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“ ” We reason from our bedrock beliefs, not to them. Infanticide and We reason from our bedrock beliefs, not to them. Infanticide and slavery are not forbidden in our society because the arguments against these practices are stronger than the arguments in favor of them, but because the practices revolt us. We would not listen to anyone who cared to make arguments in favor of them. —Judge Richard Posner, Overcoming Law (technically an Appeal to Disgust, showing why pure logic is best left to Vulcans).

A logical fallacy is an error in the logic of an argument[1][2] that prevents it from being logically valid or logically sound but does not prevent it from swaying people's minds.

Examples of fallacies include the straw-man fallacy in which one distorts another person's argument that often makes his or her argument easier to attack. As with most fallacies the straw-man fallacy may result from sloppy thinking or more dubiously used on purpose. The ad hominem is also a common fallacy where you attack the person who makes the argument (their history, personality, ideologies, etc.), even though the validity of an argument is likely entirely independent of the character of a person who makes it. This is frequently used in political discourse. Another common fallacy is the non sequitur, in which someone takes premises and then forms a conclusion that the premises do not logically support. When a fallacy is identified, one should be careful not to assume that therefore the conclusion is wrong. This is another well-known fallacy called the Fallacy fallacy. One may be wrong in how one arrived at a conclusion, but that doesn't mean the conclusion itself is wrong. It may be true based on some other premise or logical conclusion. For example, one may say:

P1: Bears have four legs.

P2: All three legged animals are mammals.

C: Therefore a bear is a mammal.



In this case there are multiple problems both with the premises themselves and the conclusion which is a non sequitur. One cannot justify that conclusion based on the two premises. However it is not wise to then conclude that because this argument is fallacious, bears are not mammals. A bear of course is a mammal, though this is logically concluded by an entirely different set of arguments.

Logical fallacies often result from some particularities of human intuition. A logical fallacy is not necessarily a Bayesian fallacy,[3] so given a particular circumstance, jumping to the conclusion will be more likely than not, and get baked into human thinking as a heuristic.[4] When the heuristic is applied outside its reasonable bounds, it becomes a cognitive bias.

The problem is that this can lead to one being grievously wrong about reality.[5] So one may form an opinion by a heuristic (System 1 thinking), but one needs to show oneself working to make sure that one hasn't just said something silly (System 2 thinking).

This particularly applies to thinking about science, because scientific thinking is unintuitive for most people unless trained into it; and to arguing your points in general, because heuristics are full of glaring exceptions.

Explanation [ edit ]

See the main article on this topic: Syllogism

Must be used in argument [ edit ]

One common error when first learning about logical fallacies is to fail to realise that a fallacy can only be present if it is used as part of an argument.[6] For example, "So-and-so is a socialist" is not an ad hominem fallacy (see below) because it is simply a statement. So-and-so may be a socialist. "So-and-so is a socialist, therefore s/he is wrong" is an ad hominem because a conclusion is being drawn, and the conclusion has nothing to do with the premise. It attacks the opponent; not the opponent's argument. This can be more complicated than it sounds, however, because the conclusion that s/he is wrong is often implied.

Likewise, "You are an idiot" is merely an assertion. Further, "you are saying idiotic things, therefore you are an idiot" may be a valid argument regardless of whether the premise (the opponent is saying idiotic things) is true. However, it is only a sound argument in the event the premise is true, and if "saying idiotic things" makes one an idiot. (Even geniuses have said idiotic things. Just ask their spouses.)

Validity versus truth [ edit ]

Just because an argument is valid does not mean the conclusion is true. A valid argument simply means that if the premises are true, the conclusion must be true as well. A sound argument is a valid argument with the additional requirement that the premises (and thus the conclusion) are true.[4] For instance, consider the following argument.

P1: All humans are cows.

P2: All cows are plants.

C: All humans are plants.



Although the conclusion is false and the premises are false, this is still a valid argument because if the premises were true, the conclusion must be true as well. Since at least one premise is false, the argument is valid but not sound.[5]

“ ” What we have here is a blatant example of What we have here is a blatant example of argument by assertion . It's therefore clear your mother was a whore, and you flunked out of elementary school —Colonel Custer[7]

It is not acceptable to merely state that one's opponent is using a fallacy (as above). One must explain how the opponent's argument is fallacious (e.g., they claim that you are a shill), why it is wrong (there's no evidence that you are a paid government disinformation agent), and what that means for their argument (if you're not a shill, then your arguments can't be handwaved away).[8]

This need not be a drawn-out paragraph. Even "your ad hominem is irrelevant to my argument, so my argument stands" is sufficient.

