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Error

ERROR

A mistake in a court proceeding concerning amatter of lawor fact, which might provide a ground for a review of the judgment rendered in the proceeding.

The nature of the error dictates the availability of a legal remedy. Generally speaking, mistaken or erroneous application of law will void or reverse a judgment in the matter. Conversely, errors or mistakes in facts, upon which a judge or jury relied in rendering a judgment or verdict, may or may not warrant reversal, depending upon other factors involved in the error. However, appellate decisions make a distinction—not so much between fact and law, but rather, between harmless error and reversible error—in deciding whether to let stand or vitiate a judgment or verdict.

In litigation, a harmless error means that, despite its occurrence, the ultimate outcome of the case is not affected or changed, and the mistake is not prejudicial to the rights of the party who claimed that the error occurred. In other words, the party claiming error has failed to convince an appellate court that the outcome of the litigation would have been different if the error had not occurred. Most harmless errors are errors of fact, such as errors in dates, times, or inconsequential details to a factual scenario.

On the other hand, error that is deemed harmful in that it biased the ultimate decision of a jury or judge, constitutes reversible error, i.e., error that warrants reversal of a judgment (or modification, or retrial). A reversible error usually refers to the mistaken application of a law by a court, as where, for example, a court mistakenly assumes jurisdiction over a matter that another court has exclusive jurisdiction over. A court may erroneously apply laws and rules to admit (or deny the admission of) certain crucial evidence in a case, which may prove pivotal or dispositive to the outcome of the trial and warrant reversal of the judgment. Occasionally, a court may charge the jury with an instruction that applies the wrong law, or with an improper interpretation of the correct law. If the party claiming error can prove that the error was prejudicial to the outcome of the case or to the party's rights, the error will most likely be deemed reversible.

An example of potential harmful or reversible error of both law and fact might involve the age of a rape victim in a criminal trial for statutory rape, (where guilt is premised upon the actual age of the victim, and not on whether the sexual conduct was consensual).

In appellate practice, a party may not appeal an error that it induced a court to make (as by petitioning or moving the court to make a ruling which is actually erroneous). Appellate decisions refer to this as an invited error and will not permit a party to take advantage of the error by having the decision overruled or reversed.

The general use of the term error is often distinct from the use of the word mistake, especially in the law of contracts. In such cases, a mistake of law or fact (in the making of a contract, or performance thereupon) might result in a finding of harmless or reversible error, but the terms are not transitional.

cross-references

Clerical Error; Plain-Error Rule.

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error (sampling and non-sampling)

error (sampling and non-sampling) There are many sources of inaccuracy, or error, in a survey. Sampling error consists of bias in sample selection procedures, plus random sampling error. Non-response bias can be measured and analysed after interviewing is completed. There is scope for less visible and less measurable error in the interviewing process itself, and in the subsequent coding and classification of replies. Interviewer bias affects some interviews, and interviewers do occasionally make mistakes, such as overlooking a whole section of a questionnaire. Coding errors arise when data are prepared for analysis. They consist of simple mispunches, from striking the wrong key to code a reply, and misclassification, as when a job description is not read or understood correctly, and is allocated to the wrong occupation code. Edit and consistency checks after data preparation will identify some but not all coding errors. Surveys require rigorous attention to detail at every stage in the process to reduce error to the minimum. Even small inaccuracies at each stage can mount up to an appreciable amount of total error in the end.

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error

er·ror / ˈerər/ • n. a mistake: spelling errors. ∎  the state or condition of being wrong in conduct or judgment: the crash was caused by human error. ∎  Baseball a misplay by a fielder that allows a batter to reach base or a runner to advance. ∎  technical a measure of the estimated difference between the observed or calculated value of a quantity and its true value. ∎  Law a mistake of fact or of law in a court's opinion, judgment or order. ∎ Philately a postage stamp or item of postal stationery showing a major printing or perforation mistake. PHRASES: see the error of one's ways realize or acknowledge one's wrongdoing.

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Error

226. Error

  1. Breeches Bible, the the Geneva Bible, so dubbed because it stated that Adam and Eve made themselves breeches. [Br. Hist.: Brewer Dictionary, 101]
  2. Cortez alluded to in a poem by Keats, mistaken for Balboa, as discoverer of Pacific Ocean. [Br. Poetry: On First Looking into Chapmans Homer]
  3. Wicked Bible, the misprinted a commandment as Thou shalt commit adultery. [Br. Hist.: Brewer Dictionary, 102]
  4. seacoast of Bohemia Shakespearean setting in a land with no seacoast. [Br. Drama: Shakespeare The Winters Tale, III,iii]

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error

error
1. The difference between a computed, observed, or measured value or condition and the true, specified, or theoretically correct value or condition.

