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Related to Sophism: sophistry, solipsism, Sufism



an inference or reasoning that substantiates some known incongruity, absurdity, or paradoxical statement contradicting generally accepted notions.

Aristotle called sophisms false proofs in which the grounds for the conclusion are only apparent and derive from a purely subjective impression caused by insufficient logical or semantic analysis. The initial persuasiveness of many sophisms—their “logical” character—is usually related to a well-concealed error on the semiotic or logical level. Errors on the semiotic level may involve metaphorical speech, homonymy and polysemy, and amphibology, which violate the unambiguous character of the thought and lead to a confusion of the meanings of terms. Errors on the logical level include deceptive substitution of the basic thought (thesis) of the proof, the taking of false premises for true ones, violation of the permissible methods of reasoning (the rules of logical inference), and the use of “unauthorized” or even “forbidden” rules or actions, such as division by zero in a mathematical sophism. The last-mentioned mistake may also be considered semiotic because it is related to agreement concerning “correctly constructed formulas.”

The ancient “horn sophism,” which is ascribed to Eubulides, runs as follows; “That which you have not lost, you have. You have not lost horns. Therefore, you have horns.” In this case the ambiguity of the major premise is concealed. If the major premise is understood to be universal and to mean “everything that you have not lost,” the inference is logically flawless but uninteresting because the major premise is obviously false; if the major premise is understood to be particular, the conclusion does not follow logically. This became known, however, only after Aristotle had created logic.

A modern sophism has it that as we grow older the “years of life” not only seem shorter but are in fact shorter: “Every year of your life is 1/n of your life, where n is the number of years you have lived. But n + 1 > n. Therefore, 1/(n + 1) < 1/n.”

Historically, the concept of sophism has always been associated with the idea of deliberate falsification, this in line with Protagoras’ admission that the task of the Sophist is to represent the worst argument as the best by devising clever tricks in speech and reasoning, ignoring the truth, and concentrating on practical advantage or success in debate. (Of course, Protagoras himself fell victim to the “Euatlos’ sophism.”) Usually associated with this same idea is the “criterion of reason” formulated by Protagoras: man’s opinion is the measure of truth. Plato remarked that reason must not involve a person’s subjective will, lest it become necessary to recognize the validity of contradictions—which, incidentally, the Sophists argued—and therefore to consider all statements sound.

This thought of Plato’s was developed in the Aristotelian principle of noncontradiction and, in modern logic, in interpretations demanding that absolute consistency be proved. Brought from the field of pure logic into the field of “factual truths,” it gave rise to a special “style of thinking” that ignored the dialectics of “interval situations.” In interval situations, Protagoras’ criterion, more broadly understood as the relativity of truth to the conditions and means of knowing truth, proves very significant. This is why many lines of reasoning that lead to paradoxes but are otherwise flawless are defined as sophisms even though they essentially demonstrate the interval nature of the corresponding epistemo-logical situations. An example is seen in the “pile sophism”: “One grain is not a pile. If n grains are not a pile, then n + 1 grains are also not a pile. Therefore, any number of grains is not a pile.” This is just one of the “paradoxes of transitivity” that arise in situations of “indistinguishability.” A situation of indis-tinguishability is a typical example of an interval situation in which the property of the transitivity of equality is not preserved during the transition from one “interval of indistinguishability” to another, thus making the principle of mathematical induction inapplicable in such situations.

The attempt to see in this an “intolerable contradiction” that is characteristic of experience and that mathematical thought “overcomes” in the abstract concept of the number continuum (J. H. Poincaré) is not supported, however, by the general proof of the removability of such situations in the sphere of mathematical thinking and experience. Suffice it to say that the description and practice of using the “laws of identity” (equality), which are so important in this sphere, generally depend, as in the empirical sciences, on the meaning given to the expression “one and the same object” and on the means or criteria of identity that are used. In other words, whether one speaks of mathematical objects or, for example, objects of quantum mechanics, the answers to questions of identity are necessarily linked to interval situations. Moreover, it is by no means always possible to oppose a solution “above this interval” to a particular solution to the question “within” the interval of indistinguishability, that is, to substitute the abstraction of identity for the abstraction of indistinguishability. But only in the latter case can one say the contradiction has been “overcome.”

Apparently the Sophists themselves were the first to understand the importance of the semiotic analysis of sophisms. Prodicus considered the doctrine of speech and the correct use of names to be paramount. Sophisms are frequently analyzed and used as examples in Plato’s dialogues. Aristotle wrote a specialized work entitled Sophistical Refutations, and the mathematician Euclid wrote the Pseudaria, a distinctive catalog of sophisms in geometric proofs.


Akhmanov, A. S. Logicheskoe uchenie Aristotelia. Moscow, 1960.
Bradis, V. M., V. L. Minkovskii, and A. K. Kharcheva. Oshibki v matematicheskikh rassuzhdeniiakh, 3rd ed. Moscow, 1967.


References in periodicals archive ?
SEOUL - A chief North Korean negotiator in talks with South Korea on energy aid to the North on Friday said speculation Friday on North Korean leader Kim Jong Il's health is ''sophism,'' according to a report by Yonhap News Agency.
Elsewhere he seems less than well-informed: Bacon never said that "knowledge is power" (17); his classification of knowledge was not "quite conservative," as Gaukroger claims (94), for Grazia Tonelli Olivieri has shown that Bacon was the first author ever to group the arts and sciences according to the three faculties of the soul; Gaukroger records that Spedding's version of the important early work Of Tribute; or, giving that which is due "is corrupt," but has not noticed that the complete text was first published in my Francis Bacon; by "colours" Bacon did not mean "general precepts of argument, or commonplaces" (102), but sophism, false "semblances" of good or evil.
He then tries with a bit of sophism to discredit not an argument but a hypothetical analogy of Goldberg's by suggesting that Nebraska is really no more conservative than New York.
* The use of "emergency contraception" after forced sexual intercourse, in part because Vatican experts regard the so-called "morning after pill" as a "chemical abortion." The idea that an embryo is simply "a bunch of cells," according to the document, is a "sophism ...
Here, none the less, the debate proves itself to be trapped by the cleverly maintained sophism of a fraudulent alternative: the person who accepts the idea of `exact' sciences is supposed to admit their superiority to disciplines which are obviously `inexact'; opposing them, the person who challenges this superiority should conversely deny the illusions of truth and progress.
Dieter Mehl points out that "the elegant sophism proposed by Saturn," which permits him to grant the letter of both Arcite and Palamon's requests, "has the neatness of a comic denouement" (160).
The adepts of "pure conversations," qingtan, among Wang Xizhi's contemporaries could indeed have been capable of such sophism, but, as I will attempt to prove shortly, Wang Xizhi was not of their number.
At the same time, the music intriguingly closes in on the writer's characteristic sophism, an evasive blend of portentous moralism and lurid ambiguity, of cynicism and voyeurism, of fascination and rebuke.
Hager's own didactic sophism parallels his description of Sidney's in the Defence of Poetry.
But the editorial, in historical context, was pure sophism. The Journal spent most of the last decade arguing, much more eloquently, for greater executive privilege - and against such laws as FACA and FOIA.
This seems to be on grounds equivalent to the sophism that because there are fictions about concentration camps, the concentration camps must have been a fiction.
The next day Bioy telephones to say that he has found in another copy of the work the article in question and that the passage he had paraphrased the night before reads: "For one of those gnostics, the visible universe was an illusion or, more precisely, a sophism. Mirrors and fatherhood are abominable because they multiply it and extend it" (T 18).