identified by horizontal lines (cf. e. g. Ms 174, 14v). Wittgenstein, however, is inconsistent in his use of such markers, as are the editors in interpreting them. There are several examples of unmarked entries nevertheless being published in Culture and Value (cf. e. g. MS 174, 1v-2/CV 1980, 97); moreover, thematic caesurae are assumed at places where horizontal lines are missing (e. g. MS 176, 22r), and these assumptions are not always compelling (e. g. MS 173, 99v-BCr/ROC 1977, III 348 – 350 could as well have been part of “On Certainty”).

It should be remembered, therefore, that the Remarks on Colours, On Certainty, and longer passages of Vol. 2 of the Last Writings on the Philosophy of Psychology originally belong to one text. In fact, the notes published at these different places share several topics that do not, or only marginally, appear in Wittgenstein’s other writings. In this paper, I will take a closer look at one of these topics: a family of propositions that can neither be clearly assigned to linguistic rules nor to empirical propositions and which belong to a liminal space between grammar and experience. Furthermore, I want to show that the dualism between grammar and experience is already undermined in the remarks on rule-following in the Philosophical Investigations. I will then present a thesis on how certainties are related to rule-following as seen by Wittgenstein.

2 The liminal space between rule and empirical proposition in On Certainty

In the remarks compiled in On Certainty, Wittgenstein deals with commitments (cf. Pritchard 2016) that can be expressed by propositions such as 'This is my hand,' 'There is a tree,' 'My name is A.K.,' or 'The earth is very old.' What such certainties have in common with grammatical propositions – such as 'solitaire is a game for one player' – is their normative power. That is, we would not demand evidences, not accept alleged counter-evidences, nor take doubts seriously. Empirical propositions about me, my body, my environment or about the age of the earth are only possible if those certainties are presupposed without question. Usually, they are standards for what we would accept as empirical propositions. In this respect, certainties are similar to rules. But they also differ from the latter: while the sentence 'You do not play solitaire alone' is nonsensical since we do not use the word 'solitaire' that way, it is possible that I wake up after a surgery and find that this is not my hand, but a prosthesis. I could turn out that this is not a tree if, for example, there is heavy fog. One day, I might have to notice from other people’s reactions that I can no longer rely on my memory or even remember my own name. We can imagine a king brought up in the belief that the world ist not very old, but began with him (OC 1974, 92). The negation of certainties is not nonsensical.

Wittgenstein even considers it conceivable that “something really unheard-of happened.” For example, “houses gradually turning into steam without any obvious cause” or cattle standing on their heads, laughing and speaking comprehensible words (OC 1974, 513). In such a situation, we could continue to hold on to our certainties and conclude, for instance, that we must be hallucinating. In this case, certainties would function like grammatical rules: if one puts two apples in a basket, and then another two, and thereupon realises that there are now five apples in the basket, one does not doubt mathematics, but still accepts '2+2=4' as standard of experience and concludes that one must have been mistaken; perhaps the basket was not really empty, or three apples were grabbed instead of two. But in the case Wittgenstein imagines, we could also treat certainties as empirical propositions now falsified. Whether certainties would continue to function as norms or rather like revisable empirical propositions in unusual circumstances, is not clearly defined by their logical status. Therefore, one cannot state in general terms, i. e. for all conceivable cases, whether certainties determine the space of possible facts or rather have to be considered as statements of fact themselves. This is probably also what Wittgenstein has in mind when he says that holding on to certainties can have something in common with a “decision” (OC 1974, 386).

The possibility that a certainty loses its status is not, however, limited to such extreme situations. Wittgenstein involuntarily gives an example of this: “No one has ever been on the moon” (OC 1974, 106 etc). At the beginning of the 1950s, when Wittgenstein wrote this sentence, it expressed a certainty; today it no longer holds. Wittgenstein captures the historical mutability of at least some certainties in a memorable image: “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 […] the river-bed of thoughts may shift” (OC 1974, 96 – 97).

Certainties seem to be something in between rules and empirical propositions. They may oscillate between grammar and experience, and they can change their status. Wittgenstein asks: “Is it that rule and empirical proposition merge into one another?” (OC 1974, 309). A little later, he implicitly answers in the affirmative: “But wouldn't one have to say then, that there is no sharp boundary between propositions of logic and empirical propositions? The lack of sharpness is that of the boundary between rule and empirical proposition” (OC 1974, 319).

