Special note: we’re in the process of rewriting this page–if you think we ought to add anything, or if you think we ought to clarify something, or you have fun examples of any of the fallacies you’d like to share, please don’t hesitate to let us know in the comments below.

What’s a non sequitur?

In Latin, a dead language in nearly every respect save portentous phrases like salva veritate and names of important philosophical notions, the phrase non sequitur literally means “it does not follow.”  What “does not follow” is the conclusion from the premises of an argument.  When that happened, in ancient Rome and in the Middle Ages, people would scream “non sequitur!”  In a broader sense, a non sequitur is a logical fallacy, from the Latin fallacia, meaning “trick.”  So a fallacy is a kind of trick, a logical trick.  Yet another term for a logical trick is sophism, which recalls the ancient Greek Sophists, famous for their dishonest argumentative trickery.

Reasoning fallaciously is something like cheating or stealing. You attempt to acquire something that you have not earned or paid for. Unlike cheating however, when one reasons fallaciously one does not, despite appearances to the contrary, actually acquire anything.  After all, the whole point of argument is proof–if your proof fails, you don’t earn your conclusion–even if some people think you do.  Your conclusion may turn out to be true independently of your argument, but that doesn’t make your reasoning good.  It just makes you lucky.  The cheater may be a better athlete, but that doesn’t mean the cheater deserves to win by cheating.

Very roughly then (as we have at this moment no stable theory) a fallacy is a systematic and egregious defect in an argument.  To continue the cheating analogy, we might liken a fallacy to a penalty in a football game.  Penalties are the typical ways one tries to break the rules (i.e., to cheat)–offsides, holding, face masking, etc.  There are certainly more ways to violate the rules than these, and determining which penalty has been committed sometimes involves a great deal of interpretation on the part of the referee, but the general concept is clear to anyone who knows about football.  As it’s possible to group football penalties into categories, it’s also possible to group informal fallacies into categories.  As football offensive lineman are prone to holding, ideologically driven arguers will tend to distort (straw man–see below) their opponents’ arguments in order to “win.”

But we think the analogy to football ends there.  Dealing with fallacies isn’t like the referee’s hand motions in a football game.  It involves–or rather should involve–some explanation.  Nothing annoys us more, in fact, than people who scream the fallacy name without offering any accompanying analysis.  For us it’s the analysis that’s important.  The name is just a kind of shorthand placeholder for the general problem.

What are the fallacies?

There are two basic types of fallacy–formal and informal.  A formal fallacy is a systematic defect in deductive reasoning.  Here’s an example of one:

Since all dogs are animals and all cats are animals, it follows that all cats are dogs.

The problem here is the formal fallacy of the undistributed middle.  The defect concerns the logical form of the argument, not the content of the propositions.  For a more detailed discussion of formal fallacies, click here (page not up yet).

By contrast, informal fallacies regard the content.  An informal fallacy is a systematic and diagnosable defect in inductive (broadly speaking, non-deductive) reasoning.  It usually involves some kind of distortion of the content of the argument.  These may be distortions of relevance, probative force, or meaning for instance.  Aristotle, the first to engage in the systematic study of fallacies, identified 13 different fallacies in his On Sophistical Refutations.  For those click here.   Nowadays informal reasoning texts tend to present anywhere from 18 to 25.  Some scholars have identified many more.  Here are two examples: one and two.

Following a lot of informal logic texts and for the sake of simplicity we group the the informal fallacies into three basic categories–fallacies of relevance, fallacies of weak induction (or fallacies of evidence) and fallacies of presumption and ambiguity.  These correspond to the three typical types of distortion in informal reasoning: distortion of relevance, of evidence strength or probative force, and distortions of meaning.

The following is a list of the fallacies one is likely to run across in every day arguments found in op-ed pages and elsewhere.  As time permits, we will add somewhat cartoonish examples of the fallacies for the sake of the curious public.  The egregiousness of the examples shouldn’t be viewed however as a claim that all instances of fallacies in everyday life will be similarly absurd and egregious (and consequently that any non-cartoonish instance of a fallacy which we point out is a failure of charity on our part).  They usually won’t be so silly.  Their lack of silliness, in fact, is the reason they are called “fallacies”–they’re deceptions.  Besides, the hyperbolic example is merely a pedagogical technique.  The list, by the way, is by no means comprehensive; every day we are surprised to see the lengths to which people will go to win their arguments.  We might add a couple of our own “discoveries” at the end.

