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The possibility of error is related to the existence a norm. Connections are spelled out to the notion of infallibility and to that of a modifying predicate, to traditional truth theories in connection with “truth of things”, as well as the primacy of the negative cases, for instance “false friend”.


Error Norm Infallibility Modifying predicate 
On August 3rd, 1650, one Oliver Cromwell, Lord General of the New Model Army, and shortly to become Lord Protector of the Commonwealth of England, wrote “To The General Assembly of the Kirk of Scotland; or, in case of their not sitting, To the Commissioners of the Kirk of Scotland”.1 In his letter the following famous sentence occurs:

I beseech you in the bowels of Christ think it possible that you may be mistaken.

Upon reflection part of his statement strikes me as extra-ordinary:

think it possible that you may be mistaken.

He did not ask the members of the General Assembly to think it possible that they actually were mistaken in the case at hand, but only that they should consider it possible that they may be mistaken. The modality is a double one. Of course, you may rightly say, as one knows from painful experience, one can always be wrong, so why should it be necessary to have this pointed out so firmly, even to the lengths of bringing the “bowels of Christ” into the matter.2

So, what does that thinking that one could not be wrong entail? What does it take NOT to think that? What are the conditions under which it is possible to be wrong? Can it, in fact, be impossible for someone ever to go wrong? Is there someone who is not just always right, but is always right out of necessity?

In order to narrow down the issue we note that always being right as a matter of actual fact does not mean that error is ruled out or that it is not possible to go wrong. A century and three quarters after the Cromwell letter, another English military leader, namely His Grace the Duke of Wellington, when premier of Britain, in response to Lord Dudley’s protest that it was a “mistake” to view a certain letter from Sir William Huskisson as one of resignation, answered: “There is no mistake; there has been no mistake; and there shall be no mistake.”3 Nevertheless, surely Wellington could have been mistaken, here or on other occasions, even though we may, for the sake of the argument, grant that, as a matter of actual fact, His Grace never did make a mistake.4 Someone, who perpetually avoids making mistakes, could very well go wrong, or have gone wrong, but has, by hook or crook, skill or luck, managed to avoid doing so. We have here an interesting issue that is related to what Arthur O. Lovejoy famously dubbed the Principle of Plenitude in his William James lectures (1936): every possibility (“potentiality”) will, at some stage in time, become actualized. With respect to error the Principle seems clearly unwarranted: one would not wish to claim that somebody who has led an entirely blameless life, morally and epistemically, without ever falling into error, could not have erred.

The possibility of error presupposes a “norm of rightness” against the background of which (in terms of which) the hiatus between appearance and reality can be upheld. Another example from the Napoleonic era helps to make this clear. The Tyrolean Andreas Hofer led an insurrection against Napoleon’s troops in 1809–1810, but was caught by the French and executed in February 1810. Pleas were made to the Emperor Franz I of Austria, entreating him to intercede with the French for the life of Hofer. In this connection it was pointed out that Hofer was such a good Tyrolean patriot. The Imperial response famously was: “Yes, but is he a patriot for me?” (my emphasis). Accordingly, in the case under discussion His Imperial Majesty was unable, or disinclined, to acknowledge the conceptual distinction between patriots and patriots-for-me. In the same fashion, when there is no conceptual difference between how it seems and how it is, one cannot be mistaken. We may here recall Frege’s (1893, xv–xvi) impressive testimony, from the Preface to the Grundgesetze, on the difference between Fürwahrhalten and Wahrsein. A position that equates right with right-for-me we may call a “Habsburg position”, in view of the Imperial stance on Andreas Hofer. The famous Protagorean proposition “Homo mensura”, that is, “man is the measure of things”, can be taken as the expression of a Habsburg position. If there is no difference between how it seems and how it is, then error is ruled out. Ivan Karamazov’s stance of “moral nihilism” is summed up in the slogan “If God is dead, then everything is permitted” (which saying apparently cannot be found in Dostoyevsky). Contraposing we obtain: If error is possible, there has to be a rightness norm. This leads to an a posteriori proof for the existence of God:

God exists, because I have been mistaken.