Wittgenstein's expression “lack of sharpness” indicates also another aspect; the family of certainties is quite divergent in itself. Not all of them stand between rule and empirical proposition in exactly the same way. Some are closer to rules, others to experience. There can even be something like a smooth transition between rule, certainty, and experience: the sentence ‘This is my hand’ can express a certainty, but if such a sentence was used in everyday-contexts, it would probably function as a grammatical proposition (an ostensive definition of the word 'hand'). Grammatical rule and certainty are hardly distinguishable in this case. But what about 'There is a conifer'? And if we go further to 'There’s a rabbit running,' we have clearly to reckon with a likelihood of mistake, even more so in the case of 'There’s a ship on the horizon;' finally, in the case of statements about planets that are based on astronomical measurements, we are in the realm of empirical hypothesis. The smooth transition between rule, certainty, and empirical proposition may incline us to attribute the varying degree of certainty to the varying favour of the epistemic situation and thus to the varying probability of a mistake. But Wittgenstein insists on a qualitative leap from the possibility or impossibility of a mistake in the sense of the probable to the possibility or impossibility in the sense of the conceivable: “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” (OC 1974, 54). What Wittgenstein refers to as “at one point,” however, cannot precisely be determined.

The idea of rules and empirical propositions “merging” into one another has not played a major role in the interpretation of Wittgenstein so far. Michael Kober, for example, advocates an interpretation that aligns certainties with rules or norms (Kober 1993). Circumstances in which certainties turn into empirical propositions are taken into account by a contextualism: the normativity of certainties is limited to certain contexts, while in other contexts they can be verified or falsified through experience. This cotextualist solution is motivated by Kober’s commitment to the dualism of rule and experience – depending on the context, certainties are either this or that – rejecting a genuinely ambivalent status of the latter. Rush Rhees’ reading of On Certainty is an example of the opposite one-sidedness (Rhees 2003). He insists on the empirical content of certainties and comes into trouble when trying to explain their normative power. Both approaches fail to do justice to what constitutes the specificity of certainties: Certainties relativise the dualism of grammar and experience, belonging to a liminal space in between.

3 The liminal space between rule and empirical proposition outside of On Certainty

The interpretation favoured here, however, might be criticised for relying on a narrow textual basis. In On Certainty, a transitional space between rule and empirical proposition is explicitly mentioned only in the remark already quoted, formulated as a question: “Is it that rule and empirical proposition merge into another?” (OC 1974, 309). It is at this point that it becomes relevant to also include considerations of Wittgenstein that were assigned to Remarks on Colours and Last Writings on the Philosophy of Psychology, Vol. 2.

In Remarks on Colours, we read: “Sentences are often used on the borderline between logic and the empirical, so that their meaning changes back and forth and they count now as expressions of norms, now as expressions of experience.” (ROC 1977, I 32) This remark appears in the context of Wittgenstein's reflection on the fact that a white coloured glass is not transparent, whereas green coloured glass is, or that the colour grey cannot be luminous. Surely, one would hardly call a luminous colour 'grey'. But if 'yellow is a luminous colour' and 'grey is a neutral colour' were nothing but grammatical propositions, one could reduce a proposition like 'The painting shows a yellow figure glowing against a neutral grey background' to the proposition 'The painting shows a yellow figure against a grey background.' This reduction, however, is connected with a loss of information. The first proposition speaks of a colour experience that can occur in varying intensity, the second does not. Statements about the qualities of colours, therefore, oscillate between rule and empirical proposition (cf. ROC 1977, II 80). The same is true of the proposition: 'Pure yellow is lighter than pure, saturated red.' “Where,” Wittgenstein asks, “do we draw the line here between logic and experience?” (ROC 1977, III 4). And a little later, he notes: “And don’t I have to admit that sentences are often used on the borderline between logic and the empirical, so that their meaning shifts back and forth and they are now expressions of norms, now treated as expressions of experience?” (ROC 1977, III 19).

Another interesting remark has found its way into the Last Writings on the Philosophy of Psychology, Vol. 2: “Is the impossibility of knowing what goes on in someone else physical or logical? And if it is both – how do the two hang together? / For a start: possibilities for exploring someone else could be imagined which don’t exist in reality. Thus there is a physical impossibility. / The logical impossibility lies in the lack of exact rules of evidence” (LW Vol. 2 1992, 94e/Ms176,50v). – 'I cannot know what is going on in another person' again oscillates between rule and experience: There is no machine that would make a person’s thoughts visible to everyone: this is an empirical or “physical” fact. That we have no exact rules concerning the validity of evidence for what we call the inner life of another person, is a grammatical or “logical” observation.

From this brief synopsis we can see that Wittgenstein, in his latest notes, repeatedly puts forward the idea that there might be a liminal space between rule and experience, and that there appear to be propositions that oscillate between the two. The recurrence of this idea in different contexts indicates that Wittgenstein considered it very seriously. Nonetheless, he also seems to see it as something surprising or objectionable; his remarks remain cautious and questioning.

