The Erosion of Certainty
The Erosion of Certainty


This paper gives an account of the eroding action operated by Wittgenstein on the concept of ‘certainty’. Wittgenstein’s difficulties in totally refusing Moore’s ‘common-sense’ certainty and in leaving the Tractarian reminiscences behind engender ambiguities in his discourse. Yet, all the dichotomies that seem to stem from Wittgenstein’s opposition between scientific certainty and certainty as unquestionable sureness will prove, in the end, onlyapparent. The certainty of Über Gewissheit is polymorph, and the title that Wittgenstein’s executors gave to the collection of his last notes is ineluctably poly-sense.

Table of contents

    In his “Defence of Common Sense”, Moore had bumped into the deadlock of the correct analysis of truisms. He had spotted the key-role of the sense-datum and its non-coincidence with the external object which one claims to exist; other than that, he could only conclude that sense-data have a go-between role for our experience of the world, yet no account of their ultimate nature is available. In “Proof of an External World”, he had urged that the external world existed, and had existed independently from our present, and past, perception – the premise of the first proof being the gesture of showing his hands; the premise of the second proof, his trustful, introspective appeal to memory.

    In Wittgenstein’s opinion, the reason why it makes no sense to doubt of what introspection and sense data tell me is not the truisms’ content being evident, rather their belonging to a form of life. The truth-conditions of a proposition do not depend on its mirroring a reality, but on a wider set of propositions within which the proposition fits. Although this does not seem to differ much from what Wittgenstein has been theorizing up to 1950, this is not the case:

    When one says that such and such a proposition can’t be proved . . . that does not mean that it can’t be derived from other propositions; any proposition can be derived from other propositions. But they may be no more certain than it is itself. (Wittgenstein ²1974, §1)1

    This foreshadows a picture of knowledge where the verbal dimension is central. A proposition such as ‘here is one hand’ could be derived from the proposition: ‘here is my body’, but cannot be known: they both belong to the background of knowledge. Knowledge in the proper sense relates to tallying with facts – the objective establishment of truth which links to the possibility of doubt; with hypothetical statements “which, if they turn out to be false, are replaced by others” (OC 402). Ungrounded sureness is instead defined by description, to which “[a]t some point one has to pass from explanation” (OC 189); it is made of norms that logically exclude a mistake, and are born out of practice. The lack of sureness has to do with the possibilities of madness, but not with error. Yet, the border between madness and oddness is not so sharp:

    I might . . . interrogate someone who said that the earth did not exist before his birth . . . . And then it might be that he was contradicting my fundamental attitudes, and . . . I should put up with it2. (OC 238)

    Certainty in the sense of knowledge can be grounded on sense-data and memory, but not certainty in the sense of sureness, because the assumptions which sureness is embedded in are unshakable convictions.

    This links to the distinction between ‘empirical propositions’ and ‘norms of descriptions’ – propositions whose form is empirical, but whose content is logical. Whereas empirical propositions are hypothetical, the norms of description fit into a world-picture, which “is the matter-of-course foundation for” (OC 167) scientific research. “[T]he same proposition may get treated at one time as something to test by experience, at another as a rule of testing” (OC 98). A key question arises: are the procedures to state when a proposition has to be considered empirical or methodological strictly rigorous and merely depending on the different contexts within the same and stable system of beliefs? An example of how a proposition can thus switch is outlined by von Wright:

    Consider . . . the proposition that I have two hands. . . . I have undergone an operation . . . . I wake up and am not . . . clear what has happened . . . . Was . . . one of my hands amputated? I look and see them both. Then my knowledge that I still have two hands can be said to rest on ‘the evidence of my senses’. But I did not learn that I have two hands by looking at them and counting. (von Wright 1982: 170-171)

    In normal circumstances, I should “test my eyes” (OC 125), not whether I have two hands. The exceptions within normal circumstances confirm a rule (of trusting one’s own senses) which no one has yet ever explicitly been taught. Is the limit according to On Certainty a Tractarian limit between what can and cannot be said? If so, Moore’s objections to skepticism would be a misfired attempt to say what can only be shown; hence Moore’s failure to provide a comprehensive analysis of truisms. Yet, Wittgenstein is not satisfied with the opposition between what can and cannot be expressed: “that isn’t the end of the matter” (OC 37), he says. The issue has not been concluded once and for all in the Tractarian dichotomy:

    The propositions describing [my picture of the world] might be part of a . . . mythology 3 [which] may change back into a state of flux [and] the river-bed of thoughts may shift. (OC 94-95, 97)

