Lecture 24 min.
A sophism is a logically incorrect (unsound) argument, inference or persuasive statement (argumentation) that is deliberately passed off as correct.
Sophism (from the Greek σόφισμα, "skill, craft, clever invention, trick") is:
Sophism as a teaching device was introduced by the ancient Greek sophists in the Greek city-states around the 5th century BC. They were professional teachers who taught noble youths eloquence, oratory and the art of public debate in preparation for a political or other career. Unlike philosophers, who pursued scholarly inquiry within the methodology of institutionalized philosophical schools, the sophists were privately hired teachers and relied on a pluralistic, problem-solving methodology.
Philosophers accused the sophists' methods of subjectivism and relativism, which resulted in a negative assessment of the sophists' activity as "sophistical". Plato ("Euthydemus", "Protagoras", "Theaetetus") exposed sophisms and the methods of resolving them as "apparent knowledge", "phantom likenesses of knowledge, but not true ones" ("Sophist"). Aristotle regarded sophisms as "drilling" rather than a scientific search for truth, and in "On Sophistical Refutations" compiled the first classification of sophisms, the tricks of the sophists, distinguishing 13 kinds of sophisms arising from ambiguities of two sorts: 6 connected with turns of speech, and 7 paralogisms, or incorrectly constructed arguments.
Aristotle used the word sophism for "apparent proofs", in which the soundness of the conclusion seems correct and owes itself to a purely subjective impression caused by insufficient logical or semantic analysis. The persuasiveness at first glance of many sophisms, their "logicality", is usually connected with a well-disguised error:
— a semantic one, arising from the metaphorical nature of speech, from homonymy or polysemy of words, amphibolies, etc., which violate the unambiguity of thought and lead to confusion of the meanings of terms;
— a logical one, such as substitution of the main idea (the thesis) of the proof, or taking false premises for true ones, failure to observe the permissible ways of reasoning (the rules of logical inference), use of "unauthorized" or even "forbidden" rules or actions, for example division by zero in mathematical sophisms (the latter error can also be considered semiotic, since it is connected with the convention about "well-formed formulas").
Here is one of the ancient sophisms (the "horned one"), attributed to Eubulides: "What you have not lost, you have. You have not lost horns. Therefore, you have horns." Here an ambiguity of the major premise is disguised. If it is understood as universal, "Everything that you have not lost...", then the conclusion is logically impeccable but uninteresting, since it is obvious that the major premise is false; if it is understood as particular, then the conclusion does not follow logically. The latter, however, became known only after Aristotle formulated logic.
And here is a modern sophism that purports to show that with age the "years of life" not only seem but actually are shorter: "Each year of your life is its 
part, where 
is the number of years you have lived. But 
. Therefore, 
."
Historically, the concept of "sophism" has invariably been associated with the idea of deliberate falsification, following Protagoras's admission that the task of the sophist is to present the worst argument as the best by means of ingenious tricks in speech and reasoning, caring not for truth but for success in debate or for practical gain. (It is known that Protagoras himself became the victim of the "sophism of Euathlus".) The same idea is usually associated with the "criterion of ground" formulated by Protagoras: man's opinion is the measure of truth. Plato had already noticed that the ground must not lie in a person's subjective will, otherwise one would have to admit the legitimacy of contradictions (which, incidentally, the sophists did assert), and therefore to consider any judgments well-founded. This thought of Plato was developed in Aristotle's "principle of non-contradiction" (see Logical law) and, in modern logic, in interpretations and demands for proofs of "absolute" consistency. Carried over from the domain of pure logic into the domain of "factual truths", it gave rise to a particular "style of thinking" that ignores the dialectic of "interval situations", that is, situations in which Protagoras's criterion, understood more broadly as the relativity of truth to the conditions and means of its cognition, turns out to be very significant. This is precisely why many arguments that lead to paradoxes and are otherwise impeccable are classified as sophisms, although in essence they merely demonstrate the interval character of the epistemological situations connected with them. Thus the "heap" sophism ("One grain is not a heap. If grains are not a heap, then 
grain is not a heap either. Therefore, any number of grains is not a heap") is only one of the "paradoxes of transitivity" arising in a situation of "indistinguishability". The latter is a typical example of an interval situation in which the transitivity of equality, in passing from one "interval of indistinguishability" to another, is generally not preserved, and therefore the principle of mathematical induction is inapplicable in such situations. The tendency to see in this an "intolerable contradiction" inherent in experience, which mathematical thought "overcomes" in the abstract concept of the numerical continuum (H. Poincaré), is not, however, supported by a general proof that situations of this kind can be eliminated in the sphere of mathematical thought and experience. Suffice it to say that the description and practice of applying such important "laws of identity" (equality) in this sphere, just as, generally speaking, in the empirical sciences, depends on what meaning is given to the expression "one and the same object" and what means or criteria of identification are used. In other words, whether it is a matter of mathematical objects or, say, of objects of quantum mechanics, the answers to the question of identity are ineliminably connected with interval situations. Moreover, it is far from always possible to set against one solution or another of this question "inside" the interval of indistinguishability a solution "above this interval", that is, to replace the abstraction of indistinguishability with the abstraction of identification. And only in this latter case can one speak of "overcoming" the contradiction.