2. An incorrect result resulting from some failure in the hardware of a system.

3. An incorrect step, process, or data definition in for example a program. See also semantic error, syntax error.

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error

error, in law: see appeal.

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error

errorjarrah, para, Tara •abracadabra, Aldabra •Alhambra • Vanbrugh •Cassandra, Sandra •Aphra, Biafra •Niagara, pellagra, Viagra •bhangra, Ingres •Capra • Cleopatra •mantra, tantra, yantra •Basra •Asmara, Bukhara, carbonara, Carrara, cascara, Connemara, Damara, Ferrara, Gemara, Guadalajara, Guevara, Honiara, Lara, marinara, mascara, Nara, Sahara, Samara, samsara, samskara, shikara, Tamara, tiara, Varah, Zara •candelabra, macabre, sabra •Alexandra • Agra • fiacre •Chartres, Montmartre, Sartre, Sinatra, Sumatra •Shastra • Maharashtra • Le Havre •gurdwara •Berra, error, Ferrer, sierra, terror •zebra • ephedra • Porto Alegrebelles-lettres, Petra, raison d'être, tetra •Electra, plectra, spectra •Clytemnestra • extra •chèvre, Sèvres •Ezra

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Error

ERROR

Truth is commonly defined as the conformity between intellect (knowledge) and reality. As the contrary of truth, error may be defined as a lack of conformity between knowledge and reality. Error is related to falsity as the specific to the generic: Falsity may be ontological (falsity in thingspossible only in an improper sense); moral (falsity in speechlying); or logical (falsity in thoughterror). Thus error is logical falsity. As lack of conformity, error is to be distinguished from ignorance, which is defined as lack of knowledge.

Error is positive or negative. Positive error distorts reality. Negative error fails to detect some aspect of reality but does not distort it. If the undetected reality is not connaturally knowable, the error is merely negative. If it is, the error is privative. Thus to judge that white is black is positive error. Not to hear sound waves below a minimum frequency is merely negative error. Not to see a certain color in the spectrum under normal conditions is privative error.

Cognitive powers are naturally ordered to truth. Yet error is possible because knowledge is not mere passive reception but an active synthesizing and interpreting of innumerable, diverse data. Among the cognitive acts, judgment is subject to positive error; under the influence of faulty judgment, conceptualization also is subject to positive error; external sense perception is not subject to positive error. As inherently finite, all cognitive powers are subject to merely negative error; and if a given power is indisposed or poorly applied, to privative error. Error of judgment is error in the strictest sense of the term.

The cause of error is the knower's precipitancy in making unwarranted judgments under the influence of passion, prejudice, haste, inattention, and the like. Avoiding error therefore requires serious effort to attain genuine evidence and careful vigilance to avoid influences other than evidence when making judgments. As an influence on voluntarity, error is equivalent in effect to ignorance. Error also has moral relevance in that man's actual sins presuppose an error of judgment equating apparent good with true good.

See Also: intellect; senses; conscience; error, theological.

Bibliography: r. p. phillips, Modern Thomistic Philosophy, 2 v. (Westminster, Md. 1948) 2:120124. f. van steenberghen, Epistemology, tr. m. j. flynn (2d ed. rev. New York 1949) 172176. p. coffey, Epistemology, 2 v. (New York 1917; reprint 1958) 2:366371. j. gredt, Elementa philosophiae Aristotelico-Thomisticae, ed. e. zenzen, 2 v. (13th ed. Freiburg im Br. 1961) 2:681684. e. valton, Dictionnaire de théologie catholique, ed. a. vacant, 15 v. (Paris 190350; Tables générales 1951) 5.1:435446. l. w. keeler, "St. Thomas's Doctrine Regarding Error," The New Scholasticism 7 (1933) 2657.

[j. b. nugent]

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Error

ERROR

When we engage in discursive thought and declarative speech, we may attain various forms of success: intelligibility, precision, correctness, and so on. These felicities are best explained by contrast with the corresponding mishaps that threaten our beliefs, assertions, and especially our claims to know something. A person's thinking may be inadequate because he is ignorant, and what he says may be deficient because it is incoherent, rough, or, perhaps most important of all, downright false.