Otherwise, one runs into the risk of fallacy dropping — claiming someone's argument is wrong without bothering to explain why — which comes dangerously close to ad hominem. (It's equivalent to shouting "your logic is bad!" and claiming victory.)

A related concept is that of logic chopping[9] where the tools of logic are used unhelpfully and only serve to obfuscate a conversation. This can include fallacy dropping, or nitpicking at statements rather than focusing on the actual discussion.

Reductio ad absurdum [ edit ]

One of the techniques that is often used to expose fallacies is reductio ad absurdum. When using this technique, one attempts to show that an argument is fallacious by showing that an argument with the same form can be used to produce a conclusion known to be false. For example, if someone commits the fallacy of affirming the consequent, one might say "by your logic, we can prove that 'Elvis Presley was a US President', as follows: If Elvis was a US President, he was famous. Elvis was famous. Therefore, he must have been a US President". It is an example of modus tollens with the form "If the logic of Argument A is valid, then Conclusion C follows from the set of true Premises P. But C is false. So the logic of A is not valid".

The exact details of how to use reductio ad absurdum is complex, so we shall refer you to the page on reductio ad absurdum instead of trying to recap it here. A good example of reductio ad absurdum in action is the page on the flat Earth model of the world which shows the absurdities that arise when one takes the flat earth model of the Earth seriously which some people still do.

The relationship of paradoxes to logical fallacies [ edit ]

Logical fallacies are a common theme of paradoxes (infinite regress, circular definitions, and equivocation). [The artist] Patrick Hughes outlines three laws of the paradox:[10]

Self-reference: An example is "This statement is false", a form of the liar paradox. The statement is referring to itself. Another example of self-reference is the question of whether the barber shaves himself in the barber paradox. One more example would be "Is the answer to this question 'No'?"

Contradiction "This statement is false"; the statement cannot be false and true at the same time. Another example of contradiction is if a man talking to a genie wishes that wishes couldn't come true. This contradicts itself because if the genie grants his wish, he did not grant his wish, and if he refuses to grant his wish, then he did indeed grant his wish (well technically he still didn’t since he can’t both grant and refuse to grant wishes), therefore making it impossible either to grant or not grant his wish because his wish contradicts itself.

Vicious circularity, or infinite regress: "This statement is false"; if the statement is true, then the statement is false, thereby making the statement true. Another example of vicious circularity is the following group of statements:

"The following sentence is true." "The previous sentence is false."

W. V. Quine distinguished between three classes of paradoxes:[11]

A veridical paradox produces a result that appears absurd but is demonstrated to be true nonetheless.

produces a result that appears absurd but is demonstrated to be true nonetheless. A falsidical paradox establishes a result that not only appears false but actually is false, due to a fallacy in the demonstration. The various invalid mathematical proofs (e.g., that 1 = 2) are classic examples, generally relying on a hidden division by zero . Another example is the inductive form of the horse paradox , which falsely generalises from true specific statements. Zeno's paradoxes are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up to a tortoise with a small head-start.

establishes a result that not only false but actually false, due to a fallacy in the demonstration. The various (e.g., that 1 = 2) are classic examples, generally relying on a hidden . Another example is the inductive form of the , which falsely generalises from true specific statements. are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up to a tortoise with a small head-start. A paradox that is in neither class may be an antinomy , which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling–Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.

A fourth kind, which may be alternatively interpreted as a special case of the third kind, has sometimes been described since Quine's work.

A paradox that is both true and false at the same time and in the same sense is called a dialetheia . In Western logics it is often assumed, following Aristotle, that no dialetheia[i] exist, but they are sometimes accepted in Eastern traditions (e.g. in the Mohists , [12] the Gongsun Longzi , [13] and in Zen[14]) and in paraconsistent logics. It would be mere equivocation or a matter of degree, for example, to both affirm and deny that "John is here" when John is halfway through the door but it is self-contradictory simultaneously to affirm and deny the event." (This is equivocation owing to.the ambiguity of the term here: Does it mean the general vicinity, the building, the room, or a particular spot one metre to the speaker's left? Once this ambiguity is resolved by defining terms, the apparent paradox promptly vanishes in a puff of logic.)