The first step is that possibility of error is conceptually (“internally” in Wittgenstein’s Tractarian terminology) related to the existence of a norm of rightness. Traditionally the norm of rightness is epistemically construed as the True, and within Ethics as the Good, that is, the Platonic-Augustinian conception of God. So, conceptually I know that, if it is possibly to be mistaken, then (the Platonic-Augustinian) God exists. However, by bitter experience most of us know that we have erred many times, epistemically as well as morally; therefore, ab esse ad posse valet illatio, it is possible to err, and so, detaching in the conceptual link, (the Platonic-Augustinian) God exists.

This religious link is furthermore brought out in the notion of Infallibility. As is well known, the Roman Pontiff, when pronouncing ex cathedra on matters of faith speaks infallibly, and bindingly on the consciences of the faithful. However, not every Papal pronouncement is covered by such infallibility. The Church has invested Divine infallibility within a human agent, in the sub-lunar domain. This makes matters delicate, because what if an infallible statement were made regarding something contingent and yet turned out wrong? Whomsoever wishes to speak with infallible authority on empirical, contingent matters runs the risk of being caught out in error. The Church, somehow, somewhere, is clearly aware of this perilous tension. It is brought out in the fact that until today there have been only two infallible papal pronouncements, to wit, the Dogma of Infallibility itself from the First Vatican Council in 1870, and the Assumption of Mary from 1950, proclaimed by Pope Pius XII. Both issues have a very internal, theological ring to them, with no discernible contingent effects. Accordingly they might be deemed safe from empirical correction. Later Pontiffs have eschewed proclaiming further infallible definitions. Pope John Paul II, though, introduced a novel category of pronouncements, which, while not infallible, come to within an inch thereof, and appear to be thought of as for ever unrevisable. Popular opinion, on the other hand, has vested Papal Infallibility in the person of the Pope, rather than in his office, which has conferred something close to operational de facto infallibility also to ordinary Papal Encyclicals, even though the binding de jure status is formally absent.

In the run-up to the First Vatican Council of 1870, Mgr Kettler, the Bishop of Fulda, asked a young German priest to prepare an historical and philosophical–theological Gutachten on the issue of Papal Infallibility. The young priest, called Franz Clemens Honoratus Brentano, did this, and with devastating personal results. In the end he found he could not make the novel dogma evident to himself, and consequently he did not accept it. Since Brentano had been ordained a priest under other premises, in a “different” Church, that is, one without papal infallibility, he rescinded the priesthood, and with it his (Concordat) extraordinary chair at Würzburg. Subsequently he was appointed to a (full) Chair at Vienna, where he became an immensely successful teacher of highly able pupils, and at the fount of three philosophical schools, to wit, the Lvow-Warsaw school of analytical philosophy, Husserlian Phenomenology, and through it, also Existentialism. Perhaps owing to his early cathartic experience of finding Papal Infallibility non-evident, Brentano retained a lifelong interest in matters of truth and evidence.5 In a public lecture to the Philosophical Society in Vienna 1889, Brentano adopted a realist stance and explained truth ontologically, as agreement with “how things are”. Late in life, after he had been struck with blindness, in brief dictated fragments of rare beauty, Brentano changed this order of priority. Truth becomes dependent on evidence: a judgment is true if it agrees with that of someone who judges with evidence. Differently put we might say that for Brentano: truth is evidentiability. Brentano construed evidence in a Cartesian fashion as “clear and distinct” perception. However, rather than taking this as a criterion for evidence he, like his master Descartes, took it to be a criterion for infallible evidence. That is, not just evidence, but real or true evidence.6