Many philosophers have been troubled in attempting to account for the occurrence of falsity in people's assertions and opinions, that is, in trying to understand how there could be such a thing as error at all. In examining these difficulties, we shall assume a man's statement is erroneous in case it is false and it reflects his belief. Thus, if a man lies, he may speak falsely, but not erroneously. We shall also assume that a person holds a false belief when he is inclined to express it in a statement that would be false. The statement would be erroneous; consequently we can say the belief it mirrors is erroneous as well.

Our inquiry will focus on a pair of famous knots:

(1) Do we believe anything when our belief is false? If a surgeon is convinced his patient will die, and he is correct, there is something he expects: the patient's demise. But if he is mistaken, there is no such event as the patient's death. Did the surgeon then expect nothing? Depicted thus, erroneous thinking seems impossible. Plato inherited this perplexity from Parmenides and finally resolved it.

(2) Granting that error can occur, is it ever voluntary? Clearly we are to blame for some of our mistakes, yet who knowingly and willingly goes in for false beliefs? This puzzle comes from René Descartes.

The Possibility of Error

Parmenides' maxim was that only beingwhat iscan exist. From this he argued that we cannot "know that which is-not nor utter it; for the same thing can be thought as can be." In other words, "You will not find thought without what is, in relation to which it is uttered" (G. S. Kirk and J. E. Raven, The Presocratic Philosophers, Cambridge, U.K., 1957, pp. 269278). According to Plato, the Sophists drew an incredible doctrine from these enigmas: They argued that error is asserting and believing "what is not," specifically, talking and "thinking contrary to the things that are" (Sophist 240c, d, F. M. Cornford translation). To state and think what is not is, however, to state and think nothing, which is not stating or thinking.

What could have led the Sophists to this paradoxical view? Naturally, it reinforced other logically quite independent doctrines of theirs regarding truth and falsity, for example, their claim that whatever seems true to any man is true for him and therefore is true (Theaetetus 161c179c). The only direct support for their denial of error, however, derives from analogies. In Euthydemus (283e288a) the stating of what is not is compared with impossibilities such as doing but doing nothing or gesturing although there is no gesture one performs. The parallel with sense perception in Theaetetus (188d189b) is renowned. If you see, hear, or touch, then there is something you perceive. To see what is not, is not seeing.

plato's theory of error

In reply, Plato suggests alternative models that will incline us to regard falsehoods as full-fledged (though incorrect) assertions. His most promising comparison is with spelling, where misspelling is the natural counterpart to stating falsely. This analogy is central to Plato's unsuccessful third definition of knowledge in Theaetetus (201d208b), and it reappears in his successful treatment of falsity in Sophist (242d253, 261d264b). We should imagine a student who tries to spell syllables and words as his teacher says them or inscribes them. When he answers, aloud or in writing, with the right letters in the right order, he uses letters to represent a thing "that is," the teacher's utterance or inscription. According to conventions of spelling, the correct sequence of letters corresponds to what the teacher said or wrote. When the student misspells, he fails to represent the teacher's utterance or inscription, and nothing corresponds to the misspelling. Does the pupil therefore spell nothing? We describe his failure more accurately by saying: "When he misspells, what he spells is not; that is, not anything said or written by the instructor." How shall we describe cases where he gets some letters right and thus represents phonetic or graphological elements of what the instructor said or wrote? Clearly he does not spell those elements. For suppose he answers, "w-i-n" after the instructor says "wine." It makes no sense to claim: "He misspelled the word, but he correctly spelled some sounds the teacher made." Further, if the student happens to give the correct spelling of another word (as in this case), we must realize that the other word "is not," because the teacher did not say it. All this is secondary, however; the significant point is that when he misspells, the pupil is nevertheless engaged in the activity of spelling. This suggests that incorrect statements are statements after all.

Let us develop this parallel. If we restrict ourselves to the simplest paradigmsPlato used the true statement "Theaetetus is sitting" and the false statement "Theaetetus is flying"we notice how words in declarative speech function like letters in spelling. Individual letters may represent sounds but do not spell them. Similarly, the name "Theaetetus" stands for a thing that is, but saying the name "Theaetetus" is not stating anything. Spelling words requires you to conjoin letters of different types, consonants and vowels, in appropriate patterns. Speech, too, is fitting words together. "If you say 'lion stag horse' or any other names," Plato remarks, "such a string never makes up a statement"; but joining a noun with a verb "gets you somewhere" and of such a compound "we say it 'states,' not merely 'names' something" (Sophist 262be).