Types [ edit ]

There is no consensus among philosophers about how to best organize fallacies. They can be classified as inductive and deductive, formal and informal, categories pertaining to the psychological factors that led people to create them, and the epistemological or logical factors that underlie them.[15] Another problem that occurs when organizing fallacies is that many of them can be placed in different areas. Consider, for example, the equality fallacy. It is a fallacy of ambiguity as it is not often clear what people mean when they say one should be treated “equally”. It is a political correctness fallacy, as liberal politicians advocate for the idea that one should be offended if people are not treated "equally”. It is a jumping to conclusions fallacy, as it assumes that the blind should be treated "equally" to someone who has 20/20 vision (which is clearly a logical error if one works at the DMV or one is responsible for hiring referees). It is an appeal to self-evident truth fallacy as the Founding Fathers of the USA claimed that "all men are created equal" is a self-evident truth even though it is quite clear that all men are not created equal as some men are smarter than others, stronger than others, taller than others, etc. It is also a loaded language fallacy as the term is imbued with emotional connotations. It is also a conditional fallacy as there are logical ways to use the word equality such as the right to be equally judged by the law. And if you doubt that the promotion of equality is a fallacy, then you probably don't know about how laws that promote equality in the USA, namely the 1964 Civil Rights Act and the Equal Employment Opportunity Act of 1972, have led to the prison rape of women by male guards.[16][17][18] But we digress.

Due to the difficulties organizing fallacies, often times sites will simply list the fallacies alphabetically and avoid attempting to organize them. While this works on some level, it is often not very helpful when trying to understand fallacies as there are a lot of them. People need to have some sort of schema in order to understand them and for this reason this page has decided to organize them for you. The primary division of fallacies utilized is formal and informal. A formal fallacy is an argument in which the conclusion would not necessarily be true whether or not its premises are correct, because it does not follow valid logical structure. An informal fallacy, on the other hand, is contingent on the argument's content or possibly the motive of the arguer. Within the informal category, the page has further subdivided the fallacies into fallacies of presumption, fallacies of relevance, and fallacies of clarity. This is a way of categorizing fallacies mentioned by the Internet Encyclopedia of Philosophy[15], is used elsewhere such as at Wikiversity, and is one of the more common ways of organizing fallacies. Another site that was used as a guide for organizing fallacies was Fallacy Files. In addition to the formal and informal fallacy sections, this page has added a section for conditional fallacies, which are broader categories that have both a non-fallacious and a fallacious component, and a section for argumentative fallacies, which are fallacious ways of presenting information that incorporate informal fallacies. While this list is quite extensive, it is not comprehensive as there are subfallacies or fallacies that pertain to specific fields of study that may not have been mentioned.

Formal [ edit ]

See the main article on this topic: Formal fallacy

All formal fallacies are forms of invalid (generally deductive) reasoning and specific types of non-sequitur.[15]

Syllogistic fallacy [ edit ]

See the main article on this topic: Syllogistic fallacy

A syllogistic fallacy is any instance in which a syllogism with incorrect structure is used.[19][20]

Fallacies of quantificational logic (also known as fallacies of predicate logic) [ edit ]

A logical mistake that involves numerical concepts such as the difference between "some" and "all".[19]

Illicit contraposition: No S are P. Therefore, no non-P are non-S.[19][21] Quantifier-shift fallacy (or scope fallacy): Every X has the relation R to some Y. Therefore, some Y has the inverse of relation R to every X.[19][21][15]

Probabilistic fallacy [ edit ]

When the conclusion reached from the premises of an argument violates the laws of probability.[19][note 1]

Bad reasons fallacy [ edit ]

Fallacy fallacy (argumentum ad logicam):

Forward: Argument A for the conclusion B is fallacious. Therefore, B is false. Converse: The conclusion B is false. Therefore, Argument A for B is fallacious. Converse of Inverse: Argument A for the conclusion B is not fallacious. Therefore, B is true. Inverse: The conclusion B is true. Therefore, Argument A for B is not fallacious.[19][21]

Fallacy of modal logic [ edit ]

The Fallacy of modal logic is a formal fallacy in which modalities play a role in creating a fallacious argument.[19]

Modal Scope Fallacy: A fallacy in which an unwarranted degree of necessity falls on the conclusion of an argument. An example would be, "if Barack is President, then he must be 35-years old or older,"[29] since it is not his presidency that causes him to be this age.