4 Agreement and constancy in our judgements

What makes the discovery of a transition between rule and empirical proposition so difficult to accept? It is the fear that a dualism still cherished in philosophy, the dualism between a priori and a posteriori, might be undermined. But this dualism is not only challenged in Wittgenstein's last writings, but already in his Philosophical Investigations. There, §242 says: “If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgements. This seems to abolish logic, but does not do so” (PI 1958, 242).

This remark belongs in the context of Wittgenstein’s dealing with the problem of rule-following. One can explain a linguistic practice by formulating a rule. But is not the rule itself in need of explanation? What rule guides the application of the rule? And again, would not the rule for applying the rule have to be explained by another rule? Since one would never come to an end with this, it seems as if a rule could never determine a course of action. “It can be seen that there is a misunderstanding here,” says Wittgenstein, “from the fact that in the course of our argument we give one interpretation after another; as if each one contented us at least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it' in actual cases” (PI 1958, 201). A summary of this argument can also be found in On Certainty: “Not only rules, but also examples are needed for establishing a practice. Our rules leave loop-holes open, and the practice has to speak for itself” (OC 1974, 139).

But the practice can only speak for itself if there is a fundamental agreement in our judgements. If we would, for example, always or mostly disagree in the results of measurements, the distinction between correct and incorrect applications of the rules of measurement would also collapse. Analogously, this holds for colours as well. In Zettel, Wittgenstein remarks: “'If humans did not in general agree about the colours of things, if undetermined cases were not exceptional, then our concept of colour could not exist.' No: – our concept of colour would not exist” (Z 1981, 350).

In the Philosophical Investigations, §242, Wittgenstein also states that the practice of measuring is determined by a certain “constancy” in the results of measurement (PI 1958, 242). It is interesting that Wittgenstein speaks of both agreement and constancy. “Agreement,” on the one hand, lets us think of those who make judgements who, under normal circumstances, do not fundamentally disagree about a given situation. “Constancy,” on the other hand, draws our attention to the judgements themselves, reminding us of the fact that, usually, they deviate from each other only within certain limits. It can easily happen that the size of an object is first given as ten centimetres, then as twelve; but if a measurement yielded ten centimetres one time and two metres the other, and if such things happened very often, it would be difficult to imagine how our rules of measurement could still exist in its practice.

Going with Wittgenstein beyond Wittgenstein, these observations lead me to the thesis: Certainties with their peculiar status between logic and experience express the agreement and constancy in our judgements which is necessary in order to have a language at all. If we did not agree that this table is around one meter high, that this colour is blue, or that this is a tree, it would be unclear how we could even have a conversation about measures, colours, or trees. We can disagree about the age of the earth (is the earth around 4 or rather around 5 billion years old?), but the whole discourse in which this disagreement can be expressed rests on the agreement that the earth is far older than our lifespan. Understanding in language requires not only agreement on definitions, but also an agreement and a constancy in judgements since the former is not independent from the latter – at least if Wittgenstein is right in maintaining that rules can only exist in practice.

This consideration makes it possible to situate certainties in the larger context of Wittgenstein's late philosophy. Moreover, it becomes comprehensible why certainties belong to a liminal space between rules and empirical propositions which defies exact demarcation. The practice of measurement presupposes the absence of an arbitrary divergence of results; it is, however, not possible to determine precisely how significant and frequent divergences may be without endangering the agreement and constancy in our judgements. The same applies to other cases: Scientific hypotheses on the age of the earth diverge considerably, whereas there is a range that must remain stable; and although it is clear that far more than the last hundred years fall within this range, there is no clear-cut definition of the latter. Similarly, it is not possible to specify a certain quality of the visual conditions and an exact distance of an object which would define a radius within which we are certain of our perceptions (and must be, if our language on perceptions is to function at all).

The fact that certainties are expressions of the agreement and constancy in judgements finally explains why certainties have also a normative power: we reject evidences that would undermine the agreement and constancy in judgements – which is intrinsically related to following linguistic rules – as long as possible. This does not mean that certainties cannot be shaken, but if large parts of our empirical judgements do indeed shift so radically that a certainty loses its status, they soon rearrange themselves within new certainties, which in turn take on a normative character. In this case, the river has shifted and created a new riverbed.


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Rhees, Rush: Wittgenstein’s On Certainty. There – Like Our Life, Oxford 2003.10.1002/9780470776247Search in Google Scholar

Published Online: 2022-03-14
Published in Print: 2022-03-14

© 2022 Walter de Gruyter GmbH, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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