Now if you proclaim, "Theaetetus is flying," when he is not airborne, you refer by name to something that is, in the course of stating what is not. There is no aerial activity of Theaetetus to correspond to what you state. If you declare, "Theaetetus is sitting," and his posture is appropriate, then something corresponds to what you state. In Plato's words, the true statement "states about [Theaetetus] the things that are"; whereas "the false statement states about [him] things different from the things that are," and therefore states "things that are not as being" (Sophist 263b).

This correspondence theory of true and false statements may be extended to thought by our assumption that a man thinks falsely in case he is inclined to express his thought in a statement that is false. So formulated, the Platonic theory illustrates how error, even though it is believing what is not, hardly consists in believing nothing. Therefore, Sophists cannot maintain that thinking erroneously is not thinking.

Plato's account is, however, needlessly anchored to the type of counterexample he used against the Sophists. The falsehood "Theaetetus is flying" happens to be "about" an existing thing, but Plato makes this feature a prerequisite for every statement, true or false. He writes: "Whenever there is a statement, it must be about something" that exists (Sophist 262e; cf. 263c). Even if this ruling allows statements about things that do not exist now but did or will exist, it excludes too much. For instance, it would be impossible for me to state falsely, "There are flying saucers." By Plato's rule, saying this is not stating unless there are flying saucers for me to talk about. So if I state that there are flying saucers, I speak truly.

Here we should invoke Plato's orthographic model. The student does not cease to spell when upon occasion he misses every letter and thus fails to represent any sounds his teacher made. By analogy, why disqualify my utterance simply because I fail to refer to existing things? A correspondence theory still explains why it is false to state, "There are flying saucers": nothing corresponds to what is stated; that is, nothing corresponds to the existence of flying saucers, because none exist.

But the correspondence theory needs elaboration before it will transform Plato's view into a general account of correct and incorrect assertion. What "things that are" would I depict if I conceded "Flying saucers do not exist"? Does the nonexistence of flying saucers correspond to what I state? How can there be such a thing? Again, what "things that are" differentiate a true subjunctive conditional, for example, "If I had watered the lawn, it would not have died," from its false contrary, "Even if I had watered the lawn, it would have died"? Does the same withered grass make one statement true and the other false?

Because of these obscurities it appears that Plato has demonstrated how incorrect belief and assertion can occur, but he has not produced an exhaustive analysis of them. Plato's demonstration shows awareness of the distinctive features of assertion, sensitivity to the differences between referring and asserting, and perspicacity about the ontological status of what a person believes; indeed, treatments of error by such twentieth-century philosophers as G. E. Moore and Bertrand Russell are not more satisfactory in these respects.

moore and russell

Moore's Some Main Problems of Philosophy, adapted from lectures he delivered in 19101911, appears to contain two incompatible theories: (1) The dyadic theory, according to which believing pairs believers and propositions. "Error," writes Moore, "always consists in believing some proposition which is false" (p. 66). (2) For complicated reasons Moore later contends that "there simply are no such things as propositions" for people to believe (p. 265), and he renounces his "attempt to analyse beliefs" (p. 266). Nevertheless, he characterizes truth and falsity of beliefs as follows: "To say that a belief is true is to say that the fact to which it refers is or has being; while to say that a belief is false is to say that the fact to which it refers is not" (p. 267). In technical terminology: "To say that [a] belief is false is to say that there is not in the Universe any fact to which it corresponds" (p. 277).

In his 1953 preface, Moore comments that his two theories may after all be consistent; perhaps he used the term proposition in different senses when he first maintained and later denied their existence as targets for believing (p. xii). Apart from this problem, fundamental questions arise concerning Moore's treatment: Are there any facts for mistaken beliefs to be about? Are they nonexistent facts "in the Universe," or perhaps existent ones outside it? Besides, the very notions of "proposition" and "fact" are notoriously obscure.

Moore hints at a different analysis when he considers a person's belief that we are now listening to a brass band. What the person erroneously believes is a "combination of us at this particular moment with the hearing of that particular kind of noise"a combination which "simply has no being" (p. 255).