Masked man fallacy [ edit ]

The masked man fallacy (also known as illicit substitution of identicals) is a fallacy that involves confusion between extensions and intensions.[19][21][15] Effectively, conflating knowing something with knowing it under all of its names. E.g. "I know who Bruce Wayne is, but I don't know who Batman is. Therefore, Bruce Wayne is not Batman."

Informal [ edit ]

See the main article on this topic: Informal fallacy

Fallacies of presumption [ edit ]

Fallacies of presumption occur when one uses a fallacious or unwarranted assumption to establish a conclusion.[15]

Jumping to conclusions [ edit ]

See the main article on this topic: Jumping to conclusions

Jumping to a conclusion occurs when coming to a judgement without taking the time to rationally evaluate the merits of the argument.[21][15]

No True Scotsman [ edit ]

See the main article on this topic: No True Scotsman

When groups are redefined on the spot such as because they are indefensible from someone pointing it out the their obvious deficiencies so the claimant revises their claim, most frequently by using numerous exceptions to a claim to make it "accurate," in spite of this resulting in the claim having no real meaning, and acts as if was the same as the original claim. Examples:

Category mistake [ edit ]

See the main article on this topic: Category mistake

Confusing what is true of a part with what is true of the whole.

False dilemma [ edit ]

False dilemma (also known as the Black-or-White fallacy, false dichotomy or false dilemma): When two opposing views are presented as the only options when they are not.[19][21][15]

The alternative advance is when both of the options presented to you are essentially the same thing, just worded differently.[21]

False equivalence [ edit ]

False equivalence: When you presume that two things are the same when they are not.[31][15]

Moral equivalence: Arguing that two things are morally equal, even though they are not.[31] Political correctness fallacy: When you presume that people's ideas are of equal value or are equally true when they are not. (Think Galileo.) In the case of argument to moderation (argumentum ad temperantiam), one is technically presuming that somewhere between two disparate positions, both of which being partially incorrect, there must be a compromise position between them that is correct. Examples: Medicare Part D was such a great bill because it was a compromise between the positions of the Republicans and the Democrats. In fact, it was so great that pharmaceutical companies are price-fixing drugs, violating anti-trust laws, and costing American taxpayers billions of dollars. Here is a 60 Minutes expose[32] of just how great the compromise between Republicans and Democrats is for America. Winner-take-all is an anti-democratic way to run a multi-candidate election, but people would have "too much of a vote" in a purely proportional system. Therefore, Republican Presidential Primaries began to be run so as to award delegates to all candidates so long as none must have gotten an absolute majority of the vote in that state.[21] Balance fallacy — Giving equal weighting to both sides of an argument, even if one really doesn't deserve the time.[15]

Fallacies of relevance [ edit ]

Red herring: A group of fallacies which bring up facts or issues which are irrelevant to the argument often in an attempt to distract the opponent and/or audience.[19][21][15][23]

Rights To Ought: The speaker deflects criticism for a behaviour or statement by declaring that they have the 'right' to perform said action. This is utterly irrelevant. Just because you can do something, does not mean it is desirable, pragmatic, or beneficial in anyway to anyone.[33] Ignoratio elenchi: Missing the point by refuting something that is not stated. Related to the straw man.

