Sophistical Refutations is the final text in the Organon, a series of works by Aristotle covering topics from logical analysis to approaches to debate. The title Organon means tool or instrument and relates to the idea that it provides a tool of logic. The order of texts within the Organon is still widely debated, as the collection was ordered by Theophrastus — Aristotle’s successor in the peripatetic school — on the basis of content and not chronologically.
The texts fit into a wider tradition of philosophy and debate progressed by Aristotle’s mentor Plato and Plato’s mentor, Socrates. In this tradition, debate was seen as a tool that could be used to establish fundamental truths. Sophistry, on the other hand, was a set of approaches used to win debates with inaccurate or weak premises. Aristotle interrogates these approaches in his text and provides a framework to identify and counter inaccurate or misleading arguments.
The text is made up of 34 chapters organized into chapters addressing the process of putting forward a premise and chapters addressing the process of answering a premise. The thirteen fallacies outlined in chapters 4 and 5 of the text are organized into verbal fallacies alongside formal fallacies and nonverbal fallacies alongside informal fallacies. Formal fallacies relate to errors in the logical structure of an argument. Logical structures are discussed widely elsewhere in the Organon. Informal fallacies relate to errors in the content of an argument rather than its structure. These fallacies range from drawing false equivalencies to launching ad hominem attacks. For more information on the 13 fallacies outlined in Aristotles’ Sophistical Refutations, read more below.
Verbal and Non-Verbal Fallacies
Before listing the 13 fallacies, it’s worth making the distinction between verbal and non-verbal as well as formal and informal fallacies. Verbal fallacies relate to the use of language to convey a point that is inaccurate or logically invalid. An example of a verbal fallacy is equivocation, where a word that has multiple meanings is used to convey different meanings at different points in a syllogism. An example of a non-verbal fallacy is the fallacy of accident, in which a rule of thumb is applied in an instance where it is not appropriate.
Formal and Informal Fallacies
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For a deductive argument to be valid, it has to follow a structure based on the rules of logic. Even if the content of an argument is true, it is invalid from a logical standpoint if it breaks from this structure. An example of this is described as the “affirming the consequent” fallacy. This fallacy inaccurately assumes that because the statement leads to the consequent, the existence of the consequent implies the statement. This follows the format that “if A leads to B and B is true then A is also true”. It does not acknowledge the fact that there may be other factors that could lead to B being true.
An informal fallacy can relate to factors outside the structure of an argument varying from misleading information to ad hominem attacks. An example of an informal fallacy in Sophistical Refutations is the fallacy of drawing an irrelevant conclusion. The argument can follow a logical framework and include information that is objectively true, but that is irrelevant to the points that are being discussed. This could give the misleading appearance that an answerer has successfully refuted a point when their response is irrelevant to any of the substantive issues that are being discussed.
Let’s now explore the 13 logical fallacies one by one.
Equivocation uses a word to establish a premise and then uses a different meaning of the same word to draw an invalid conclusion. An example of this would be the use of the term light to refer to color in the premise and weight in the conclusion. This can be considered a fallacy of four terms, based on the fact that the different meaning of the word represents two distinct concepts. Within syllogism, the requisite number of terms for a valid statement is three. This is because the argument follows the format of a major premise, a minor premise and a conclusion. The major premise and the minor premise both hinge on the same term. The conclusion is based on these three terms and is invalid if it introduces a new term.
Amphiboly describes a fallacy that arises through grammatical ambiguity. This fallacy relies on one meaning of the sentence to set the premise and uses a different meaning of the sentence to draw a logically invalid conclusion. Whereas equivocation is a fallacy that relies on the ambiguity of individual words, amphiboly relies on ambiguity arising from the grammatical or syntactical relationship of words within a statement. A common example of a syntactically ambiguous statement is “John saw a man with a telescope”. In this sentence, the modifier “with a telescope” could refer to either John or the man. Both syntactic ambiguity, described as amphiboly, and lexical ambiguity, described as equivocation, undermine the logical principle that terms in a deductive argument must be clearly and unambiguously defined.
The fallacy of composition inaccurately concludes that a characteristic applying to a part of an object applies to the whole. This is clear in demonstrative examples. For example, the statement that “a brick is lightweight, therefore a building made of bricks is lightweight” is a simple example of a composition fallacy.
More complex composition fallacies have been widely discussed by economists. One example of this is the paradox of thrift introduced by John Maynard Keynes. If all individuals within an economy save, there is reduced economic activity and a consequent reduction in income, leading to less money to save. This is an example of an instance where a factor that applies to an individual does not apply to a wider group of which they are a part. In this instance, an action that is individually beneficial becomes a negative when carried out by a whole group.
