A logical fallacy identifies a particular type of mistaken reasoning. It is important to study fallacies in order to be able to refute poor reasoning used by others and to be able to avoid using the same oneself.
If one avoids logical fallacies, then one's arguments should be valid. If the premises of one's valid arguments are true, then one's conclusions should be true.
One cannot identify an informal fallacy by its form alone. To avoid an informal type of fallacy one must additionally consider the non-logical content of an argument. Additionally, informal fallacies are not as rigorous as the formal ones, and the truth of the premises of a valid argument with an informal form merely lends support to the truth of the conclusion.
Informal fallacies generally represent mistakes in inductive reasoning.
Fallacies of ambiguity are identified by the use of a word or phrase with more than one meaning in both of its meanings in the same argument. Thus ambiguity causes the form of an argument to appear valid when it is not.
Amphiboly is a type of ambiguity in which the meaning of a logical proposition is unclear because of its grammar or structure. For example, in the quantifier-shift fallacy the scope of the quantifier "some" or "all" shifts between a premise and the conclusion in an argument.
Equivocation is a type of ambiguity that is not grammatical, as with amphiboly, but rather occurs when a single word or phrase has two distinct meanings. In the fallacy of ambiguous middle, the equivocation occurs within the middle term, that is the term occurring in both premises, in a categorical syllogism (see also syllogistic fallacy and four-term fallacy below). In the fallacy of redifinition, one argues using a new meaning for a term in the premises but then slips back to using its common meaning in the conclusion. In the fallacy of distinction without a difference, one claims there is a difference between two terms when in fact there is not.
Quoting out of context is a type of ambiguity in which a passage's meaning is changed by removing its surrounding text, and the quote is subsequently offered as evidence in an argument.
Reification is a type of ambiguity in which an abstract concept is subtly treated like a real thing.
Fallacies of vagueness occur when the appearance of soundness in an argument depends upon using a term having fuzzy boundaries or borderline cases as if it did not.
Consider two related concepts that differ from each other by a continuum of insignificant changes such that there is no non-arbitrary place at which a sharp line between the concepts can be drawn. In a slippery slope argument, in the semantic case, one uses the vagueness of the distinction between the two concepts to conclude there is really no difference between them.
An example might be to point out that the worst religious cult activities like the euphamistically named Sea Orgainsation in Scientology are comparable to Slavery. The argument can be overextended to assume that all religious groups arbitrarily defined eg by their enemies as cults are a type of slavery or even that all religions are a type of slavery. Religions regularly restrict freedom but only in the worst cases are religious followers treated as slaves. Incidentally the example above is fallacious for a second reason, it is not universally accepted that Scientology is a religion.
Overprecision is the other extreme and happens when an argument presents information as precise when in fact attaining the level of precision is impossible or irrelevant. Thus the information itself becomes suspect.
Fallacies of overgenerality include concepts that are overly general in their particular context as well as overly broad generalizations. Note the latter is also a type of weak analogy (see below). Note also that fallacies of overgenerality are similar to overprecision, except that their flaw lies in the opposite direction. Stereotyping is an example of this.
A red herring is an argument used to evade or divert the audience's attention away from the issue in question, through the introduction of some irrelevancy, toward an argument that is at best marginally related to the original issue. Thus in this type of fallacy the premises of the argument are logically unrelated to its conclusion. A red herring is most effective when one can demonstrate validation for the nonetheless irrelevant aspect of the argument.
A straw man is a weak or invented caricature of a particular position set up that can be easily refuted. One then argues to a conclusion that denies a position--the "straw man"--not held by one's opponent. Straw man arguments often attack a position at its extremes, where it is weakest.
In an appeal to consequences the accuracy of premises is determined by their perceived desirability. It should be noted we cannot determine the truth of a belief from its consequences.
Appeal to nature is the contention what is natural is inherently good and what is unnatural is inherently bad. This can be viewed as the fallacy that what is is also what ought to be.
Fallacies of emotional appeal substitute a claim intended to arouse the audience's emotions in place of evidence in order to gain acceptance of an argument's conclusion. Such fallacies include appeal to pity, envy, fear, hatred, and pride. Wishful thinking is an emotional appeal in which an argument's premise expresses a desire, whether based on virtue or prudence, for the conclusion to be true. Note we should base our beliefs upon reason rather than on emotion.
In the bandwagon fallacy, also known as appeal to popularity, one argues for an idea based simply upon the irrelevant observation many people believe it. Note popular opinion can be, and quite often is, mistaken.
Two wrongs make a right is the attempt to justify one's misbehavior by pointing out the same type of misbehavior in others or that committed by one's accuser.