Argument from ignorance [ edit ]

Argument from ignorance (argumentum ad ignorantiam): When it is claimed that a proposition is true because it has not yet been proven false or that it is false because it has not yet been proven true.[19][21][15]

Science doesn't know everything: P1: If science (or a person) can't explain X, then Y is true. P2: Science can't explain X. C: Y is true. Moving the goalposts: Science explains/discovers the X of the first premise leading to the refutation of the support for Y. New requirement: Well if science can't explain Z then Y is true. Science explains Z. New requirement: Well is science can't explain W… Inflation of conflict results if the argument refers to an incomplete agreement on a certain X, Z, or W, as sufficient to cause people not to know anything at all.[21] Confusing the currently unexplained with the unexplainable: Science hasn't explained how the Big Bang began (X), therefore Y = it will forever remain unknown.[21] One single proof: Dismissing all circumstantial evidence in favor of a single "smoking gun" that may not (and may not need to) exist. Shifting of the burden of proof (onus probandi): When one asserts something to be true without evidence for one's position, or against it in the case of a negative proof (also known as proving non-existence), and then one asks people to prove them wrong. (A person asserting a fact is the one who has to have proof, not the other way around.)[21][15] Missing data fallacy: One's hypothesis has been proven wrong. One asserts, "Well there is yet to be discovered information that will prove my flawed hypothesis or conclusion to be true."[21] Appeal to complexity: I can't understand something therefore no one else can either. This could be due to Willful ignorance.[21]

Genetic fallacy [ edit ]

Genetic fallacy: Occurs when the origin of a claim is used to establish truth or falsehood rather than the claim's current factual merits.[19][21][15]

Appeal to false authority [ edit ]

Appeal to false authority (argumentum ad verecundiam): Incorrectly asserting that respect given to some authority proves the assertion to be true.[19][21][23]

Ad hoc [ edit ]

Ad hoc (meaning literally, "for this"): When some idea is asserted purely to shore up some other idea.[21][15]

Weak analogy [ edit ]

Weak analogy: Using an analogy that is too irrelevant for it to be used to prove or disprove an argument.[19][21][15][23]

Faulty Comparison: Comparing two things as if they were related when they are not in order to convey the idea that one is better than the other is. Example: X motorcycle gets 5 times better gas mileage than the best selling Y automobile.[21][15] Incomplete Comparison: A comparison that fails to state what it is being compared to. Example: Our garbage bags are 40% stronger![21] Extended analogy (Reductio ad Hitlerum): Saying something is bad because Hitler (allegedly) did it. Sometimes called "Hitler ate sugar."[19][21] Appeal to the Moon (argumentum ad lunam): Arguing if we can put a man on the moon, then surely we can cure trisomy 13.[21] Appeal to Extremes: Misrepresenting a reasonable argument by using extreme examples to try and prove the argument to be fallacious.[21]

Fallacies of clarity/ambiguity/vagueness [ edit ]

Fallacies of clarity/ambiguity/vagueness (equivocations): Fallacies that lead to logical confusion because of a lack of logical or linguistic precision. Often (subconsciously/unconsciously) substituting the meaning of a given word in one context for another context that is inappropriate in order to make your argument. Intentional (also known as ambiguous middle term) and extensional fallacies depend on using words or phrases that are open to more than one interpretation and treating the different meanings for the same word or object as being equivalent when the differences matter although each type depends on it in a different way.[19][21][15][23]

Person 2: How do you stay in business if you only sell dozens of signs? (token)[21]

Conditional [ edit ]

See the main article on this topic: Conditional fallacy

For the purpose this list, a conditional "fallacy" is an argument that may or may not be fallacious depending on how the argument is constructed. The fallacious forms of the argument can be placed in the informal category section (and many such fallacies are already listed there).