Russell's multiple relation theory, in his Problems of Philosophy, develops such an analysis. Concerning Othello's mistaken belief that Desdemona loves Cassio, Russell says: "The relation called 'believing' is knitting together into one complex whole the four terms Othello, Desdemona, loving and Cassio" (p. 126). This belief is mistaken because there does not exist another "complex unity, 'Desdemona's love for Cassio,' which is composed exclusively of the objects of the belief, with the relation [loving] which was one of the objects occurring now as the cement that binds together the other objects of the belief" (p. 128).

The snags in this analysis are well known. How does loving cement things? In case Desdemona is indifferent to Cassio, how does believing sew them together with loving and Othello? Can believing stitch together any collection of objects? Russell noted the last two problems in his 1918 lectures, "The Philosophy of Logical Atomism" (in Logic and Knowledge ). He recognizes that the structure of Othello's belief requires that "loves" should "occur as a verb"; but he is afraid that admitting the syntactical unity of "Desdemona loves Cassio" is tantamount to "assuming the existence of the non-existent [namely,] a non-existent love between Desdemona and Cassio" (p. 225). But as Plato saw, there can be units of speechstatementsand thought without correspondents in reality.

Error and Volition

Plato did not need to convince us that false belief is possible. But Descartes's thesis, that error is always voluntary, seems a contrived solution to an entirely gratuitous theological muddle. This appearance is deceptive.

Descartes begins his Meditations with a survey of dreaming, sensory illusion, and the errors they occasion; next he shows we can prove a few things for certain, including God's existence. Then he reasons: The deity "cannot have given me a faculty [of thinking] whose right employment could ever lead me astray"; however, "it seems to follow that therefore I can never go wrong" (Meditation IV, in Descartes' Philosophical Writings, translated by P. T. Geach and G. E. M. Anscombe, p. 93). Descartes's answer to this puzzle is that men have false beliefs, but through their own doing, not God's. Men are endowed by God with such power of will that they can assent to propositions they do not know to be truethat is, to "ideas" that are not "clear and distinct." Is God to blame for this disharmony between our limited capacity for knowledge and our unlimited power of assenting? No, "will is just a single thing; it is incompatible with its nature that anything should be subtracted from it" (Meditation IV, p. 99). Besides, although we are free to, we do not have to believe propositions for which we lack conclusive proof. In order to avoid "unsuspected error," we must restrain our desire for truth and withhold assent until we know for certain. (Descartes's Principles of Philosophy XXIX, XXXII, XXXV, XXXIX, XLII explain these points in detail.)

Now if we put aside Descartes's theological preoccupations, and his advice that we should only believe what is obvious, at least two genuine questions arise:

(1) Do we exercise any control over our convictions and opinions, as Descartes's concept of "assenting" requires? Clearly, people may decide to make statements. Some criminals voluntarily confess their misdeeds, and others are forced, against their will, to admit guilt. How about belief? Can we choose to reject a proposition that seems most likely, according to available evidence, and believe another that seems less plausible? Perhaps not. But we often make decisions as we form our opinions, as we collect or neglect data and seek or ignore expert testimony. Men who undergo brainwashing are deprived of this control over the formation of their beliefs. The same holds, incidentally, for knowledge. It is absurd to say the investigator decided to know but not absurd to say he resolved to find out for certain who robbed the grocer. Moreover, children are compelled to learn things. In acquiring knowledge and forming opinions, we pursue rather obvious goals: conclusive proof and correct information.

(2) Even so, is it intelligible to suppose that people act deliberately and knowingly when they settle upon false beliefs? One everyday case should dispel the appearance of contradiction: I study the racing form, mull over the evidence, and conclude that Wayfarer is bound to take the handicap. I willingly commit myself to this belief by wagering my paycheck. I realize, however, that even well-grounded expectations like mine can prove erroneous. Consequently, if my horse loses, it is true to say, "I formed my erroneous belief willingly, after deliberation, with the intention of predicting the handicap winner; furthermore, I was aware that I could be mistaken." It was not my goal to be wrong, but it was within the scope of my intention. Anyone who aims at truth is prepared for falsity, just as a marksman is prepared to miss the bull's-eye. Can we say I erred "knowingly"? A man who punches another is hardly ever certain that his victim will be injured, but from a legal standpoint he knowingly inflicts harm if he has reason to think injury might result from his blow.

There remains another type of error, fortunately quite infrequent, where such awareness is impossible. This is the unusual situation where you are convinced you know something, banish doubt from your mind, and still turn out to be wrong. Perhaps you acted deliberately and followed your inclinations in pushing your investigation until you believed you could not be wrong. But with this degree of conviction, you cannot have the least awareness that you are mistaken. Your error, then, is not fully voluntary.