This use of true, or real, is analogous to that in true friend. It is clear that a “false friend” will not be counted among our friends. Here the use of “false” is modifying, but not qualifying: we have left the domain of friends. On the other hand, a yellow rose is still a rose. Here yellow qualifies rose, but does not modify it.7 However, when are we entitled to deploy such pairs of terms, for instance, true and false (with respect to nouns rather than to sentences), where one of the pair is modifying? We certainly have friends, but in order to call someone a friend, we are not called upon to run through our friends, either marking them with a blunt stamp of approval or withholding that mark: true friend, true friend, false friend, …, etc., much in the same fashion that asparagus may be divided into green or white ones. Something has to have happened for us to marshal these terms: “I thought he was a friend, but in the end he proved to be a false one.” Many different terms are used here. Thus we speak of a real, or true, or valid, or binding, demonstration or proof. In the Begriffssschrift from 1879, Frege used lückenlos (gap-free) with regard to Beweise.8 It is not so that one publishes a demonstration of a mathematical theorem, whereupon one then has to offer another proof that the original demonstration is a valid one. The notions of lückenhaft (“gappy”) and the concomitant lückenlos (“gap-free”) are brought into play only against the background of a suspected or diagnosed error. John Austin, who was perhaps the first to note these phenomena, made interesting points concerning “real”, and saw that it is the negative word that “wears the trousers” (Austin 1970, 85–89). It is the exceptional case that is the fundamental one, so to say. Being wrong is a concrete, particular issue, whereas being right is universal freedom from that concrete particularity. For instance, it is the presence of an epistemic gap in the chain of consecutive inferences that renders the demonstration lückenhaft. This dominance of the negative case is brought out nicely by a peculiar phenomenon from the Dutch world of bakery. In Holland, owing to complex commercial developments that we need not dwell upon, the term boter (“butter”) has come to be used indiscriminately also for what is everywhere else properly called margarine. When Dutch amateur cooks use cookbooks translated from the English this has led to culinary disasters from the use of margarine where it says ‘butter’ in the original recipe. It means that if one wants to be sure in Holland to have butter it is essential to ask (properly speaking pleonastically) for roomboter (“creambutter”), or indeed for echte boter (real butter). Here the order of priority is reversed: rather than calling margarine false butter, we use real butter for the exception to the—omnipresent—margarine case. Again the presupposition that something is suspect or wrong is fulfilled: what is known as “butter” is margarine and for the stuff involving cream we use real butter, in order to make its deviant status clear.

In spite of appearances these phenomena do not constitute a refutation of the logical law:

Every AB is B

For instance, that a false friend is not counted among our friends might seem to violate this law. However, this is appearance only. The law holds for qualifying predicates in “first-level discourse”. The corrective constructions that draw upon false, or invalid, or unreal, etc., are legitimate only against the background of a second-level diagnosis of a suspected of established error in the primary first-level activity. Their “logical grammar” (to use a term from the later Wittgenstein) requires that a presupposition of suspicion must be fulfilled before the true/false pair may be deployed to identify an “invalid proof”, etc.

A mistake, or error, is a cognitive act gone wrong. In order for us to be able to be wrong a norm is called for. Without such a norm of objectivity one cannot make mistakes. Every serious contender on the battlefield of epistemology shall have to avoid such anodyne (Habsburg) epistemic autism. How, then, do we obtain such a norm and at what level does it operate?

This question is put into perspective by considering a schematic representation of the cognitive act: Open image in new window

The epistemic act of knowledge, which we may call a “judging”, issues in a product, or object, of the act. This product is a judgement (made), which, for present purposes, we may assume, has the form

proposition A is true

The proposition A has a state of affairs SA as its ontological correlate.

In order that mistakes be possible, we need a norm of objectivity. The minimum requirement for such objectivity is that a norm of rightness for the level (1) has to be available. However, it need not be primitively available, and the history of philosophy shows examples of how it may be obtained by means of a reduction to objectivity standards at other levels. For instance, Brentano utilizes a norm of objectivity at level (2). Streamlined and modernized we may take his theory to be: a judgment is correct if it is evidentiable. Evidentability, on the other hand Brentano construed in terms of the Cartesian “clare et distincte” perception, and, like Descartes, Brentano took this criterion to establish not evidence, but infallible, or true evidence.9 When we have objectivity at level (2), it can be exported to level (1) by stating: an act is right if its result, that is, the object produced by the act, is correct. Similarly, Frege and before him Bolzano, opted for to base their objectivity norm at level (3), where every proposition is held to be true or false.10 Accordingly, the judgement made that

proposition A is true

is correct if the proposition A really is true. Finally, an ontological realist will obtain the required objectivity from a notion of obtaining applied to the states of affairs that serve as ontological correlates to propositions: A is true iff the state of affairs SA obtains. Famously, in the Tractatus, Wittgenstein holds that each state of affairs does obtain or does not obtain.11

We note that traditional truth theories are well suited to operate at different levels here. The correspondence theory fits the truth of propositions, whereas the evidence theory of truth works well for the correctness of judgments. The pragmatic, coherence and consensus theories, finally, are admirably geared towards error correction at the level of judgings. In the face of error, which judgments made are going to be jettisoned, is determined by means of such principles. Also useful in this determination are aesthetic criteria such as beauty, symmetry, simplicity, and various other considerations that are known from the Philosophy of Science.12 They provide criteria by which one attempts to fill in, or approximate, the norm of rightness. It will, of course, always be a matter of trial and error, which acts of judgement, among many candidates, will ultimately be chosen and annulled. What does not “work” (Pragmatic theory) or what does not cohere with the rest (Coherence theory), obviously, are prime candidates for annulment, whereas that about which everybody is in agreement, is equally obviously a prime candidate for being retained (Consensus theory).