Apparently, the first to understand the importance of semiotic analysis of sophisms were the sophists themselves. Prodicus considered the doctrine of speech and of the correct use of names the most important. Analysis and examples of sophisms are often found in Plato's dialogues. Aristotle wrote a special book, "On Sophistical Refutations", and the mathematician Euclid wrote the "Pseudaria", a peculiar catalogue of sophisms in geometric proofs. The work "Sophisms" (in two books) was written by Aristotle's student Theophrastus (D.L. V. 45). In the Middle Ages, entire collections of sophisms were compiled in Western Europe. For example, the collection attributed to the 13th-century English philosopher and logician Richard the Sophister contains over three hundred sophisms. Some of them resemble the statements of representatives of the ancient Chinese School of Names (Ming Jia).
Since an inference can usually be expressed in syllogistic form, every sophism can be reduced to a violation of the rules of the syllogism. The most typical sources of logical sophisms are the following violations of the rules of the syllogism:
The grammatical, terminological and rhetorical sources of sophisms are expressed
" in the sense that "each angle is ".
" in the sense of "the sum of the angles of a triangle is ".
) or 14 (i.e. 
) is meant.The psychological causes of sophisms are of three kinds: intellectual, affective and volitional. Every exchange of thoughts presupposes an interaction between 2 persons: reader and author, or lecturer and listener, or two disputants. The persuasiveness of a sophism therefore presupposes two factors: α, the mental properties of one, and β, those of the other of the parties exchanging thoughts. The plausibility of a sophism depends on the skill of the one who defends it and the pliability of the opponent, and these properties depend on various peculiarities of the two individuals.
The intellectual causes of a sophism consist in the predominance, in the mind of the person who succumbs to the sophistry, of associations by contiguity over associations by similarity, in an undeveloped ability to direct attention and to think actively, in poor memory, in unaccustomedness to precise word usage, in a poverty of factual knowledge on the subject, in laziness in thinking (ignava ratio), and so on. The opposite qualities are, of course, the most advantageous for the person defending the sophism: let us denote the former, negative qualities by 
, and the corresponding positive ones by 
.
These include cowardice in thinking, the fear of dangerous practical consequences following from the acceptance of a certain proposition; the hope of finding facts confirming views dear to us, which prompts us to see these facts where they do not exist; love and hatred firmly associated with certain ideas, and so on. A sophist who wishes to beguile the mind of his opponent must be not only a skilled dialectician but also a connoisseur of the human heart, able to manage other people's passions masterfully for his own ends. Let us denote by 
the affective element in the soul of the skilled dialectician, which he manages like an actor in order to move his opponent, and by 
those passions which are awakened in the soul of his victim and cloud the clarity of his thinking. Argumentum ad hominem, which brings personal scores into the dispute, and argumentum ad populum, which influences the emotions of the crowd, are typical sophisms in which the affective element predominates.