Genetic fallacies judge the truth or otherwise of an idea based on its origins. In appeal to poverty one argues a position is strengthened because the person promoting it is poor. In appeal to wealth one argues a person is better simply because they are wealthier or a thing is better simply because it is more expensive.
Appeal to authority is a type of genetic fallacy in which the opinion of an alleged expert is presented as evidence of the truth of a statement when in fact the authority is not an expert on the issue in question, is biased, is misquoted (see ambiguity and quoting out of context above), or is not representative of experts on the subject. Appeal to celebrity is a special case in which the authority is quoted because he or she is someone famous, despite not being a disinterested expert.
Ad hominem (to the man) is a type of genetic fallacy in which one introduces irrelevant personal attacks against the person making an argument instead of addressing the argument itself. In abusive ad hominem an insult regarding the character or other personal qualities of one's opponent is offered as evidence against his or her position. In circumstantial ad hominem some personal circumstance predisposing one's opponent to a particular position is offered as evidence against that position.
When poisoning the well, one commits a preemptive abusive or circumstantial ad hominem strike against one's opponent before he or she has a chance to make a case. In tu quoque (you too) one defends oneself from criticism by accusing one's accuser of the same misbehavior, which also makes it a type of two wrongs make a right.
In guilt by association one attacks a position by superficially associating it with a dishonorable person or group. Thus it is the converse of appeal to authority. Hitler card is a special case of guilt by association in which one criticizes a position by connecting it in some way with Adolf Hitler or the Nazis in general. Note even if Hitler or other Nazis did accept an idea, this historical fact alone is insufficient to discredit it.
Appeal to ignorance
An appeal to ignorance is an argument for a proposition on the basis it hasn't been proved false or an argument against a proposition on the basis it has not been proved true.
To argue a proposition is false because there is as yet insufficient evidence or an unconvincing explanation for it, is known as argument from incredulity. Arguments of this type may indicate either the arguer cannot yet explain a phenomenon or scientists cannot yet explain it.
Arguing a proposition is true because there is as yet insufficient evidence against it is known as shifting the burden of proof. In an argument of this type one makes a claim that needs justification and then demands one's opponent justify the opposite of the claim. Note the burden of proof can never be shifted to the negative, that something is not the case.
In the Sherlock Holmes fallacy, when one has eliminated all impossible explanations, that which remains, however improbable, must be the truth. In this manner one ends up subscribing to the remaining explanation simply because there is no evidence against it.
In god of the gaps a deity, or deities, is invoked to explain gaps in our present scientific knowledge since there exists insufficient evidence against this unfalsifiable claim. The weakness of a god of the gaps methodology is the gaps become smaller every time scientists fill them with knowledge.
In argument from silence one interprets silence as agreement. In this way the silence represents the lack of evidence the claim is false.
In the conspiracy theory fallacy, the observation the conspiracy has not been disproved is viewed as evidence it exists. Note it is likely impossible to prove a conspiracy does not exist.
Fallacies of false cause violate the rules of good reasoning regarding causation in some way. In a slippery slope argument, in its false cause form, one argues against a merely controversial action since it will inevitably lead, by a gradual series of small steps, to some admittedly bad action. It is the slide from the controversial action via the gradual intermediate steps that is the "slope" and the smallness of each step that makes it "slippery." If the causal connections between the intervening steps are weak, the resulting argument will be weak.
In cum hoc, ergo propter hoc (with this, therefore because of this) one jumps to the conclusion the correlation between two simultaneous events implies one caused the other when in fact a third event is the cause of the correlation. In wrong direction of cause and effect the direction of causation is the reverse of that in the conclusion, that is arguing the effect caused the cause.
In post hoc, ergo propter hoc (after this, therefore because of this) one argues an event following another is sufficient to imply the first caused the second. Note although it is a necessary condition the cause precede the effect in a causal relationship, it is not a sufficient condition. Superstition, magical thinking, and just so stories include post hoc thinking.
In the regression fallacy one ascribes a cause where none exists, taking ordinary statistical variation as proof specific causes are at work.
In the Texas sharpshooter fallacy one jumps to the conclusion a cluster in data must be the result of a cause when the cluster may even be the result of chance and not caused by anything. Note correlation is not causation and is not the basis for a causal conclusion but for the formation of a hypothesis that needs to be tested. The fallacy gets its name since, just as assigning significance to the outcome of an event after it has occurred, drawing a "target" onto it makes it appear to be causally determined, as if the Texan were shooting at the target. The fallacy commonly appears in creationist arguments the odds of the evolution of a specific biological structure are incredibly small. This is fallacious because it assumes evolution had the "goal" of producing that structure.