See also Correspondence Theory of Truth; Descartes, René; Moore, George Edward; Plato; Russell, Bertrand Arthur William; Sophists; Volition.

Bibliography

plato

Plato's Theaetetus and Sophist, along with excellent commentary, are translated by F. M. Cornford in Plato's Theory of Knowledge (London: K. Paul, Trench, Trubner, 1935). For further analysis of Plato's theory, see Gilbert Ryle, "Letters and Syllables in Plato," Philosophical Review 69 (4) (1960): 431451; D. Gallop, "Plato and the Alphabet," in Philosophical Review 72 (3) (1963): 364376, and Raphael Demos, "Plato's Philosophy of Language," with comments by J. L. Ackrill, in Journal of Philosophy 61 (20) (1964): 595613.

moore and russell

The views of Moore and Russell can be found in G. E. Moore, Some Main Problems of Philosophy (London: Allen and Unwin, 1953), especially Chs. 3 and 1316, and Bertrand Russell, Problems of Philosophy (London: Williams and Norgate, 1912; reset 1946), Ch. 12, and "The Philosophy of Logical Atomism," in Logic and Knowledge, edited by R. C. Marsh (London: Allen and Unwin, 1956). For a view opposed to those of Moore and Russell, see Alexius Meinong, Untersuchungen zur Gegenstandtheorie und Psychologie (Leipzig, 1904), translated by Isaac Levi, D. B. Terrell, and Roderick Chisholm as "The Theory of Objects," in Realism and the Background of Phenomenology, edited by R. M. Chisholm (Glencoe, IL: Free Press, 1960).

There is a brilliant discussion of the connection between negative judgments and falsity in Gottlob Frege's essay "Negation," in The Philosophical Writings of Gottlob Frege, edited and translated by Max Black and P. T. Geach (Oxford: Blackwell, 1952).

descartes

See Descartes' Philosophical Writings, translated by P. T. Geach and G. E. M. Anscombe (Edinburgh, 1954). Spinoza's objections to Descartes's theory that belief necessarily involves assent can be found in the Ethics, Part I, Props. 29, 32, and appendix, and all of Part II; see also the lucid analysis of Descartes and Spinoza by J. L. Evans, "Error and the Will," in Philosophy 38 (1963): 136148.

other recommended titles

Almeder, Robert. "Recent Work on Error." Philosophia 27 (1999): 358.

Bennett, Jonathan. "Spinoza on Error." Philosophical Papers 15 (1986): 5973.

Burgess, John. "Error Theories and Values." Australasian Journal of Philosophy 76 (1998): 534552.

Devlin, John. "An Argument for an Error Theory of Truth." Nous, Supp. 17 (2003): 5182.

Gomez-Torrente, Mario. "Vagueness and Margin for Error Principles." Philosophy and Phenomenological Research 64 (2002): 107125.

Howson, Colin. "Error Probabilities in Error." Philosophy of Science, Supp. 64 (4): S185S194.

Popkin, Richard. Scepticism from Erasmus to Spinoza. Berkeley: University of California Press, 1979.

Sievert, Donald. "Whose Fault Is It Anyway? Descartes's Doctrine That We, and Not God, Are Responsible for the Errors of the World." Southwest Philosophy Review 13 (1997): 3341.

Stroud, Barry. "Explaining the Quest and Its Prospects: Reply to Boghossian and Byrne." Philosophical Studies 108 (2002): 239247.

Wiland, Eric. "Psychologism, Practical Reason and the Possibility of Error." Philosophical Quarterly 53 (2003): 6878.

Williams, Bernard. Descartes: The Project of Pure Enquiry. Atlantic Highlands, NJ: Humanities Press, 1978.

Irving Thalberg (1967)

Bibliography updated by Benjamin Fiedor (2005)

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Error

Error

Sources of error

Error is the amount of deviation (or difference) between the estimated, measured, or computed value of a physical quantity and the correct value. The Latin word for error means straying or wandering. Error arises becauseof the process of measurement or approximation. There are two general types of errors: systematic error and statistical error. A systematic error is caused an unknown and nonrandom (that is, predictable) problems with a measuring device. A statistical error is caused by unknown and random (that is, unpredictable) problems with a measuring device. Another term for error is uncertainty. Errors that can be eventually eliminated are usually referred to as uncertainty.

