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| − | ==Catalog of Logical Fallacies== | + | ===Combinations=== |
| | + | It is often useful to find out how many groups of ''r'' objects can be created out of a group of ''n'' objects. This can be calculated from a function called "choose" (read aloud as "n choose r"): |
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| − | ===Argumentum ad hominem=== | + | :<math> = \binom{n}{r} \frac{n!}{(n-r)!r!}</math> |
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| − | : ''Main Article: [[Ad hominem]]''
| + | For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations. |
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| − | ([[Latin]]: "Argument directed toward the man"); An argument that attacks the character of one holding a contrary view, rather than attacking the view itself. ''Name-calling'' is a particularly crude form of this fallacy. ''Argumentum ad hominem'' is usually an attempt to accuse the other person of lying without saying so directly, or saying that his premises are somehow incompetent, irrelevant, or immaterial, or simply unreliable because they are self-serving. However, this is not good logic. If one suspects another of lying, then one should attempt to disprove the premises. One can raise a ''suspicion'' of deliberate falsehood on the part of another who has offered deliberate falsehood in the past. But the most that that can accomplish is to suggest that the other person's premises are unreliable and therefore require third-party corroboration.
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| − | ===Overgeneralization===
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| − | An argument that attempts to apply a principle to circumstances beyond the scope of its original formulation or of any reliable demonstration. The application of [[Isaac Newton]]'s original theory of relative velocity (which is that it was simply additive) to speeds approaching that of light was an overgeneralization, as [[relativity]] would later show.
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| − | Overgeneralization also is the central problem in trying to conclude something about a population from a non-representative sample, or about a larger group from a non-representative subset of that group.
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| − | ===Non sequitur===
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| − | : ''Main Article: [[Non sequitur]]''
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| − | ([[Latin]]: "It does not follow"); An argument which moves from a premise to a conclusion without showing a valid connection.
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| − | ===Proof by authority===
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| − | Also known as ''argumentum ab auctoritate'' ([[Latin]] "Argument proceeding from clout"), this is an argument that a person bases on authority, either his own or that of another person, rather than on the merits of the position. When the authority involved is a relevant source who has access to more information about the topic than the people discussing it, then the argument becomes a ''citation.'' However, a valid citation must be in an area of study, research, or mental discipline in which the authority being cited is a recognized [[expert]].
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| − | A classic example of argument from authority is a reference to a celebrity or religious leader for their opinion on a matter of science or public policy, when that celebrity or cleric has never adequately studied the subject. This kind of argument also appears in commercial advertising or political electioneering.
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| − | ===Proof by numbers===
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| − | This is an argument that a person bases on the numbers of people holding to its conclusion, rather than on the premises that might support that conclusion. "Ninety nine point nine percent of all respondents can't be wrong" is the classic phraseology. One does not effectively disprove such an argument by challenging the numbers. Instead, one reminds the other person that the numbers of people holding to any given conclusion are irrelevant to establishing the truth or falsehood of that conclusion. [[History]] is in fact replete with multiple examples, too many to mention here, of conclusions that memorable [[science|scientists]] and other great discoverers have shown to be false even though large numbers of people believed them. [[Antoine Lavoisier]], who disproved "phlogiston" as the principle of fire, was one such person. [[Christopher Columbus]] and [[Ferdinand Magellan]] make two more.
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| − | ===Proof by assertion===
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| − | An argument that states something as true without offering supporting evidence or attempting to construct a valid argument. The typical form of this "argument" is the "conclusion" of a [[non sequitur]].
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| − | ===Circular reasoning===
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| − | [[Circular reasoning]] is a form of proof-by-assertion in which one asserts a premise, then asserts a conclusion from that premise (directly or indirectly), and then tries to show that the last conclusion ''supports'' the original premise.
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| − | ===Argument from silence===
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| − | Argument from silence (in [[Latin]], ''argumentum ab silencio'') is an assertion that a proposition is false merely because no one has yet asserted evidence to confirm it--or that a proposition is true merely because no one has yet asserted evidence to contradict it. "The absence of evidence does not constitute evidence of absence." The charge of argument from silence applies in a situation in which ''no reasonable attempt has yet been made'' to develop evidence to confirm or contradict the proposition in question.
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| − | This is the opposite extreme from "manufacturing facts to support a theory," described below. The best aid to striking a balance that avoids these two opposing fallacies is [[Occam's razor]].
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| − | ===Proving too much===
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| − | A form of overgeneralization in which one attempts to use a set of premises to sustain more conclusions than he can reasonably sustain using the argument presented.