But we ought to stress, by the way, that we would tend to consider these fallacies to be very simple and avoidable kinds of reasoning errors.  Avoiding them is as simple as drawing within the lines of a child’s coloring book–it takes a modicum of care, patience and honesty.  There are many more systematic errors than these, however.  Many of these consist in among other things psychological propensities to misjudge data, misread statistics, ignore our own biases and in general to make faulty predictions.  Some of these errors are exceedingly difficult to detect and avoid.  The same is not true, however, of the fallacies listed below.

One final thing.  If this list doesn’t accord with your understanding of fallacies, feel free to leave a comment.

I. Fallacies of relevance:

Certainly one of the most common types of fallacy in informal reasoning consists in drawing conclusions from reasons that are not “logically” relevant to the conclusion. The reasons, however, seem to be psychologically emotionally, rhetorically or, we might add, politically relevant to the conclusion being drawn. When someone’s conclusion doesn’t seem to have much to do with the premises, you might be in the presence of a fallacy of relevance. Here are some basic types.

1. Ad hominem (against the person): attacking the person making an argument rather than the argument or position the person is supporting. There are three basic varieties of ad hominem (as well as numerous sub-varieties–for those see Walton, 1998 in the Bibliography).

• Ad hominem abusive: challenging someone’s argument on account of real or alleged character flaws of the arguer (when such character flaws have nothing to do with the argument being made–careful, some personal attacks are not fallacious).

E.g., Al Gore has argued that human-caused global warming must be taken seriously.  But no one could possibly take the boring, overweight, and bearded Al Gore seriously.  Gore’s claims about global warming, therefore, are crap.

• Ad hominem circumstantial: claiming that one only holds an opposing position because of vanity, self-interest, or other similar causes of bias.

E.g., Al Gore has claimed that human-caused global warming must be taken seriously, but he’s just saying that in order to drum up sales for his book (or because of his “liberal bias”), so no one should listen to Gore’s arguments.

• Ad hominem tu quoque (against the person, “you too”): challenging an opponent’s argument on grounds of hypocrisy.

E.g., Al Gore has argued that human-caused global warming ought to be taken seriously.  But Al Gore drives around in a gas-guzzling classic car.  No one could possibly take his arguments about global warming seriously.

2. Argumentum ad populum (appeal to the people): the direct or indirect appeal to the perceptions or impressions of a group of people as support for the truth of one’s conclusion when such an appeal is irrelevant.

E.g., Evolutionary biologists have argued for the teaching of the scientific theory of evolution in public schools, but many people disagree with them–many even doubt the cogency of the theory.  For those reasons we ought not to teach evolution in public schools. [This is the “direct” variety–public opinion is claimed to be evidence for that which it isn’t]

3. Straw man: attacking a diminished or absurdly weak version of an opponent ‘s argument and claiming victory over his real argument.

E.g., conservatives claim that high taxes impede economic growth.  But that’s a silly argument.  Taxes pay for roads, police, national defense, national parks and much else.  These things are requisite for economic growth.  Such conservatives arguments are therefore poppycock.  [the argument concerns the amount of taxes, not the fact of taxes–the “conservative” position has been misrepresented].

4. Red Herring: distracting the reader or listener with an argument against a related, but essentially different, argument.  Like the straw man and the ad hominem, this is what one might call a “fallacy of criticism.”  That is to say, it’s a fallacy typical of attempted refutations.

E.g., Environmentalists have charged that oil production in the North Sea has led to the depletion of local fisheries, among much else.  But oil production is necessary for economic growth.  Oil and other petrochemicals provide the fuel for the development of new and more efficient technologies.

5. Ignoratio elenchi (missing the point): drawing an alarmingly extreme conclusion from premises which would support a different or more moderate one.  Sometimes this fallacy is used as a catch-all for as yet unnamed fallacies–much like, for that matter, “non sequitur.”  In this latter sense, this is a kind of argumentative “unsportsmanlike conduct”–a catch-all for that bad behavior that has no name.  Here’s an example of the former variety of ignoratio elenchi.

E.g., it’s likely social security may run into financial difficulties around the year 2018, to avoid these difficulties it’s imperative that we get rid of social security.

6. Accident: applying a general rule to a case to which the rule should not apply.

E.g., The second amendment to the Constitution says that “the right of the people to bear arms shall not be infringed”–which part of “shall not be infringed” do gun-control advocates not understand?  Gun control, such as background checks against terrorist watch lists, obviously violates the constitutional right to bear arms.

7. Ad baculum: threatening directly or indirectly an opponent in order to get her or him to affirm your conclusion.

E.g., I’m sure the class will find my ultra-liberal arguments against the Iraq war persuasive, after all, your grade is on the line.

II. Fallacies of weak induction (evidence, insufficient evidence):

As common as fallacies of relevance, fallacies of induction (or fallacies of weak induction, fallacies of insufficient evidence) take various forms.  These differ from fallacies of relevance in that the premises are relevant to the conclusion, they just don’t offer enough evidence for the conclusion.