Physical quantities such as weight, volume, temperature, speed, and time, among many others, must all be measured by an instrument of one sort or another. No matter how accurate the measuring toolbe it an atomic clock that determines time based on atomic oscillation or a laser interferometer that measures distance to a fraction of a wavelength of light some finite amount of uncertainty is involved in the measurement. Thus, a measured quantity isonly as accurate as the error involved in the measuring process. In other words, the error, or uncertainty, of a measurement is as important as the measurement itself.

As an example, imagine trying to measure the volume of water in a bathtub. Using a gallon bucket as a measuring tool, it would only be possible to measure the volume accurately to the nearest full bucket, or gallon. Any fractional gallon of water remaining would be added as an estimated volume. Thus, the value given for the volume would have a potential error or uncertainty of something less than a bucket.

Now suppose the bucket were scribed with lines dividing it into quarters. Given the resolving power of the human eye, it is possible to make a good guess of the measurement to the nearest quarter gallon, but the guess could be affected by factors such asviewing angle, accuracy of the scribing, tilts in the surface holding the bucket, etc. Thus, a measurement that appeared to be 6.5 gal (24.6 l) could be in error by as much as one quarter of a gallon, and might actually be closer to 6.25 gal (23.6 l)or 6.75 gal (25.5 l). To express this uncertainty in the measurement process, one would write the volume as 6.5 gallons ± 0.25 gallons.

As the resolution of the measurement increases, the accuracy increases and the error decreases. For example, if the measurement were performed again using a cup as the unit of measure, the resultant volume would be more accurate because the fractional unit of water remainingless than a cupwould be a smaller volume than the fractional gallon. If a teaspoon were used as a measuring unit, the volume measurement would be even more accurate, and so on.

As the example above shows, error is expressed in terms of the difference between the true value of a quantity and its approximation. A positive error is one in which the observed value is larger than the true value; and in a negative error, the observed value is smaller. Error is most often given in terms of positive and negative error. For example, the volume of water in the bathtub could be given as 6 gallons ± 0.5 gallon, or 96 cups ± 0.5 cup, or 1056 teaspoons ± 0.5 teaspoons. Again, as the uncertainty of the measurement decreases, the value becomes more accurate.

An error can also be expressed as a ratio of the error of the measurement and the true value of the measurement. If the approximation were 25 and

KEY TERMS

Calibration A procedure for adjusting the performance of measuring equipment to ensure a precise, predetermined level of accuracy.

Electronic noise Spurious signals generated in electrical measurement equipment that interfere with readings.

Uncertainty The degree to which a measurement is unknown.

the true value were 20, the relative error would be 5/20. The relative error can be also be expressed as a percent. In this case, the percent error is 25%.

Sources of error

Measurement error can be generated by many sources. In the bathtub example, error could be introduced by poor procedure such as not completely filling the bucket or measuring it on a tilted surface. Error could also be introduced by environmental factors such as evaporation of the water during the measurement process. The most common and most critical source of error lies within the measurement tool itself, however. Errors would be introduced if the bucket were not manufactured to hold a full gallon, if the lines indicating quarter gallons were incorrectly scribed, or if the bucket incurred a dent that decreased the amount of water it could hold to less than a gallon.

In electronic measurement equipment, various electromagnetic interactions can create electronic interference, or noise. Any measurement with a value below that of the electronic noise is invalid, because it is not possible to determine how much of the measured quantity is real, and how much is generated by instrument noise. The noise level determines the uncertainty of the measurement. Engineers will, thus speak of the noise floor of an instrument, and will talk about measurements as being below the noise floor, or in the noise.

Measurement and measurement error are so important that considerable effort is devoted to ensure the accuracy of instruments by a process known as calibration. Instruments are checked against a known, precision standard, and they are adjusted to be as accurate as possible. Gasline pumps and supermarket scales are checked periodically to ensure that they measure to within a predetermined error.

Nearly every developed country has established a government agency responsible for maintaining accurate measurement standards. In the United States, that agency is known as the National Institute of Standards and Technology (NIST). NIST provides measurement standards, calibration standards, and calibration services for a wide array of needs such as time, distance, volume, temperature, luminance, speed, etc. Instruments are referred to as NIST Traceable if their accuracy, and measurement error, can be confirmed by one of the precision instruments at NIST.