A circular argument is an argument where the conclusion is assumed in one of the premises. Also known as begging the question, it requires the very point at issue to be conceded from the beginning, which of course should not be done.
In no true Scotsman a proposition is assumed to be true in order to dismiss any apparent counter-examples to it as irrelevant, thus making the proposition unfalsifiable. A loaded question is a question that is "loaded" with a disputed presupposition. In stolen concept a premise assumes that which one is attempting to disprove.
A category error occurs if one assumes the properties of a whole object are equivalent to the properties of its parts. In division one assumes if the whole has a property then all of its parts will too. In composition one assumes if every part has a property then the whole will too.
False dilemma is the fallacy of setting up two alternatives as the only ones when in fact there are more than two. In the perfect solution fallacy one demands a solution be rejected if it is not perfect.
In the fallacy of sweeping generalization, or accident, one treats a general rule as if it were universal. The possibility of an exception, that is an accident, is ignored.
Weak analogy fallacies occur when two ideas are shown to have properties in common, and this is then used to show therefore they have other properties in common that in fact they do not.
Unrepresentative sample, also known as overgenerality, is a type of weak analogy in which a generalization about a population is made via statistical inference when there is insufficient similarity between the sample and the population, either due to a biased or overly small sample, to support the conclusion. The case with too small a sample is known as hasty generalization, converse accident, or jumping to conclusions. In the anecdotal fallacy a special exception or anecdote leads one to overestimate the probability of certain events occurring.
In the fallacy of slothful induction one dismisses reasonable evidence of an idea as insufficient. Thus it is the opposite of hasty generalization (see weak analogy above). Slothful induction is an inductive fallacy of faulty generalizations, meaning the premises only weakly support the conclusion.
In the moving goalpost syndrome evidence is dismissed and greater evidence is demanded. The fallacy gets its name since one moves the standards of proof, the "goalpost," when one's previous standard has been met.
In special pleading one argues for an exception to be applied in a specific case and provides only irrelevant justification as to why that case deserves to be excepted.
In one-sidedness, or suppressed evidence, one presents only evidence favoring one's conclusion, omitting evidence against it. Note in inductive reasoning it is important to consider all evidence before reaching a conclusion.
Unlike the informal fallacies, formal types are based solely on their logical form, and the truth of the premises of a valid formal argument ensures the truth of its conclusion. Formal fallacies generally represent mistakes in deductive reasoning.
A probabilistic fallacy is one in which the inference from the premises to the conclusion violates the laws of probability.
In the gambler's fallacy one argues after a "run" the next trial is less likely to continue the run, or in other words an independent random sequence will "even out." Note what makes a sequence random is that its members are statistically independent of each other, and two events are statistically independent when the occurrence of one has no statistical effect upon the occurrence of the other. That is, independent random variables cannot show trends that can be extrapolated into the future.
The opposite of the gambler's fallacy is the hot hand fallacy in which one argues after a "winning streak" the next trial is more likely to continue the run.
Masked man fallacy
In the masked man fallacy one illicitly substitutes an apparently equivalent term in a premise although the context does not allow doing so. The fallacy gets its name from the following example of its application:
"Do you know this masked man?"
"But he is your father. Are you saying you don't know your own father?"
Bad reasons fallacy
In a bad reasons fallacy one jumps to the conclusion a proposition is false if an argument for it is bad, due to false premises or invalidity. Note although the conclusion of a sound argument is always true, the conclusion of an unsound argument may be true or false. Also note in argumentation it is not necessarily the case if the other side loses then you win.
In the fallacy fallacy one concludes because an argument for a proposition is fallacious, it must be false. It is the case of the bad reasons fallacy in which invalidity is cited as the reason an argument for a proposition is bad.
Fallacy of propositional logic
Propositional logic describes the logical relations which hold between simple propositions and compound propositions as a result of truth-functional combinations. A fallacy of propositional logic then is any "non-validating" form of propositional logic. One can use truth-functions to determine whether forms in propositional logic are validating.
In affirming the consequent, the second premise of an argument affirms the consequent of the first premise while the conclusion is the antecedent of the first premise. That is, if A is true, then B is true; B is true; therefore, A is true. Note "B" can usually be true for reasons other than just "A."
In denying the antecedent, the second premise denies the truth of the antecedent of the first premise and concludes by denying the truth of the first premise's consequent. In other words, if A is true, then B is true; A is false; therefore, B is false. Note from the fact a sufficient condition for a proposition is false one cannot conclude the proposition's falsity since "B" can usually be true for reasons other than just "A."
