Definition
Fallacy is the use of invalid or faulty reasoning 
Some fallacies are committed intentionally to manipulate or persuade by deception, while others are committed unintentionally due to carelessness or ignorance 
Aristotle was the first to systematize logical errors into a list, as being able to refute an opponent's thesis is one way of winning an argument 
Richard Whately defines a fallacy broadly as, "any argument, or apparent argument, which professes to be decisive of the matter at hand, while in reality it is not" 
Types of Fallacies
Formal 
An error in logic in the argument's form.
Non Sequiturs 

Propositional fallacies 

Quantification fallacies 

Syllogistic fallacies 
Informal 
Reasons other than structural, require examination of the argument's content 

Faulty generalizations 

Red herring fallacies 
Conditional or questionable 
Arguments disregard or confusion 
Other systems of classification
The most famous are those of Francis Bacon and J. S. Mill
Bacon divided fallacies into 4 Idola (Idols, False Appearances), summarize the kinds of mistakes the human intellect is prone.
Offendicula of Roger Bacon
Opus maius,J. S. Mill book of his Logic,
Jeremy Bentham's Book of Fallacies (1824).
Whateley's Logic, A. de Morgan, Formal Logic (1847)
Sidgwick, Fallacies (1883)
Formal fallacies
Appeal to probability 
Takes something for granted because it would probably be the case Something can go wrong (premise). Therefore, something will go wrong (invalid conclusion) 
Argument from fallacy 
Aka fallacy fallacy, assumes that if an argument is fallacious, then the conclusion is false If P, then Q. P is a fallacious argument. Therefore, Q is false 
Base rate fallacy 
Making a probability judgment based on conditional probabilities, without taking into account the effect of prior probabilities Police officers have breathalyzers displaying false drunkenness in 5% of the cases the driver is sober. However, the breathalyzers never fail to detect a truly drunk person. One in a thousand drivers is driving drunk. The police officers stop a driver at random, and force the driver to take the test. The test is positive. You don't know anything else about him or her. How high is the probability he or she really is drunk? Many would answer as high as 0.95, but the correct probability is about 0.02. To find the correct answer, one should use Bayes's theorem 
Conjunction fallacy 
Assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying a single one of them Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. Which is more probable? Linda is a bank teller. Linda is a bank teller and active in the feminist movement. The majority of those asked chose second option. However the probability of two events occurring together is always less than or equal to the probability of either one occurring alone 
Maskedman fallacy 
Substitution of identical designators in a true statement can lead to a false one Lois Lane believes that Superman can fly. Lois Lane does not believe that Clark Kent can fly. Therefore Superman and Clark Kent are not the same person 
Propositional fallacies A propositional fallacy is an error in logic that concerns compound propositions. For a compound proposition to be true, the truth values of its constituent parts must satisfy the relevant logical connectives and, or, not, only if, if and only if 
Affirming a disjunct 
Concluding that one disjunct of a logical disjunction must be false because the other disjunct is true Max is a mammal or Max is a cat. Max is a mammal. Therefore, Max is not a cat 
Affirming the consequent 
The antecedent is claimed to be true because the consequent is true; if A, then B; B, therefore A If someone owns Fort Knox, then he is rich. Bill Gates is rich. Therefore, Bill Gates owns Fort Knox 
Denying the antecedent 
The consequent is claimed to be false because the antecedent is false; if A, then B; not A, therefore not B If you are a ski instructor, then you have a job. You are not a ski instructor, Therefore, you have no job 
Quantification fallacies A quantification fallacy is an error in logic where the quantifiers of the premises are in contradiction to the quantifier of the conclusion 
Existential fallacy 
An argument that has a universal premise and a particular conclusion ^{Every unicorn definitely has a horn on its forehead} 


Informal Fallacies
Informal fallacies Arguments that are fallacious for reasons other than structural (formal) flaws and usually require examination of the argument's content. 
Appeal to the stone 
argumentum ad lapidem Dismissing a claim as absurd without demonstrating proof for its absurdity A: Infectious diseases are caused by microbes B: What a ridiculous idea! A: How so? B: It's obviously ridiculous 
Argument from ignorance 
argumentum ad ignorantiam It asserts that a proposition is true because it has not yet been proven false (or vice versa) There may be seventy kazillion other worlds, but not one is known to have the moral advancement of the Earth, so we're still central to the Universe 
Argument from incredulity 
Appeal to common sense "I cannot imagine how this could be true; therefore, it must be false." Argument from ignorance 
Argument from repetition 
argumentum ad nauseam, argumentum ad infinitum signifies that it has been discussed extensively until nobody cares to discuss it anymore; sometimes confused with proof by assertion 
Argument from silence 
argumentum ex silentio conclusion is based on the absence of evidence, rather than the existence of evidence 
Argument to moderation 
ad temperantiam false compromise, middle ground, fallacy of the mean. Assuming that the compromise between two positions is always correct 
Argumentum verbosium 
See: by verbosity 
Begging the question 
petitio principii providing what is essentially the conclusion of the argument as a premise Opium induces sleep because it has a soporific quality A kind of circular reasoning 
Shifting the burden of proof 
See: onus probandi I need not prove my claim, you must prove it is false 
Circular reasoning 
circulus in demonstrando when the reasoner begins with what he or she is trying to end up with; sometimes called assuming the conclusion Whatever is less dense than water will float, because such objects won't sink in water 
Circular cause and consequence 
The consequence of the phenomenon is claimed to be its root cause. Correlation does not imply causation 
Continuum fallacy 
Improperly rejecting a claim for being imprecise Fred is cleanshaven now. If a person has no beard, one more day of growth will not cause them to have a beard. Therefore Fred can never grow a beard 
Correlativebased fallacies 
Correlation proves causation post hoc ergo propter hoc a faulty assumption that because there is a correlation between two variables that one caused the other. Suppressed correlative where a correlative is redefined so that one alternative is made impossible 
Divine fallacy 
Argument from incredulity. Because something is so incredible / amazing / ununderstandable, it must be the result of superior, divine, alien or paranormal agency 
Double counting 
Counting events or occurrences more than once in probabilistic reasoning, which leads to the sum of the probabilities of all cases exceeding unity 
Equivocation 
Misleading use of a term with more than one meaning Ambiguous middle term a common ambiguity in syllogisms in which the middle term is equivocated Definitional retreat changing the meaning of a word to deal with an objection raised against the original wording. 

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