In an exchange of opinions we influence not only the mind and feelings of the interlocutor but also his will. Every argumentation (especially oral) contains a volitional element, an imperative element of suggestion. A categorical tone that admits no objection, a certain facial expression, and the like (
) act irresistibly on persons who are easily susceptible to suggestion, especially on crowds. On the other hand, the passivity (
) of the listener particularly favors the success of the opponent's argumentation. Thus every sophism presupposes a relationship among six psychological factors: 
. The success of a sophism is determined by the magnitude of this sum, in which 
is the index of the dialectician's strength, and 
is the index of his victim's weakness. An excellent psychological analysis of sophistry is given by Schopenhauer in his "Eristic" (translated by Prince D. N. Tsertelev). It goes without saying that logical, grammatical and psychological factors are most closely interconnected; therefore a sophism that represents, for example, from the logical point of view a quaternio ter.
Sophisms are usually mentioned in passing and with obvious disapproval. And indeed, is it worth pausing to reflect on such arguments as these:
"The one who was sitting has stood up; whoever has stood up is standing; therefore, the one who was sitting is standing";
"Socrates is a man; a man is not the same as Socrates; therefore, Socrates is something other than Socrates";
"This dog is yours; he is a father; therefore, he is your father"?
And what is such a "proof" worth, say: "In order to see, there is no need to have eyes, since without the right eye we see, and without the left we also see; apart from the right and the left we have no other eyes, so it is clear that eyes are not necessary for sight"! Or this unexpected "conclusion": "But when people say 'stones, logs, iron', these are things that are silent, and yet they speak"!
The sophism "The Horned One" became famous back in ancient Greece. Even now it wanders from encyclopedia to encyclopedia as a "model" example. With its help one can assure anyone that he is horned: "What you have not lost, you have; you have not lost horns; therefore, you have horns."
However, horns are a trifle compared with what can in general be proved with the help of this and similar arguments. To convince a person that he has horns, hooves and a tail, or that any arbitrarily chosen father, even one who is not a human being at all, is precisely his father, and so on, is possible only through deception or abuse of trust. And that is, as the criminal code puts it, fraud. It is no accident that the teacher of the emperor Nero, the ancient Roman philosopher Seneca, in his "Letters" compared sophisms to the art of conjurers, whose manipulations we cannot explain, although we firmly know that in reality everything is done quite differently from how it appears to us.
In the ordinary and widespread understanding, a sophism is a deliberate deception based on a violation of the rules of language or logic. But it is a subtle and veiled deception, so that it is not immediately, nor by everyone, that it can be exposed. Its aim is to pass off a falsehood as truth. Resorting to sophisms is reprehensible, as is deceiving and suggesting a false idea in general.
A sophism, as an error made deliberately with the intention of misleading someone, is usually contrasted with a paralogism, understood as an unintentional error in reasoning caused by a violation of the laws and rules of logic. A paralogism seems much preferable to a sophism, since it is essentially not a deception but a sincere mistake and is not connected with an intent to substitute falsehood for truth.
Most often sophisms are connected with the mind's insufficient self-criticism and its inability to draw proper conclusions, with its striving to grasp what is not yet within its power. Quite often a sophism is simply a defensive reaction of ignorance, or even of stupidity, that does not wish to admit its powerlessness and yield to knowledge.
A sophism is traditionally regarded as an obstacle in discussion and debate. The use of sophisms leads the reasoning off to the side: instead of the chosen topic, one has to talk about the rules and principles of logic. But in the end this obstacle is nothing serious. The use of sophisms, from the standpoint of the problem under consideration, is purely external in character, and with a certain skill in the logical analysis of arguments a sophism is not hard to detect and convincingly refute. Sophisms sometimes seem so accidental and frivolous that the well-known German historian of philosophy W. Windelband classed them as jokes: "The great success that these jokes enjoyed in Greece, especially in Athens, is due to a youthful inclination for witty pranks, the southerner's love of chatter, and the awakening of rational criticism of everyday habits."