The fallacy of division arises from the opposite approach. This fallacy inaccurately concludes that what is true for the whole is true for the individual parts. An example of this would be arguing that because a class achieves an average grade is over 80%, all students in the class have achieved over 80%. Statisticians often discuss the division fallacy in relation to inaccurate interpretations of statistics. An example of the division fallacy comes up in Simpson’s Paradox. In Simpson’s Paradox, a group of data would show a given trend when combined but show completely different trends when separated into subsets of this group. In this case, drawing conclusions about trends in subsets of data from a combined body of data would lead to inaccurate results. This shows the relevance of Aristotle’s Sophistical Refutations in the information age, providing a framework for identifying misleading information.
The section described by Aristotle as Prosody has widely been interpreted to relate to ambiguity arising from different accents denoted by diacritic marks. Although this section does not have as clear an interpretation as other sections in the text there is a clear application to the way that stress can be placed within a sentence to change the meaning. This would lead to some of the same issues that arose from lexical ambiguity addressed in the section on equivocation or syntactic ambiguity addressed in the section on amphiboly.
6. Forms of Expression
The fallacy of forms of expression relates to ambiguous language or phrases. In many cases, figures of speech will have a metaphorical meaning which is completely different to the literal meaning. Using these in an argument predicated on the ideas of logical reasoning can confuse the audience and make it difficult to interpret statements. This approach could be used to draw a false equivalency by using a figure of speech with a metaphorical meaning and using the same language in its literal meaning to draw a comparison. The language is being used in a different context with a different meaning but ostensibly sounds similar.
7. Accident Fallacy
The fallacy of accident is an instance of Secundum Quid, which involves an attempt to apply a rule of thumb to a situation where it does not apply. This fallacy ignores the reasons why a rule of thumb may not apply to a specific instance. This can be viewed as creating an inaccurate generalization. This fallacy is also described as a faulty generalization, with a similar fallacy in mathematics described as an inappropriate generalization. This involves proof being demonstrated by an example in order to invalidly conclude that a statement definitively has wider applicability.
8. Secundum Quid
The other instance of Secundum Quid is the converse accident fallacy which involves the opposite process. The converse accident fallacy uses facts which are exclusively applicable to exceptional cases to create generalizations that are applicable to all cases. The rules are only applicable to cases due to their exceptional circumstances and so are not appropriate for more general cases. While the accident fallacy takes rules applicable to general cases and applies them to a qualified exception, the converse accident fallacy takes rules applicable to a qualified exception and applies them to general cases.
9. Irrelevant Conclusion
The irrelevant conclusion fallacy describes an argument that, although its content may be factually accurate and logically valid, is not relevant to the issue which is being debated. This results in a distraction from these issues. Often this involves taking a related issue so that it appears relevant to the debate. A number of terms are used to describe this fallacy. In Latin, the term is ignoratio elenchi which means ignoring refutation. It is also colloquially described as someone using a red herring or missing the point. Although this may distract from the substantive issues in a debate, it is not necessarily intentional and ostensibly seems like a valid argument as it does not require logical invalidity or factual inaccuracy.
10. Begging the Question
A begging-the-question fallacy uses circular reasoning to make a point supported by an unsubstantiated assumption. An example of this is the statement, “This song is better because it has more variation”. The premise is as accurate as the conclusion, but as the premise that more variation is better has not been demonstrated, it begs the question of why that is the case. The statement presented in the format “A is true therefore B is true”, and is often difficult to identify. This is because, logically, the statement is valid. However, without demonstrating the premise, the statement is not substantively persuasive.
11. False Cause
The false cause fallacy is an informal fallacy with one form of this fallacy commonly described with the phrase “correlation does not imply causation”. This fallacy takes two events that correlate with each other and ascribes a causal link between them. In some cases, this can reverse the causal link. In other cases, there may be no causal link. Additionally, two patterns may be correlated because they both share the same cause while remaining unlinked to each other. This fallacy can be compelling in instances where two patterns are viewed as closely related by an audience.
12. Affirming the Consequent
A conditional statement in logic is frequently described as an “if, then” statement, meaning that “if A is true then it follows that B is true”. The fallacy of affirming the consequent takes a conditional statement that may be true and reverses the statement. An example of this would be taking the statement “the window is open so the room is cold” and reversing the “if, then” component to say “the room is cold so the window is open”. Although both statements may be true, it takes a cause that is applied in a specific instance and mistakenly reframes it as a general rule. This approach ignores the fact that there may be a wide range of possible causes that could lead to a specific event.
13. The Fallacy of Many Questions
The fallacy of many questions involves asking a question that requires an answer that would admit an unproven or unaccepted presupposition. These questions involve assumptions that support the argument of the questioner but are not accepted by the respondent. Although many questions require assumptions in order to be answered, in many cases, these assumptions are widely accepted. This fallacy requires that the complex question includes assumptions about information which is disputed. In this instance, answering the question would involve the respondent conceding a point to the questioner.