One may distinguish between an error and a mistake; in a mis-take it is clear from the outset what has gone wrong. For instance, I wanted to pick up a fork, but my aim was bad, I picked (“mis-took”) a spoon instead. In this case the error-correcting mechanism is clear and trivial: put the spoon down and pick the fork instead. Similarly, when there is controversy about results in elementary arithmetic, say in a restaurant about the bill, the procedure for correction is clear. Both you and the waiter add up the sum from top to bottom, and the other way as well, and when you both get the same results (One goes on checking until this is achieved.) it is accepted by all. Here, in such activities, there is a common, shared standard for error correction. On the other hand, regarding say, a physical theory that does no longer account for the empirical phenomena, the situation may arise where one wants to say: “There must be an error in there somewhere, but I have not a clue where it lies.” Similarly a Chess player having lost an important game may well ask: “I was White and still I lost, but I am aware of no error in my play. Where did I go wrong?” Here, clearly there are no ready procedures available for error correction. In the chess case, for instance, when there is a ready diagnosis of the error, one speaks of an opening trap, or of a knight fork, etc.

There are, however, a number of over-arching ideas in 20th century philosophy that might be seen as resting upon (procedures for) the elimination of trivial mistakes. I am thinking of Collingwoods’s absolute presuppositions, Sorel’s Social Myths, Wittgenstein’s Forms of Life, the Denkstile of Ludwig Fleck’s Denkollektive, and of course, most famously, the paradigms of Thomas Kuhn.13 (In view of the many examples here, there might well be further such notions in contemporary philosophy of which I am unaware.) A paradigm, I wish to suggest, crucially provides, or builds on, a shared mechanism for correction of “trivial” mistakes. Alternatively, we may say that a paradigm, among other things, determines which errors are trivial mistakes. Clearly issues of analyticity and conventionalism are relevant here, but those themes would need another paper, or even a monograph, for their proper exploration.

Also rationality clearly involves reaction to diagnosed error. Hence only he who can err is rational. Man became rational only with the Fall, after Eve’s discovery of the uses to which an apple can be put. Thus, if man is, par excellence, the animal rationale, then man fully became man only after the Fall and ensuing expulsion from Paradise. In the bliss of Paradisiacal existence there are no errors, but also no possibility of being rational. The fruits of the Tree of Knowledge yielded knowledge of Good and Evil, of Right and Wrong. Also lying, that is, the deliberate telling of known falsehood with the intention to deceive, would not occur in Paradise. This was seen clearly by Jonathan Swift, in the fourth chapter of his account of Gulliver’s fourth voyage, to the country of the “Houyhnhms” (pronounced “Who whinnies”?), that is, the noble horses:

My master heard me with great appearances of uneasiness in his countenance; because doubting, or not believing, are so little known in this country, that the inhabitants cannot tell how to behave themselves under such circumstances. And I remember, in frequent discourses with my master concerning the nature of manhood in other parts of the world, having occasion to talk of lying and false representation, it was with much difficulty that he comprehended what I meant, although he had otherwise a most acute judgment. For he argued thus: “that the use of speech was to make us understand one another, and to receive information of facts; now, if any one said the thing which was not, these ends were defeated, because I cannot properly be said to understand him; and I am so far from receiving information, that he leaves me worse than in ignorance; for I am led to believe a thing black, when it is white, and short, when it is long.” And these were all the notions he had concerning that faculty of lying, so perfectly well understood, and so universally practised, among human creatures.

The noble Houyhnhms inhabit the paradisiacal state. Error and lying do not occur and are incomprehensible to them.