    Empirical propositions are the water of the river. The limit-propositions form the river-bed. Their grammatical function has been fixed, yet it is not unchangeable. Furthermore, no matter how hard or friable the river-bed is, it can shift: the possibility of change does not simply concern the different use one can make of a proposition according to the different contexts within a fixed frame of reference. The border between the contingent and the unsayable in the Tractatus was cogent; inOn Certainty the unsayable becomes contingent. Within a system, there is no possibility of imagining how an unheard-of shift of the system itself would occur. Wittgenstein says that logic is not an empirical science, but “the same proposition may get treated at one time as something to test by experience, at another as a rule of testing” (OC 98): the border is fuzzy because of the impossibility of a clear-cut definition of the point where a mistake ceases to be improbable and becomes inconceivable. Wittgenstein’s disproof of the myth of the rule as an entity other than its praxis has to be distinguished from the prospect of conflicting belief-systems (or even, of the unheard-of). Only the first element is present in all of Wittgenstein’s later works; both can be found inOn Certainty. Wittgenstein embraces, within the set of limit-propositions, also propositions that should be fully granted an empirical status. He says: “if Moore says he knows the earth existed [long time before my birth], most of us will grant him [that]” (OC 91); yet, he adds, “why should not a king be brought up in the belief that the world began with him?” (OC 92). Neither Moore nor the king has telling grounds. There follows, a shift of belief would depend on a shift in the way one looks at the world. Both Moore and Wittgenstein make the mistake of embracing within the set of truisms, among others, statements about the age of the earth. Yet, while this confusion does not affect Moore’s epistemology, it leads Wittgenstein to conclude that the main criteria of both endorsing a world-view and all knowledge within it are simplicity, symmetry, and practical convenience; one could build houses even believing that the earth is flat, because this belief has no practical effects relative to their construction. A hypothesis can get assumed as a truism. This is not entirely questionable: there are indeed facts which apparently cannot be explained by science, until the latter is more advanced. An example can be found in Wittgenstein: no one had ever been on the moon in his lifetime; the opposite was for Wittgenstein himself unconceivable. Some propositions which have always been assumed as truisms can indeed become falsifiable. In Wittgenstein’s view, nonetheless, if the adults of a tribe claim they have been on the moon in their dreams, and that dreams are the means to get there, we can conclude that it is true that no one has ever been on the moon only if we are thinking within our system. Truth is system-related; and this, one may question, for systems get reversed (all main axioms of mathematics standing nonetheless fast) with no need for truth to be culture-related, because science is not confined to simplicity, practicability and symmetry.

    Wittgenstein, among the “unshakably fast” (OC 144) elements of a system both includes beliefs of tangible and intangible nature. A distinction thus appears not to be required between a child’s belief in God and a child’s belief that the earth existed long before he was born. The axis around which the body of my knowledge rotates is fixed not because it is made of “intrinsically obvious” (OC 165) elements, rather what we learn is a “host of interdependent propositions” (OC 274) hard to doubt because they are not isolated, yet related through experience: this is why the probability of subversion is low – the immobility has not much to do with the different (either empirical or grammatical) use one can make of a proposition within a fixed frame of reference. Knowledge relies on “generally accepted axioms” (OC 551) in which one believes. Wittgenstein claims that the fundamental contradictions of mathematics do not affect its application (e.g. even if the figure of a square’s diagonal cannot be put into a fraction, it can still be applied as an indicator of the diagonal’s length). Yet, the key point is that “something must be taught us as a foundation” (OC 449) in order for us to perform actions – no matter if, eventually, “there seems to be no clear boundary between [the cases] where doubt is unreasonable [and others] where it seems logically impossible” (OC 454); therefore, “even when the calculation is . . . fixed for me, this is only a decision for a practical purpose” (OC 49). Similarly, logic has to be seen by looking at the practice of language, and what belongs to logic has the “character of a rule” (OC 494). Yet a rule is defined as emerging from man’s animal instinct of survival, not from ratiocination. Whether Wittgenstein considers or not logic and mathematics to be subject to alteration, the axioms of empirical science do not seem to be impervious to paradoxical changes; and because many of those axioms actually belong to mathematics, Wittgenstein seems to be indirectly claiming that no single bit of certainty is invulnerable to revision: “[i]f something really unheard-of happened?” (OC 513) that twisted the system, all its axioms would be dragged away with it. Wittgenstein is not arguing per absurdum that this cannot occur. He holds, for instance, that some irregularity in the events of nature might occur, so that the law of induction would prove no more valid, yet one may as well be able to make inferences, although not according to that law. Yet, we do not have the need, or the frame of mind to think of the unheard-of. Unthinkable possibilities, therefore, do not contrast the senselessness of doubt within our system. This nevertheless does not protect us from the following: “I can’t be making a mistake, – but some day, rightly or wrongly, I may think I realize that I was not competent to judge” (OC 645).