So a sophism is merely a muddled proof, an attempt to pass off falsehood as truth. It is accidental in character, unrelated to the substance of the topic under consideration, and is a purely external obstacle on the path of the argument being conducted. It follows that there is no profound content behind it requiring special explanation. Nor do any real logical difficulties show themselves in a sophism as the result of a knowingly incorrect application of semantic and logical operations. In short, a sophism is a pseudo-problem.
Such is the standard interpretation of sophisms, winning in its simplicity. Behind it stands a centuries-old tradition. However, despite its apparent obviousness, it leaves far too much unsaid and unclear.
First of all, it completely abstracts from the historical circumstances in which sophisms were born and in which their subsequent, often eventful life unfolded. Studying sophisms torn out of their native environment is like trying to form a complete picture of plants using only herbaria.
Sophisms have existed and been discussed for more than two thousand years, and the intensity of the discussion has not diminished with the years. If sophisms are merely tricks and verbal ruses exposed already by Aristotle, then their long history and the persistent interest in them are incomprehensible.
There are, of course, cases, and perhaps not rare ones, in which errors in reasoning are used with the intention of misleading someone. But this clearly does not apply to the ancient sophisms.
When the first sophisms were formulated, the rules of logic were not known. To speak in this situation of a deliberate violation of the laws and rules of logic is possible only with a stretch. Something else is going on here. After all, it is not serious to suppose that with the help of the sophism "The Horned One" one could convince a person that he is horned. It is also doubtful that anyone hoped, with the help of the sophism "The Bald Man", to convince those around him that there are no bald people. It is incredible that sophistic reasoning could make anyone believe that his father is a dog. What is at issue here, obviously, is not "the horned", "the bald" and the like, but something entirely different and more significant. And precisely in order to emphasize this circumstance, a sophism is formulated so that its conclusion is knowingly false, directly and sharply contradicting the facts.
The emergence of sophisms is usually connected with the philosophy of the sophists (ancient Greece, 5th–4th centuries BC), which substantiated and justified them. However, sophisms existed long before the sophist philosophers, and the best known and most interesting were formulated later in the philosophical schools that took shape under the influence of Socrates. The term "sophism" was first introduced by Aristotle, who characterized sophistry as apparent rather than real wisdom. He classed as sophisms both Zeno's aporias, directed against motion and the plurality of things, and the arguments of the sophists proper, and all those sophisms that were discovered in other philosophical schools. This indicates that sophisms were not the invention of the sophists alone, but were rather something common to many schools of ancient philosophy.
It is characteristic that for the general public, Socrates, Plato and Aristotle himself were also sophists. It is no accident that Aristophanes in the comedy "The Clouds" presented Socrates as a typical sophist. In a number of Plato's dialogues the person trying to tangle up his opponent with subtle questions sometimes looks more like Socrates than Protagoras.
The wide prevalence of sophisms in ancient Greece can be understood only by supposing that they somehow expressed the spirit of their time and were one of the features of the ancient style of thinking.
The relationship between sophisms and paradoxes is another topic that receives no development within the framework of the usual interpretation of sophisms.
Unlike sophisms, paradoxes are treated with full seriousness: the presence of a paradox in a theory points to an evident imperfection of the assumptions underlying it.
However, it is obvious that the boundary between sophisms and paradoxes is not at all definite. In the case of many specific arguments it is impossible to decide, on the basis of the standard definitions of sophism and paradox, to which of these two classes the given arguments should be assigned.
The separation of sophisms from paradoxes is so indefinite that a whole series of specific arguments are often referred to outright as sophisms that are not yet paradoxes or are not yet classed as paradoxes. This is the case, in particular, with the sophisms considered below, "The Medimnus of Grain", "The Veiled One", "Protagoras and Euathlus" and a whole series of others.
From general considerations alone it is clear that the matter of sophisms is far from as simple as it is usually presented. Their standard interpretation took shape, of course, not by accident. But it obviously does not exhaust the whole essence of the matter. A special and, moreover, concretely historical analysis is needed, which alone can show the narrowness and limitations of this interpretation. At the same time it must reveal the role of sophisms both in the development of theoretical thinking and, in particular, in the development of formal logic.
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