In affirming a disjunct, an "inclusive or" is interpreted as an "exclusive or." That is, A or B is true; A is true; therefore B is false.
In denying a conjunct, the negation of a conjunction, "not both A and B," is interpreted as implying at least one conjunct, either A or B, must be true. To put that another way, A or B is false; A is false; therefore, B is true. Note if we know one of the conjuncts is false, we cannot infer from that information the other is true, since it can also be false.
In commutation of conditionals, an "if" is interpreted as an "if and only if." That is, if A is true, then B is true; therefore, if B is true, A is true. This is similar to the fallacy of affirming the consequent except it concludes the truth of an implication (if B is true then A is true) but not the truth of the term ("A") in this instance.
In improper transposition, the antecedent and consequent are negated in the conclusion but not switched. That is, if A is true, then B is true; therefore, if A is false, B is false. Note the switched form (if A is true, then B is true; therefore, if B is false, A is false) is valid.
A categorical syllogism is one in which the premises and conclusion are categorical propositions and has exactly three terms, or variables. A syllogistic fallacy then is any non-validating form of categorical syllogism. Note if a categorical syllogism commits none of the sub-fallacies below, it has a validating form.
Undistributed middle term is any form of categorical syllogism in which the middle term, the one occurring in both premises, is not distributed at least once. A term is said to be distributed if the proposition implies any proposition resulting from replacing the term with a more specific term. Thus the subject term is distributed in propositions of the form "all A are B," the predicate term is distributed in propositions of the form "some A are not B," and both terms are distributed in propositions of the form "no A are B." A syllogism with an undistributed middle term is then of the form "all A are C; all B are C; therefore, all A are B." Note in a valid categorical syllogism the middle term must be distributed in at least one of its occurrences.
Illicit process is any form of categorical syllogism in which a term that is distributed in the conclusion is undistributed in a premise. Note in a validating form of categorical syllogism any term distributed in the conclusion must be distributed in the premise in which it occurs.
Illicit major is the case of illicit process in which the major term, the predicate in the conclusion, is distributed in the conclusion but not in the major premise, the one in which the major term appears. That is, all A are B; no C are A; therefore, no C are B. Note "all A are B" does not imply "only A are B."
Illicit minor is the case of illicit process in which the minor term, the subject of the conclusion, is distributed in the conclusion but not in the minor premise, the one in which the minor term appears. That is, all A are B; all B are C; therefore, all C are A.
Affirmative conclusion from a negative premise is any form of categorical syllogism with an affirmative conclusion and at least one negative premise. That is, some/all A are (not) B; some/all B are (not) C; therefore, some/all A are C, with at least one of the premises negative. Note all validating forms of categorical syllogism that have a negative premise must also have a negative conclusion.
Negative conclusion from affirmative premises is any form of categorical syllogism with affirmative premises and a negative conclusion. That is, all/some A are B; some/all C are A; therefore, some/all C are not B; or some/all A are B; some/all B are C; therefore no A are C. Note any validating form of categorical syllogism with affirmative premises must have an affirmative conclusion.
Exclusive premises is any form of categorical syllogism with two negative premises. That is, no A are B; no C are A; therefore, no C are B. Note at least one premise of a valid categorical syllogism must be affirmative.
The four-term fallacy is an argument containing four terms derived from a validating syllogism but using the same word with two different meanings in distinct terms. Since the fact that the argument has four terms is concealed by an equivocation on two of the terms in the argument, this is also an instance of the fallacy of equivocation. Furthermore when the equivocation is on the middle term the resulting fallacy is an instance of ambiguous middle term (see ambiguity and equivocation above). Note all valid categorical syllogisms must have exactly three terms.
Fallacy of quantificational logic
Quantificational logic, also called predicate logic, describes simple propositions combined in complex ways that go beyond what can be done in categorical syllogisms. Quantificational fallacies then are non-validating arguments of a quantificational form.
Illicit conversion refers to switching the subject and predicate terms of a proposition of a type for which this is not a validating inference. Illicit contraposition refers to switching the subject and predicate terms and negating each in a proposition of a type for which this is not a validating inference.
One commits the existential fallacy if one argues to a conclusion implying a certain class is nonempty from premises that do not imply such. In some are/some are not, one confuses logical implication and conversational implication by assuming "some are" statements logically imply "some are not" statements when in fact that is only the case conversationally. The quantifier-shift fallacy is also a fallacy of quantificational logic (see also ambiguity and amphiboly above).