Kristin Lewotsky

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Error

Error

Error is the amount of deviation in a physical quantity that arises as a result of the process of measurement or approximation . Another term for error is uncertainty.

Physical quantities such as weight, volume , temperature , speed, or time must all be measured by an instrument of one sort or another. No matter how accurate the measuring tool—be it an atomic clock that determines time based on atomic oscillation or a laser interferometer that measures distance to a fraction of a wavelength of light some finite amount of uncertainty is involved in the measurement. Thus, a measured quantity is only as accurate as the error involved in the measuring process. In other words, the error, or uncertainty, of a measurement is as important as the measurement itself.

As an example, imagine trying to measure the volume of water in a bathtub. Using a gallon bucket as a measuring tool, it would only be possible to measure the volume accurately to the nearest full bucket, or gallon. Any fractional gallon of water remaining would be added as an estimated volume. Thus, the value given for the volume would have a potential error or uncertainty of something less than a bucket.

Now suppose the bucket were scribed with lines dividing it into quarters. Given the resolving power of the human eye , it is possible to make a good guess of the measurement to the nearest quarter gallon, but the guess could be affected by factors such as viewing angle , accuracy of the scribing, tilts in the surface holding the bucket, etc. Thus, a measurement that appeared to be 6.5 gal (24.6 l) could be in error by as much as one quarter of a gallon, and might actually be closer to 6.25 gal (23.6 l) or 6.75 gal (25.5 l). To express this uncertainty in the measurement process, one would write the volume as 6.5 gallons +/-0.25 gallons.

As the resolution of the measurement increases, the accuracy increases and the error decreases. For example, if the measurement were performed again using a cup as the unit of measure, the resultant volume would be more accurate because the fractional unit of water remain ing—less than a cup—would be a smaller volume than the fractional gallon. If a teaspoon were used as a measuring unit, the volume measurement would be even more accurate, and so on.

As the example above shows, error is expressed in terms of the difference between the true value of a quantity and its approximation. A positive error is one in which the observed value is larger than the true value; in a negative error, the observed value is smaller. Error is most often given in terms of positive and negative error. For example, the volume of water in the bathtub could be given as 6 gallons +/-0.5 gallon, or 96 cups +/-0.5 cup, or 1056 teaspoons +/-0.5 teaspoons. Again, as the uncertainty of the measurement decreases, the value becomes more accurate.

An error can also be expressed as a ratio of the error of the measurement and the true value of the measurement. If the approximation were 25 and the true value were 20, the relative error would be 5/20. The relative error can be also be expressed as a percent . In this case, the percent error is 25%.


Sources of error

Measurement error can be generated by many sources. In the bathtub example, error could be introduced by poor procedure such as not completely filling the bucket or measuring it on a tilted surface. Error could also be introduced by environmental factors such as evaporation of the water during the measurement process. The most common and most critical source of error lies within the measurement tool itself, however. Errors would be introduced if the bucket were not manufactured to hold a full gallon, if the lines indicating quarter gallons were incorrectly scribed, or if the bucket incurred a dent that decreased the amount of water it could hold to less than a gallon.

In electronic measurement equipment, various electromagnetic interactions can create electronic interference , or noise. Any measurement with a value below that of the electronic noise is invalid, because it is not possible to determine how much of the measured quantity is real, and how much is generated by instrument noise. The noise level determines the uncertainty of the measurement. Engineers will thus speak of the noise floor of an instrument, and will talk about measurements as being below the noise floor, or "in the noise."

Measurement and measurement error are so important that considerable effort is devoted to ensure the accuracy of instruments by a process known as calibration . Instruments are checked against a known, precision standard, and adjusted to be as accurate as possible. Even gas pumps and supermarket scales are checked periodically to ensure that they measure to within a predetermined error.

Nearly every country has established a government agency responsible for maintaining accurate measurement standards. In the United States, that agency is known as the National Institute of Standards and Technology (NIST). NIST provides measurement standards, calibration standards, and calibration services for a wide array of needs such as time, distance, volume, temperature, luminance, speed, etc. Instruments are referred to as "NIST traceable" if their accuracy, and measurement error, can be confirmed by one of the precision instruments at NIST.

Kristin Lewotsky

KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calibration

—A procedure for adjusting the performance of measuring equipment to ensure a precise, predetermined level of accuracy.

Electronic noise

—Spurious signals generated in electrical measurement equipment that interfere with readings.

Uncertainty

—The degree to which a measurement is unknown.

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