Apart from mistakes, that is, the subcategory of readily rectifiable errors, we also have blunders, that is, readily avoidable errors, that is, errors that could and should have been avoided. I have quoted British historical figures twice; in order to redress the balance it seems only fitting to conclude this excursion on errors by recalling a saying that has been attributed both to Fouché, as well as Talleryand, apropos the abduction and summary execution of the Duc d’Enghien in March, 1804. When someone called this Napoleonic miscalculated deed a crime, Anthoine Jaques Claude Joseph, Comte de Boulay de la Meurthe, famously noted:

C’est pire q’un crime, c’est une faute.

(It is worse than a crime, it is a blunder.)


  1. 1.

    Cromwell's letter is printed in Carlyle (1871, 632).

  2. 2.

    Reliable theological authority informs me that the "bowels of Christ" were held to be the seat of Divine mercy; the corresponding German term would be Barmherzigkeit. Thus what Cromwell wrote could be rendered as: For the Mercy of Christ, think it possible that you may be mistaken.

  3. 3.

    When I spoke on this material at Kirchberg 2001, my Geneva colleague Kevin Mulligan, who was in the audience, gave a discrete though quite audible cough at this point, insisting that Wellington, who was born in Dublin, should be considered an Irish military leader. In the quarrel between the unbending characters of Wellington and Huskisson the point is moot who was (most) in the wrong. The Dictionary of National Biography, volume 60, page 198, citing Gleig and Palmerston, interestingly gives the quotation as: "There is no mistake, there can be no mistake, and there shall be no mistake "(my emphasis). If those were indeed the Ducal words, they would put Wellington at an intransigent par with his Scottish Presbyterian Brethren in the Protestant Ascendency. On the other hand, this might be judging him too harshly. After all, Wellington's finest, and some might even say only, achievement in an otherwise rather bleak Premiership was the Catholic Emancipation Act of 1830.

  4. 4.

    It has been represented to me that, immediately before Waterloo, Wellington's handling of the Quatre Bras campaign, where Marshal Ney held the French operational command, was less than perfect. Had that command been entrusted to Marshal Davout, who was instead serving as Minister of War in Paris, it does not seem unlikely that matters might have turned out radically different for Wellington's coalition forces.

  5. 5.

    "Evidence" is a dangerous term to use in modern philosophy. Its meaning has become corrupted by the Anglo-Saxon legal sense of evidence for something; the OED correctly gives evidence of (what is evident) as its first meaning.

  6. 6.

    Brentano's Vienna lecture Über den Begriff der Wahrheit (1889) and his late fragments Über den Satz: veritas est adequatio rei et intellectus and Gedankengang zur Lehre von der Evidenz (1915) are found in his (1930).

  7. 7.

    The notion of modification, and the role it plays in Bolzano, Brentano, and Husserl is well treated in Stepanians (1998, ch. 10).

  8. 8.

    I am indebted to Michèle Friend for bringing the Fregean notion of a gap-free demonstration to my attention.

  9. 9.

    See Brentano (1930, 144, Sect. 3).

  10. 10.

    Frege (1903, Sect. 63) and Bolzano (1837, 76).

  11. 11.

    Wittgenstein's claims this for elementary sentences in the Tractatus, 4.21; truth conditions for complex sentences are then dealt with by recursion on their generation using the N operator, as set out in the main proposition 6.

  12. 12.

    I have dealt with the traditional accounts of truth and how they may serve in these "roles of truth" at some length in my (2004).

  13. 13.

    For information on the notions in question, see the works listed in the bibliography under the relevant author.



Text of an invited lecture at the workshop “Anti-realistic Notions of Truth”, Certosa di Pontignano, Siena University, September 2010. I have spoken to this material on other occasions: as an invited lecture at a Wittgenstein Conference in Kirchberg 2001, as concluding address at Svenska Filosofidagarna, Uppsala 2005, as a Fellow’s lecture at SCAS Uppsala, May 2009, where the drafting of my text was made, and in Per Martin-Löf’s seminar “Ontological versus Epistemic Aspects of Logic”, Paris, November, 2010. I am indebted to organizers and participants alike for the opportunities to speak and ensuing stimulating discussions. Henk-Jan de Jonge, longstanding colleague in the College of Deans at Leiden University, and emeritus Professor of New Testament exegesis, helped with the “bowels of Christ”, whereas Caspar Sundholm was a tireless source of information on the Duke of Wellington.

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Authors and Affiliations

  1. 1.Leiden UniversityLeidenThe Netherlands

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