Appeal to authority: When an appeal to authority is done correctly, then it can be called an appeal to a qualified authority and is not a fallacy. When it is done incorrectly, it can be called an appeal to false authority. Determining what is or is not a qualified authority is the subject of epistemology and it is beyond the scope of this fallacy list. While determining an authority's qualifications is often viewed from a scientific vantage point, it is not limited to that field of study. The "He said she said" problem is also a question of whether an authority is qualified or not.[15] Is/ought problem (also known as Hume's law): The is/ought problem stipulates that "what is" is fundamentally distinct from "what ought". Consider the issue of black rhinos. Descriptions about what is happening to black rhinos (what is) cannot determine whether rhinos ought to be environmentally protected or allowed to go extinct (what ought). The ought is a human value that is associated with the "what is" but it is not a "what is" itself as it is contingent on subjective experience which varies from person to person (though there are some oughts that are more universal than others). Most of the problems pertaining to the is/ought problem have been placed in the conditional category as they are contingent on the values a person or society stipulates to be true, though some of the fallacies associated with is/ought problem have been placed in the informal category due to relatedness to other fallacies. For example, the "rights to ought fallacy" was placed under the "appeal to the law fallacy" due to their close association. The following are fallacies associated with the is/ought problem that are often seen as being examples of fallacious reasoning.[15] Moralistic fallacy: Concluding "what ought" determines "what is". Example: Homosexuality ought not to occur and therefore it is not something that is natural.[21] Naturalistic fallacy: Concluding "what is" determines "what ought". Example: Pedophilia is natural and therefore it ought to be allowed.[21][15] McNamara fallacy: Making a decision based only upon things that can be quantified and ignoring things that have a qualitative component. Example — Quantitative argument made: Denying education to people that are here illegally will save taxpayers X amount of dollars. Qualitative argument ignored: Seven-year-old is on the street instead of school because his parents are at work and he or she has no adult supervision.[21] Economic fallacies: Economics can be thought of as collective ought. We ought to promote laissez-faire capitalism or we ought to promote socialism, for example. Given that economics is entangled with what people believe ought to occur, economic fallacies can be characterized as a subcategory of the is/ought problem. Hyperbolic discounting: When one chooses to ignore the future in order to focus on present rewards. Example: Present: Fracking boosts the local economy! Future: Florida is under the sea.[15] Sunk cost: I have spent X amount of money searching for this sunken treasure and its not anywhere where I thought it would be. Well I better spend some more money or else all the money I spent would have been wasted. Example: Oak Island money pit.[21] Broken window fallacy: A fallacy that asserts that the destruction of property in things like natural disasters actually boosts the economy. It fails to factor in what the money would otherwise be used for if it wasn't being used for reconstruction.[21] Just in case fallacy: Basing one's judgement on the worst-case scenario without adequately factoring in the cost-to-benefit ratio that would cause one to come to a different conclusion. For example, one could conclude that one should spend money on flood insurance for a home in the middle of the Mojave desert due to the very unlikely scenario that changing weather patterns could cause ones home to be caught in an unprecedented deluge of water.[21] Game theory fallacies: These fallacies are conditional. When game theory is done properly as it was by John Nash , then it is not a fallacy. When it is done improperly, then it is ad hoc.[31]

Argumentative [ edit ]

For the purposes of this list, argumentative fallacies are ones that occur in communication, both the verbal and written forms of it. These fallacies often incorporate many of the informal fallacies listed above when they are presenting information.

Person 1: There are reports of you having an affair with your intern. (Ambiguous: Is this supposed to be the one affair Person 2 is reportedly having with one particular intern or one of multiple interns with whom Person 2 is concurrently having affairs?)

Person 2: Let me tell you about my new tax plan.[21][15]

Fallacy collections [ edit ]

There are lots of fallacy collections on the Web. Some of them promote a particular agenda, but most fallacies listed in them are real and present in arguments everyday. Unfortunately, many are deprecated.

Here is a list of websites, ordered roughly by usefulness:

Deprecated ones, listed ad hoc:

Sinclair Community College( ) Global Tester( ) Anti-Mormon Illogic( ) Objectivism( ) Evolution_V_Creation forums( ) Peter A. Angeles( ) Sine Wave( ) Carleton University( ) P5( ) Mathenomicon( ) Vanessa Hall( ) J. P. Craig( ) Informal Fallacies( ) Autonomist( ) Gordon, Hanks, & Zhu( ) Freemasonry( ) Taking Sides( ) Jeff Richardson( ) Chisnell.com( )

In a nutshell [ edit ]

Stop Misusing Logical Fallacies (Professor Dave Explains

Logical Fallacies (GCFLearnFree.org

See also [ edit ]

Логическая ошибка Русскоязычным вариантом данной статьи является статья

For those of you in the mood, RationalWiki has a fun article about Justification generator.

Notes [ edit ]

↑ This was placed in the formal category due to the fact that statistics are based in mathematical logical proofs. ↑ [25] Using some form of statistical inference is the only mathematically valid way to evaluate evidence and determine the likelihood of guilt and innocence, but using Bayesian statistics is against USA's laws. ↑ [27] According to a federally-funded study made available online by the National Criminal Justice Reference Service, 2-8% of reported rapes in Los Angeles, California were false allegations.