1. Causal fallacies. There are four common varieties of causal fallacy.

• Oversimplified cause: Underestimating the complexity of causes that bring about some event or fact by selectively picking out one of them and asserting that it is the only or the most important cause.

E.g., since the Bush tax cuts went into effect, unemployment is down, revenues are up, new home starts have begun rebounding, one can only conclude the tax cuts have worked as planned!

• Post hoc ergo propter hoc: claiming that simply because one fact follows another that the preceding event or fact is the cause.

E.g., since the U.S. invasion of Iraq, there have been no major terrorist attacks inside the United States.  You’d have to be a fool not to see a connection.  The war in Iraq has terrorists on the run.

• Non causa pro causa: claiming that two events or facts are causally linked simply by virtue of correlation.

E.g., one sees a surprising correlation between areas of low barometric pressure and negative attitudes toward Major league baseball.   Low pressure discourages fandom for Major league baseball.

• Gambler’s fallacy: alleging a causal link between otherwise distinct events which are joined by a causally irrelevant factor, such as a night of gambling.

E.g., In the time I’ve been playing craps, I’ve lost 70% of the time.  If I continue playing, the odds are that my luck will even out.

2. Argumentum ad verecundiam (Appeal to unqualified authority): Appeal to an overtly biased or otherwise unqualified person in support of one’s position in an argument.

E.g., Michael Crichton, science fiction author, as written a work of fiction on the subject of “global warming hysteria.”  In view of Crichton’s expertise, and the hundreds of footnotes and several appendices in his recent work of fiction, it’s evident that scientific claims of global warming are not what they seem.

3. Slippery slope: alleging that accepting the conclusion of an opponent’s argument will invariably lead to an increasing series of dastardly consequences.

E.g., Allowing the government to advocate social policy through the tax system will inevitably result in their intrusion into every area of moral choice with the tax system.  Our private liberty will be at risk.

4. Weak analogy: overstating the importance of similarities between two otherwise different events, or  claiming a likeness between two circumstances or events which does not hold.

E.g., following World War II the allies occupied Germany for many years.  We still have troops there now, as a matter of fact.  We should not therefore be surprised that we still have troops in Iraq, it’s only been five years, after all.

5. Hasty generalization: drawing a conclusion from an inadequate or unrepresentative sample.

E.g., those people who work for PETA have no regard for the problems of racial minorities.  I once in college met a few of them who said animals’ rights mattered at least as much as human rights.

6. Argumentum ad ignorantiam: claiming that the absence of a clear answer to a question implies either an affirmative or negative answer (and not simply ignorance about the right answer).

E.g., no one has ever shown that there isn’t an Atlantis, as a result, it must be true that there is one.

III. Fallacies of ambiguity or presumption:

1. Equivocation: drawing an inference on the basis of an incorrect semantic analysis of a term.

E.g., Stealing means to gain by means other than earning, since the Catholic Church favors welfare programs for the poor, they favor stealing.

2. Composition: reasoning from the characteristics of the parts to the characteristics of the whole.

E.g., I don’t understand why the Cubs aren’t a more competitive baseball team–each of the players is an outstanding athlete–that should make for an outstanding team.

3. Division: reasoning from the characteristics of the whole to the characteristics of the constituent parts.

E.g., The American relay team was the fastest at the Worlds.  They beat the Jamaican team handily.  Since Speedy McGee was a member of the team, speedy McGee can outrun any member of the Jamaican team.

4. Petitio Principii (begging the question): assuming the conclusion to be demonstrated as one of the premises.  There are at least two distinct varieties: (1) the repetition of the premises in the conclusion.  This usually invovles slight verbal changes which mask the fact that the premises and conclusion say the same thing.  For instance,

E.g., Abortion is unconstitutional because it traduces the principles of the constitution.

Begging the question also happens when (2) one assumes some key and disputed premise:

E.g., Abortion is unconstitutional because the constitution does not mention it.

5. False Dichotomy or False Dilemma: arguing that only two alternatives are possible, and concluding that since one is untenable, the other must be correct.

E.g., One can either support the current administration’s policies, or one can embrace socialism.

6. Amphiboly: drawing an inference on the basis of an incorrect grammatical analysis.  I can’t be certain I’ve ever seen an actual case of this in an argument.  Here is a famous example:

E.g., This morning I shot an elephant in my pajamas, how he got there I’ll never know!

7. Complex Question: deviously asking two questions disguised as one such that one cannot answer one with answering the other.

E.g., Mr. Clinton, why didn’t you do more to stop Al Qeda?