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| − | ===Double standard===
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| − | The unequal use of a criterion, and its different application in different cases. This is actually a form of [[hypocrisy]].
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| − | ===Your theory does not work under my theory, so your theory must be wrong===
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| − | : ''Main article: [[Your theory does not work under my theory, so your theory must be wrong]]''
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| − | The judgment of a theory by the premises and assumptions of another theory, rather than against its own premises and assumptions. This is a variation on proof-by-assertion.
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| − | ===Manufacturing facts from a theory===
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| − | : ''Main article: [[Manufacturing facts from a theory]]''
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| − | The assertion as fact of an undemonstrated, unobserved idea for no better reason than that a given theory requires that fact. We deal here with the assumption of a fact ''not in evidence.'' In the early stages of formulating a model, this sort of behavior is acceptable. But when repeated efforts to demonstrate such a new fact ''have failed'', the proper logical response is to discard or revise the theory, and not merely to assume that the "fact" still exists and "someone hasn't tried hard enough" to find it. This is ''especially'' true when someone develops evidence that the inferred "fact" ''could not possibly exist.''
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| − | This is yet another form of proof-by-assertion, and is the source of many controversies in modern [[astronomy]], some of them strikingly bitter.
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| − | ===Genetic fallacy===
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| − | In general, this is the attempt to aver (that is, assert as true) or reject a theory by citing its origins as either reputable or disreputable. The usual expression of this fallacy is "Consider the source!" Thus it becomes a form either of ''argumentum ab auctoritate'' or of ''argumentum ad hominem'', depending on whether one seeks to verify or disprove the theory by this method.
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| − | When the origin of ''evidence'' or of ''premises'' is relevant to the reliability of the same, then asking a hearer to "consider the source" is valid. Judges in courts of [[law]], for example, routinely reject as unreliable the testimony of any witness who has demonstrably lied about a point that matters in the case at hand. The facts that such a witness is asserting might still be true, but they cannot stand without corroboration from another, more reliable witness.
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| − | But when corroboration is established, the origins of a conclusion, however tainted, become irrelevant.
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| − | As an example, [[Gregor Mendel]] established the genetic theory that remains current today, even though Mendel's experimental technique was badly flawed, and he even stands accused of falsifying key data. But succeeding [[science|scientists]], using accepted methods of verification and statistical assessment, have achieved results consistent with this theory. Thus the theory remains valid even though Mendel's original presentation was fraudulent. Any attempt today to discredit Mendel's theory on account of Mendel's sloppy methods would be an example of a genetic fallacy.<ref name=Genetic>[http://www.fallacyfiles.org/genefall.html Genetic Fallacy] on [http://www.fallacyfiles.org/ The Fallacy Files]</ref>
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| − | ===Tautology===
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| − | A [[tautology]] ([[Greek]] '''ταυτα''' ''tauta'', "these") is an argument that becomes a repetition of a definition. Literally it means "the study of this" or "the study of these." Such an argument, or statement, can prove nothing beyond itself and is useless as a premise.
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| − | ===Contradiction===
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| − | A [[contradiction]] is a statement that contradicts its own terms. [[Aristotle]] famously stated that contradictions cannot exist. In any case of a contradition, some of the premises must be false.
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| − | Contradictions normally form part of a proof by ''exclusion''. But contradictory arguments are some of the most common flawed arguments, and are closely akin to double standards (see above).
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| − | ===Conflation===
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| − | [[Conflation]] is the treatment of two different concepts as one. The most common form of conflation informs the proverbial accusation, "You are comparing apples to oranges."
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| − | ===Loaded question===
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| − | : ''Main Article: [[Loaded question]]''
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| − | A [[loaded question]] is a question that assumes facts, usually unflattering, that are not in evidence, with the intent of trapping the other person into admitting those facts. The classic loaded-question example is "When did you stop beating your wife?" Another example is, "Do you disbelieve in [[global warming]], which 99.9 percent of all reputable scientists now accept?" (It is also an example of proof by numbers of adherents.)
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| − | ===Special pleading===
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| − | : ''Main Article: [[Special pleading]]''
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| − | [[Special pleading]] means applying to other people a set of standards that one is not willing to apply to oneself, without offering sufficient grounds, called the ''relevant difference'', to support such exemption. Special pleading is a special case of the double standard, and is one of the most despicable forms of hypocrisy. A political or military leader who urges his subjects (or those under his command) to observe "iron rations" without similarly depriving himself leaves himself open to a charge of special pleading.
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