    Wittgenstein arguments imply that it is hard for conflicting belief-systems to intercommunicate. In one of his parable4, he takes an airplane to some place whose inhabitants have never heard about the possibility of flying. He explains to them how he flew there, but they respond he may be in error. Wittgenstein thus considers the possibility of convincing them by describing the whole event. What could occur now, he reckons, is that they would admit him not to be mistaken, yet to have dreamt the whole episode or been induced by a magic to that belief. He does not grant these people the possibility of at least believing that he was transported by a magic machine: the only thing that they can be imagined to be able to admit is that it was a dream. The possibility of convincing even once one has found a common language is excluded.

    The complexity of one key passage deserves attention:

    “I know” has a primitive meaning . . . related to “I see” . . . . “I know” is supposed to express a relation, not between me and the sense of a proposition . . . but between me and a fact. So that the fact is taken into my consciousness. (Here is the reason why one wants to say that nothing that goes on in the outer world is really known, but only what happens in the domain of . . . sense-data.) This would give us a picture of knowing as the perception of an outer event through visual rays which project it as it is into the eye and the consciousness. Only then the question arises whether one can be certain of this projection. And this picture [shows] how our imagination presents knowledge, but not what lies at the bottom . . . . (OC 90)

    A misled picture makes one fall into the sceptical trap: if knowledge is a consequence of a projection of a fact operated by my senses, I am led to ask how I can be sure of this projection. A satisfactory answer does not come; it seems, consequently, that one can be sure only of sense-data, but not of what lies at the bottom of our knowing. Wittgenstein is implying that knowledge is ultimately a relation between me and the sense of a proposition: “a proposition … only gets sense from the rest of our procedure of asserting” (OC 153). Only this way doubt will not arise about what lies at the bottom. Knowledge is related to sense-data, but any deep belief in this relation to the point of making it the essence of knowledge entails that we are tempted to go beyond them in order to prove the existence of the external world. Sense-data are the indubitable limit, yet so indubitable that the domain of sense-data dissolves into that of language.

    One may observe that the procedure of asserting is for Wittgenstein modelled on the practice of every-day action; yet a belief’s resistance to change is subordinated to a hermeneutics which makes the distinction between the authority of the human form of life and the one of text-books feeble. Wittgenstein says that we learn countless things from the authority of adults. Experience is for Wittgenstein not able to disconfirm anything belonging to the ungrounded frame whose propositions characterize “my interpretation of experience” (OC 145) and cannot therefore be put to test, and should not even be put into text. However, the very fact that the frame ultimately “swallows” (OC 143) all empirical consequent beliefs and actions makes even the text prevail on empirics. Everything can potentially fit into an ungrounded frame, as long as it is “removed from traffic” (OC 210). Historiography itself is conceptualized as a language game of meaning ascription to events: although Wittgenstein concurs that it is subordinated to the belief in the existence of the earth at least when the events described occurred, he does not grant any definite border between propositions which cannot be “subject to testing” (OC 162) and the reports of historiography. The propositions contained in textbooks are virtually as incorrigible as Moore’s truisms. This does not simply mean that testing must come to an end, at some point, in order not to block research; more profoundly, even Moore’s truisms can be reduced to pure text, and every certainty is ultimately verbal; it is, altogether, story.


    1. Moore, George E. 1925 “A defense of common sense”, in: Moore, George E. 1959 Philosophical Papers, London: Gorge Allen & Unwin Ltd..
    2. Moore, George E. 1939 “Proof of an external world”, in: Moore, George E. 1959 Philosophical Papers, London: Gorge Allen & Unwin Ltd..
    3. Von Wright, George H. 1982 “Wittgenstein on Certainty, in: von Wright, George H. 1982 Wittgenstein, Oxford: Blackwell, 162-182.
    4. Wittgenstein, Ludwig ²1974 Über Gewissheit, G. E. M. Anscombe and G. H. von Wright eds., Eng. Tr. by Denis Paul and G. E. M. Anscombe, On Certainty, Oxford: Blackwell.
    Hereafter referred to as OC (abbreviation of “On Certainty”), followed by paragraph number.
    My emphasis.
    my emphasis.
    Cf. OC 671.
    Silvia Lanzetta. Date: XML TEI markup by WAB (Rune J. Falch, Heinz W. Krüger, Alois Pichler, Deirdre C.P. Smith) 2011-13. Last change 18.12.2013.
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